Tricky Tales

Tuesday, March 02, 2010

derivative

I think, calculus teaches you a lot more than you might imagine.

For example, it teaches me when to stop studying. Basically, its when d(grades) / d(time spent) is too low, to make a difference. And actually, thats true for a lot of other things as well.

Studying is like a curve. The first part of the curve is quite steep, so you have to study, otherwise you'll really fail badly.

But come to some point, its better to go do something else with your time.

Fortunately, as I write this, I'm still in the first part of the curve, so I think I'll go do some more studying.

Wednesday, December 30, 2009

Misfire

I unearthed this poem, scrawled down in the little black notebook we used during BMT. It must have been written 5 years ago, during one of my more lucid and literary moments in the jungles of Pulau Tekong. It is dedicated to my BMT 'buddy' Tor Weijian, who is still very much alive now, lest anyone think otherwise.

Alas! Poor Weijian, I knew him well
E'en as the bugle sounds the death knell
For he has borne me on his back
A thousand times, like a field pack
On a route march, through barbed wire
While o'erhead rang enemy fire.

He was my buddy. From my section
He died trying Immediate Action.
Peering down his rifle muzzle
Like a young boy with a puzzle
He sealed his fate with an errant click
Leaving a head wound 10 cm thick.

Weijian's now in a better place
Alack, sweet child, without his face.

Saturday, June 14, 2008

I've been trying my hand recently at writing, not in the ordered, fixed-rhyme-scheme form that I normally write in, but rather in free verse. So here is my latest poetic offering:

Digital Love

We lie in a grassy patch
Looking up at the eternal night sky
And watching the shooting stars fly by
Like on a Windows screen saver.

You gaze lovingly at me
'Silent sniper of surreptition'
And I, in return, at you
'Lovely lady of the lake'.

I'm not really a dark elven archer
And neither are you a fairy princess
(Dark elves and fairies don't mix)
But, like you said before, whatever =.=

We've progressed beyond mere roleplaying
-The ordered realm of make-belief-
To something heart-poundingly real,
Not fantasy within a fantasy.

This is not quite Romeo and Juliet
Nor exactly Orpheus and Eurydice
We are not the stuff of legends
But at least we have a happy ending.

If we can transcend time (zones) and space,
Race and religion,
And the need for physical attraction,
We're not too bad off, are we.

We leaned forward; I in my bedroom,
You in your cybercafe
And shared a kiss, warm enough
To melt the heart of the fabled ice queen.

-End-

Some points to note:
This poem is not autobiographical.
Free verse is actually harder to write because there is no fixed structure, whereas with my normal rhyme scheme I merely have to pick from a selection of words which rhyme, and arrange them in a pre-determined order.
I tried to capture the essence of an online relationship: the surreal (fantasy setting, computer graphics, role-playing) interspersed with the real (two people in love). Maybe it is a bad poet who gives away the meaning of his poem, but this is for my future reference too.
For my critics, who must be thinking of what nonsense I am getting up to in my fantasy world, let me reiterate: this poem is NOT autobiographical.

Friday, May 30, 2008

Caylus Strategy

1. Introduction

This strategy guide is by no means definitive. Information has been obtained through observation and repeated trials, and the strategy presented here is a collation of my findings from these trials. I will attempt to present an effective way of understanding and playing this game as optimally as possible.

2. Contents/Changes

I will be continually updating this page whenever I come across new insights. This section tables the various topics and discussions that are presented below, and documents any changes made to them.

- Basic Strategy
- Conversion Ratios
- The 8 resources
- Discussion of Buildings
- Multiplayer dynamics
- Early game strategy
- Mid game strategy
- End game strategy
- Risk taking
- Case Studies

2a. Terminology

In this guide I will often use terminology which may differ from that in the official rulebook. Here I will define the terms I use most often in this guide.

Phases
placement phase: phase where players take turns to place workers
activation phase: phase where workers are activated up till the provost, leading to
castle phase: building in the castle
scoring phase: the scoring phases that happen 3 times during the game

Placements
Play on the provost: play on the merchant's guild
Play in first: play in first place in the stables
Play on the money(3 coins): play on the trading house

Buildings
2F: 2 Food 1 Cloth building, I believe its generically called Farm
2C: 2 Cloth 1 Food building, not sure what it's called
2S: 2 Stone building (Quarry)
2W: 2 Wood building
WV or Weak Vendor: 2 coins -> 1 cube building
WM or Weak Market: 1 cube -> 4 coins building
Carp2: the carpenter in front
FF: Food farm >
SF: Stone farm > These 3 refer to the stone buildings which generate commission
WF: Wood farm >
F/W: Red building that produces food/wood
F/C: Red building that produces food/cloth

I should refer to all other buildings by their names.

Resources: All 5 types of resources and money are classified under the broad term Resources.

3. Basic Strategy

Caylus is a game of conversion. Players start out with resources (cubes and money). Every move is an attempt to convert some resources into other resources and VP. Hence, it is apparent that the player who best converts his resources into VP wins. There are several ways to go about doing this.

a. Making more conversions than other players
Players who make more successful conversions than other players will have an advantage. The game is designed such that most plays yield a tangible conversion (with several exceptions, such as spending 4 coins to obtain 3 coins). In some cases, this conversion may not be optimal (such as playing on the weak vendor or weak market). However on the whole the more successful moves a player makes, the stronger the player's position will be. A successful move is defined as a conversion which yields a tangible benefit, such as any play which is not denied by the provost. An unsuccessful move is a move which yields no tangible benefit, hence causing a loss of the playing cost, such as playing on any building and not using its ability, or playing on the merchant's guild (the provost), which yields no tangible benefit of its own. This is not to say that you should never make a move which will turn out unsuccessful. Sometimes it is necessary to make a move which will not succeed to achieve a certain aim, generally to prevent opponent's moves from succeeding. (Playing on the provost to move it back is one good example).

There are two recommended ways to obtain more successful conversions than other players:
1. Playing cheaply after other players have passed. This is accomplished either by owning the inn, or playing on your own buildings. Needless to say, the more plays you make, the more conversions you are likely to succeed.

2. Being first in turn order. Being first generally ensures that you make more plays than everyone else. If someone passes before you, you have made more plays than him, and potentially other players who pass after him. If you pass first, nobody else can make more cheap plays than you (unless they have the inn).

b. Making better conversions than other players
Always make the best plays first. Ie. If 2 food/1 cloth(2F) is open, and so is the food farm(FF) (provides 2 food AND 1 cloth), and both are reasonably far back, always play on the food farm as opposed to 2F. Likewise, play on vendor before weak vendor, and market before weak market. These are pretty obvious comparisons. As regards differences between buildings of the same level, and of different resources or special squares like the castle, refer to the discussion of buildings for further details.

4. Conversion Ratios

As emphasized in the above section, since the game revolves around conversion, the optimal strategy to making the best conversions is understanding conversion ratios. I will refer to a conversion as spending a COST to obtain a BENEFIT. The net gain from the conversion is the difference between the benefit and the cost.

There are 3 costs associated with each placement:
Placement Cost: The amount of money that it costs to place a worker (typically 1 coin)
Activation Cost: The amount of resources that it costs to use the building's effects (eg. 1 coin 1 cloth for jousting, a stone and another cube for mason)
Opportunity Cost: What you could have placed instead. Think about it as every placement that you make allows each other player to make one more placement before you. Therefore you want to make the placements which maximize net gain, since on the next turn there will be several less options to place on.

The concept of opportunity cost requires some explanation. Since most squares confer a net benefit when played on, each turn a player gets is an opportunity for him/her to gain any one of these benefits. The opportunity cost of an action is reduced the more players already passed, as less players will be able to utilize the remaining squares. The opportunity cost of an action is also reduced as fewer squares remain because there are less possible positions other players may play on. This will be covered in more detail in discussions of passing and the inn. Take note that the opportunity cost of a placement is zero once all other players have passed, because no other player can possibly place on a square which you do not play on. Passing hence reduces the opportunity cost of placement for other players (although it generally increases the placement cost as well).

There is a fourth cost to placement, but it is a hidden cost, and sometimes it is not really a cost. I call it the protection cost, or rather, the cost to ensure that your building gets activated. This will be covered in more detail when the provost is discussed.

There are two benefits associated with each placement:
Direct Benefit: The direct benefit of the placement, be it cubes, VP, etc.
Denial Benefit: In general, every placement prevents all other players from making that same placement. This is a crucial point to note, and a benefit which is often overlooked, causing beginners to be often afraid of "playing in front".

The activation and placement cost are easy enough to calculate, and hence derive the concrete benefit of a building. Lets go through a few examples to prove the point.
Weak Vendor: 2 coins -> 1 cube. Because it takes at least 1 coin to place, the actual conversion rate is 3 coins -> 1 cube. This should only be carried out if the one cube you obtain is valued higher than 3 coins.

Building Granary using building track favor: 3 food + 1 gold -> 10 VP and -1 residence. The intrinsic value of 3 food + 1 gold is 4VP, so the net gain is 6VP and a loss of income of 1 coin per turn. Naturally, this means that you should consider the income loss as part of the cost of building the granary (or any prestige building). Anyway, seeing that the granary (and library) are worth only 6VP, that makes it no better than constructing a 6 point stone building on the last turn (which is worth 5.66 VP). The exception is if all the stone buildings have already been constructed.

In order to maximize the conversion rate, choose the buildings which offer the highest net gain.

One common misconception here is that net gain should be considered in an absolute sense, rather than in a percentage sense. This is particularly applicable to buildings with multiple activation options, eg. the church. The first option allows you to convert 3 coins into 3 VP, while the second option allows you to convert 5 coins to 5 VP. To a beginner, the conversion ratios are seemingly equivalent, because both allow you to trade coins to VP at a 1 to 1 ratio. But clearly, converting 5 coins provides a higher net gain. Assume money is valued at about 0.5 VP a coin (this is probably the average value, mid game), then the first option nets you 1.5VP, while the second nets you 2.5VP. Clearly, the second option is far better.

How then, should we value the different resources in the game, and the various buildings? We hence proceed to our next discussion...

5. The 8 Resources

Earlier, I defined a resource as the 5 types of cubes and money. How then are there 8 different resources? Basically, a player's worth in the game can be measured or estimated by his standing in these 8 resources, they are namely the 5 types of cubes, money, buildings, and position on favor tracks. VP is not classified as a resource, as the value of VP is constant throughout the game, and VP cannot be spent (losing VP is another matter altogether).

After preliminary studies, I have came up with a brief model of the value of resources. First, let us discuss the end game value of resources. Buildings are worth 0VP at the end game. Normal cubes are worth 1/3VP each, Gold is worth 3VP each, and money is worth 1/4VP each. Position on favor tracks is worth 0VP. It shouldn't be that hard to work out these figures or to realize that at the end game, none of these resources has any potential whatsoever.

However, before the end of the game, each resource is potentially worth more, because it can potentially be converted to VP. The earlier in the game, the more opportunities it can be converted to VP, hence resources are generally worth a lot more in the beginning than in the end game. The only resource whose value seems somewhat constant and separate from the flow of the game is money, and this is because each player has a constant source of money, and money is always a part of conversion cost. The value of money will be discussed in greater detail in a later section.

In general, as with economics in the real world, the value of each resource depends on its supply and demand. The more readily available a resource is, the less its value. Likewise, the more opportunities for a resource to be spent, the more valuable it is. To a player who cannot build prestige buildings (either because he does not possess a residence, or he is not at the top of the building track and the architect is absent), gold is always worth a flat 3VP. On the other hand to a player who can easily access prestige buildings, gold is worth much more than the base endgame value.

We shall now consider the various consumers and producers of resources in the game, and hence determine the value of various resources. At the start of the game, there are 5 cube producers, and several cube consumers. There are 3 ways to get extra money, and many ways to spend it. First, let us examine the consumers.

The main cube consumer in this game is the castle. To build in the castle, you need 3 different cubes (which I will call a set or a section), one of which must be food. The first section you build in any phase of the castle is worth 7 points, the second is worth an additional favor, and any more sections you build might get you more favors. Also there is the favor for building the most. Naturally, the castle is a pretty good consumer of cubes because you can spend multiple sets of cubes with one placement. Exact castle mechanics will be discussed in a subsequent section. The next main consumer is building. Building using the carpenter consumes wood and another resource, and building using the building track just consumes one resource. Building residences consumes cloth, and building using the mason consumes stone. Buildings provide some of the greatest rewards in the game. Most buildings net you slightly less than 1VP a turn for the rest of the game, and allow you to play on it for 1 coin regardless of the number of players who passed. Also, the stone farms provide you a cube whenever activated by another player, thus making them some of the most useful buildings in the game. Buildings will be discussed in greater detail in the next section. Lastly, at the start of the game, the jousting square is a good consumer of cubes, as it provides a favor (It also consumes money).

We can summarize the value of resources as follows:
1. A resource is more valuable if there are more ways to consume it.
2. The castle is the most common consumer of resources - hence a resource is valuable if it contributes to a set.
3. A resource is more valuable if consuming it provides a better reward.

It can be seen that cloth is the most valuable consumer of resources at the start of the game, because it can be used for the castle, and jousting. Stone is somewhat useful as it can be used to make a set in the castle, however, in the absence of the mason stone is only as valuable as wood. Food would generally be regarded as the 2nd most useful resource, because not only is it a requirement in the castle, it is also one of the most common building materials. In particular, it is necessary to build the 3 stone farms (which are regarded to be the best buildings in the game). Should the mason be built, stone would become more useful than food, because it provides an additional consumer of resources (and also because no player starts with any, as opposed to all players starting with 2 food).

In the mid-game, the value of resources changes according to their scarcity. By this time, several resource production buildings would have been built. Thus, the more producers of a resource there is, the less valuable the resource is. Value of resources is still determined by the same mechanism, number of consumers, except that by this point, potential consumers are no longer valued as highly as actual consumers are. What this means is that, if a means of consuming a resource is not present, like for example, a way to turn cloth into a residence, residences can no longer be considered a consumer of cloth unless a lawyer is built first. Likewise, gold should not be regarded as being worth more than 3VP if there is no way to convert it into a prestige building. At this point, if a player has a lot of gold, he should find ways to convert it into prestige buildings, if the means of doing so is not immediately available.

In the end game, especially in the last 2 turns, the value of resources drops sharply towards its end game value. At this point, it is crucial to secure means of converting the resources effectively into VP, more so than obtaining the resources themselves. There is no longer any potential value of resources. More will be discussed in end-game strategy.



6. Discussion of Buildings

Buildings are of key importance in the game. They have 3 key features, all of which affect the game significantly. In fact, buildings are the one way a game changes from play to play. A game that sees the lawyer as the first building is going to be significantly different from one in which the lawyer is not built at all.

These are the main impact of buildings:

a. They affect the supply and demand of resources in the game. The more buildings that provide a particular resource, the higher the supply of that resource and hence the lower its value. The more buildings that consume that resource, the higher the demand of that resource and hence the higher its value. In a game with a marketplace, a lawyer, and no bank or vendor, the supply of money will be very high, as the market and lawyer provide a great supply of money, and the lack of a vendor or bank reduces the amount of money consuming locations to effectively 3 or 4 (placement, provost, WV, possibly church). However, cubes will be in shortage, as the marketplace and lawyer both consume cubes, and the lawyer tends to eliminate the cube producing red buildings from the game. In such a game cubes will become much more valuable than money.

b. They provide a good source of VP for the owner, at the expense of providing a service for the other players. Building the mason early will provide a good source of VP every turn as it is bound to be played on (however this will stop once all the stone buildings have been constructed). However, it also opens the capability to build stone buildings to other players. If you are on the building track, you do NOT want to build the mason. Likewise, building the bank or alchemist provides alternative sources of gold. You do NOT want to build them early if you cannot utilize the gold effectively (ie. convert to prestige buildings). It is important to note, though, that buildings also give you the service, hence you want to build buildings which you would use as well, in order to make up for one of your shortcomings. If you are not on the building track, you will want to build the mason to give you access to stone buildings, and the lawyer and architect to construct residences and prestige buildings. Failure to do so will result in those becoming inaccessible to you.

c. They can be played on for 1 coin after players have passed. This is a crucial point beginning players often forget. Leaving your own buildings open till the last few workers are placed allows you to place cheap workers so as to pass later, even if these workers will not be activated. When calculating how many more placements an opponent can make given the number of players passed, do not forget to count the number of buildings he owns and can play on. Likewise, to eliminate this advantage from a player (assuming he is not in the inn), play on his buildings early and leave your own buildings open (unless you are in the inn). This is of particular importance if a player is going to have to pass early.

6a. Buildings as a source of VP

Buildings provide some of the best VP sources in the game. Apart from its initial VP, it can provide a steady stream of VP throughout the game. This VP cannot be ignored – a building strategy works precisely because of this effect. A building that is on or before the bailiff will probably be played on. Buildings will be played on by other players approximately n-1/n of the time, hence in a game with more players, the benefit of building as a VP source is greater.

A game of Caylus can last between 9 to 18 turns, although it can possibly finish sooner than 9 turns, if a lot of production buildings are built. On average though, a game lasts about 12 turns. Hence, the first building built should see about 12 plays, and in a 4 player game, approximately 9 plays will be by other players. Hence, the first building spot is worth approximately 9 points during the game. Subsequent buildings are worth less and less, as they are built later, and will only see significant play once the bailiff has advanced past them.

All these values are for a 4 player game. For a 3 player game, multiply by about 0.8, for a 2 player game, multiply by about 0.6, and for a 5 player game, multiply by about 1.1.


Building Position Avg. additional points worth
9 (1st building)       9
10                        8
11                        8
12 (1st scoring)      7
13                        7
14                        6
15                        5
17 (After gold mine) 4
18 (2nd scoring)      3
19                        3
20                        2
21                        2
22                        1
23                        1
24 (3rd scoring)      0
25                        0

The number above is not fully reflective of actual usage. For example, if the architect was built in position 10, it would most likely be worth at most 2 or 3 points during the game, instead of the 9 points predicted. As such, it is a really bad idea to build the architect that early. Factor in these modifiers for the following buildings.

Lawyer    -- Max 6 (-25% for each player on building track)
Mason     -- Max 7 (-25% for each player on building track)
Vendor    -- 70% usage (100% with market)
Architect -- Max 3 (-1 for each player on building track), 0 if no residences.
Bank      -- 50% usage (75% with market)
Alchemist -- 50% or less usage
Tailor    -- Max 2
Church    -- 50% usage (75% with market)

To read the above chart, if it says Max X, that is the maximum amount of points you are expected to reap from that building, assuming you too use it on a regular basis. Why is this the case? For example, a lawyer is expected to be used at most 8 times, as there are 6 replaceable red buildings, and most players do not replace their own buildings. If someone is on the building track, he/she most likely does not even need to use the lawyer to build residences, so subtract some amount of utilization.

If a square says 50% usage, it means it can be expected to be used 50% of the time. That means, if a building by virtue of its position would earn 8 bonus points, but it is only used 50% of the time, it should be expected to generate about 4VP by the end of the game. Buildings such as the bank do not see constant usage as players often do not have money or the resources necessary to use it. As can be seen, the market improves the utilization of money based buildings by a lot.

The three stone farms also provide a benefit additional to the VP gained from placement. Each farm provides the owner with a choice between two cubes whenever another player activates the building. A cube, as discussed earlier, is worth potentially a lot more than the 1/3 VP at the end of the game. When used in the 3rd castle phase, each cube is worth 1VP at least (not counting the favor). When used to build a 6 point stone building, each cube is worth 3VP. As can be seen, the stone farms are the most sought after buildings in the game. Each provides its owner with a significant benefit well and above the placement VPs tabulated above. Try to build them whenever possible. Also, after building them, you now have a source of cubes no other player has access to. To make the most of this source of cubes, follow the guidelines presented in section 5, ie. keep the supply of that cube low by not building the corresponding wooden production building (another way to think about it is to preferentially build the stone production buildings for which the wooden production building of that type has not been built yet). For example, if the 2C and 2F building has already been built, the value of the food farm is severely reduced. If the wood farm or stone farm are still available you should build those first. (Probably the stone farm, as the value of stone/cloth is generally worth higher than food/wood, especially if the 2F building is already out. Also, increase the demand for that cube: the demand for stone cubes is greatest in prestige buildings, the demand for cloth cubes is greatest in the lawyer and jousting, and to a smaller extent the tailor.

In summary, buildings provide a solid consistent source of VP. Stone buildings also provide a large initial VP for at most 2 cubes. This makes them some of the best ways to convert cubes into points in the game.

6b. Buildings as a way to ‘shape’ the game

At the beginning of the game, there are exactly 16 places to play on, of which about 12 are reasonable first-turn plays (gold, the two buildings after the bailiff, and jousting are rejected as first turn plays). Now, if no buildings are ever built, there will remain these 16 places to play on for the rest of the game. Of course, that will never happen (if people are playing optimally), because as already discussed above, buildings are a fantastic source of VP, also, buildings shape the game, by increasing the number of possible moves, and by controlling the supply and demand of the various resources in the game. The winner is generally the player who shapes his playing style to the shape of the game, and/or shaping the game to his playing style and setup.

I have already discussed briefly above that buildings affect the supply and demand of various resources. Now I will explain exactly how each building affects the supply and demand of the different resources in detail.

Before I begin, however, I would like make an important distinction. From the table in section A, we can see how buildings that appear later will see less plays. In particular, the building spaces can be seen as separated into two segments, before and after the gold mine. The 7 buildings before the gold mine will see significantly many plays: the VP gained from having others play on these buildings will generally exceed the original VP of the building. Also, these buildings will have significant impact on the game. I refer to these as the 'first 7'. On the other hand, buildings built after the gold mine will see significantly less plays and are generally built for their building VP, rather than to accumulate VP from players' placements. These buildings can also be specially built to make up for the builder's weakness. As such, they generally have little impact on the game.

When I discuss the impact the various buildings have on the game, I am generally implying that these buildings appear early enough to shape the game. A building built much after the gold mine would make no difference than if it were not built at all, especially in the case of production buildings. Also, the earlier the building, the greater the impact it will have on the game. Take these into account as we begin our discussion of the buildings.

Production buildings

In most games, it can be expected that the three stone production buildings will be built. Hence, when discussing most other buildings, an underlying assumption is that these three stone buildings will eventually appear. However, if some of the stone production buildings are not in the first 7, their effect on the supply will not be as great, and the player can safely ignore or downplay their effect on the game.

2F: Building the 2F production building greatly increases the supply of food in the game as the 3 stone production buildings already supply 3 food a turn (and potentially 2 more to the owners). Since the main use for food is castle building, the presence of 2F causes the constraining factor in building castle sections to shift to the other resources. As players find it easy to obtain food, the struggle to obtain effective combinations of other resources increases. In a game with 2F and no other wood production building, SF becomes the most powerful building to play on, followed by WF. Likewise the value of stone and cloth will be significantly higher compared to food. Even wood’s value will increase proportionally.

2W: This building is seldom built. Wood is generally regarded as the least valuable resource. If 2W is built, it becomes even less valuable. This is mainly because there is no late game consumer of wood cubes, except the castle, and that requires more than just wood to build.

2S: The 2S increases the supply of stone in the game significantly. Since there is only one source of stone to begin with, the game would not be saturated with stone just because of the presence of 2S, as there are enough consumers of stone such as the castle, mason, and prestige buildings. If 2S is in the game, the supply of stone will not be that big of an issue. Instead, competition for stone consumers will be fiercer, such as the usage of the mason to build 6 point stone buildings, and the construction of prestige buildings. It is highly possible, in a game where 2S and either bank or alchemist is built, for all the stone prestige buildings to be constructed. Hence, if 2S is present, focus your efforts on converting all that stone into VP through the mason or prestige buildings.

2C: The 2C brings the supply of cloth in the game to reasonable levels. In the absence of 2C, cloth is far and away the scarcest resource, as there is only one original source, and only 2 individual sources in the 3 stone production buildings (and potentially 2 for the owners). Cloth is also the most consumed resource in the game, as it is very useful in the castle (being usually the scarcest non-food resource), required for residences and jousting, as well as building the church, which provides a favor and is often a hotly contested stone building. In a game with 2C, cloth is reasonably sufficient, and you may consider using cloth to build in the castle as opposed to a resource whose wood production building has not been constructed. Also, since cloth is reasonably present, jousting becomes a good way of consuming cloth, and residences are always welcome. In a game without the 2C, cloth becomes a far more scarce resource, so much so that trips to the vendor are often spent on buying 2 cloth cubes, and cloth is seldom spent in the castle. Jousting too, should be carried out sparingly, especially if the F/C has already been replaced by a residence.

Conversion Buildings

Vendor: The vendor is a very popular building to build, and with good reason. Firstly, it gives 4 points, which is better than the 2 points for the other wood production buildings. Secondly, and more importantly, it can be built using ANY 2nd cube. That means its cost is less than the other wood buildings, because generally wood or stone is used to build it (stone only if the mason is not built). Thirdly, it makes up for shortages of any particular resource, because the person playing on the vendor will generally purchase 2 cubes which are in greatest scarcity. However, the downside of the vendor is that it consumes money, and hence raises the value of money in the game. In a game with the vendor (and no marketplace), money becomes crucial as it allows you to spend on the vendor to obtain cubes of your choice. The fact that you can obtain any cube of choice makes the vendor so powerful, despite its high cost of activation. Lean towards the money favors and playing on the money in a game with the vendor.

Market: The market adds a good source of money into the game. Like the vendor, it is very popular to build. Despite the fact that it consumes 1 cube, this cost is rather insignificant, as players will most often convert the least valuable cube into 6 coins – a massive benefit. In a game with the marketplace, money will be relatively abundant as long as you play on the marketplace once in 2 or 3 turns, and occasionally the trading house. In a game with the market (which is nearly every game), utilizing the money is the key to victory. Money can be converted at the bank, vendor and church. The bank and vendor are generally regarded to be more valuable than the church, because though the church converts at a 1 coin to 1 VP rate, the bank converts at 3 coins to 1 gold, which is worth more than 3 VP if converted to a prestige building. The vendor converts 1.5 coins to 1 cube of any type, which may be worth more than 1.5VP if used effectively (like in a prestige building, or stone building).

Church: This is more likely to appear in the first 7 than the bank, and it is built simply for the favor. Since it offers a pretty poor conversion rate and net gain (as money is worth pretty much in the early-mid game), it is seldom used unless the marketplace is also in play. The presence of the church does not really shape the game at all, except probably to give its owner a place to play when other players have passed.

Bank: This building is unlikely to appear in the first 7. If it does however, it makes gold very abundant in the game. That greatly favors the construction of prestige buildings. Should the bank be in play, residences become a very important resource, although some means of constructing prestige buildings is still needed. Try to get many residences (the money helps with the purchase of gold too) and the means to build prestige buildings.

Alchemist/Architect/Tailor: These buildings have nearly no impact on the game, and it is very rare that they appear in the first 7.

Lawyer: The all important lawyer, which allows residences. The lawyer greatly increases the value of cloth, as it is required to build a residence. The lawyer also changes the game greatly, especially if it appears early in the first 7. Because the first buildings replaced are generally the red buildings, the lawyer will change the supply of whatever red building is eliminated. The only one which does not really shape the game is the removal of the carpenter. Removing the weak market reduces the supply of money, removing any cube source reduces the supply of that cube (removing cloth is especially drastic, and will cause the lawyer to become somewhat defunct). Lawyers also increase the amount of money and reduce the number of playable spaces, causing people to pass earlier and hence save money. The net result is a huge surplus of money in the game, which should be channeled into the vendor/bank/church if available.

Mason: The most sought after wooden building in the game, once it is built, at least for the first few turns. The mason opens up stone buildings to all players, in particular the three stone production buildings, and the church. As mentioned above, these buildings are the most valuable in the game, and hence the mason, once it is constructed, is likely to see a play every turn until these 4 buildings have been constructed, whereby it will see less frequent plays until all the stone buildings are constructed. The mason increases the value of stone greatly, potentially making it more valuable than cloth if the user is not on the building track. A very early mason (1st or 2nd building) will generally devalue the building track, as players not on the building track will be able to use the mason to build the all-important production buildings. On the other hand, a mason that appears slightly later, or after the first production building has been built using the building track, is generally ineffective at shaping the game as by then, most players will be on the building track and be using it to build the stone production buildings. A good piece of advice would be to build the mason early (preferably in the 2nd position) if you do not plan to go on the building track. Another way to think about it is to not go on the building track if the mason is built early.

6c. Building summary – When to build what

What to build and when to build it depends greatly on the nature of the players, and the playing strategy you choose for the game. Generally, the early game will define what buildings should appear in the game. As the first 7 buildings affect the game the most, you should try to build buildings in the first 7 to maximize their impact on the game. As the buildings progress beyond the first 7, building them is mainly for their immediate VPs, so less caution can be exercised.

A good way of deciding what to build and when to build it is to follow these few simple rules:

1. Build to match your favor track weaknesses, and never to make up for opponent’s weaknesses. For example, if you are on the building track, do NOT build the mason if your opponents are not on the building track as well. Likewise, do not build the lawyer. If you are on the money track, don’t build the marketplace, build the vendor and church instead.

2. Build buildings that you can use most effectively. For example, if you have much more money than your opponents do, you want to build buildings that consume money. Likewise, if you are the only player with residences, then building the architect will benefit only you. It will be likely that your opponents will not use your building at all. That is not necessarily a bad thing, because generally the benefit a building provides is better than the 1VP it gives its owner, so losing out that 1VP by using a building yourself is not a big deal. As an added incentive, you can save the building till your last worker even if others have passed, since nobody else will play on it.

3. Be wary about the position of the new building. A new building, since it provides a brand new functionality to the game, is generally going to be rather popular. If it is well behind the provost, it will be a relatively safe play for the first player, who will obtain some large benefit. In this case, if you have played in first in the stables, you might want to consider building a building then seizing it as your first move. A good example of this is the mason (although it is unlikely that no player has built any buildings in the first 3 or 4 turns).

4. Flooding the first 7 with buildings is a good strategy. If you own a majority of the buildings in the first 7 (4 in a 3 or 4 player game, 3 in a 5 player game), you will receive a majority of the placement points during the game. If you own a large majority (5 in a 3 player game, 4 in a 4 or 5 player game), you will earn a significant number of placement points each turn and may even avoid your own buildings so as to encourage greater trading of points (which of course, benefits you the most). In such a game you want the game to be slow, so play with the provost and move it back often.


7. Multiplayer Dynamics

This section is dedicated to multiplayer dynamics in Caylus games with 3 or more players. If you only play 2 player Caylus, you may skip this section.

The multiplayer aspect of this game is what differentiates this game tremendously from other non-random games like chess. It is also what some people might term the “random” factor of this game. When viewed from an analytical perspective, there is nothing random at all about other player’s moves. The important factor here is understanding the playing style of your opponents and adjusting your game to suit that style.

I could probably devote an entire book to multiplayer dynamics. Due to space constraints, I will break this large chapter down into smaller subsections. Since games with a different number of players function very differently, there will even be individual sections for each number of players. Firstly, I will begin by describing concepts applicable to all numbers of players, then discuss concepts specific to particular numbers.

Anyhow, this is a brief list of the subsections in this chapter:

A. Basic multiplayer concepts
B. Passing and the Inn
C. The Castle
D. The Provost
E. Turn Order
F. Dealing with different playing styles
G. 3 Player Strategy
H. 4 Player Strategy
I. 5 Player Strategy

7A. Basic Multiplayer Concepts

In a two player game, choices between moves are often dictated by the resulting benefit to both players. If a move should benefit me more than my opponent, I would be willing to make it. In a multiplayer game however, it is never that clear cut. If there is a clear move that would benefit you the most of all players, you would do it. But what if a move benefits you but benefits another player more? What if a move would hurt you but hurts a single other player more? Should you make that move?

Firstly, a few simple guidelines on playing style. Players generally respect opponents who have sportsmanship, and who do not make moves that would potentially spoil the gaming experience for the other players. In this entire chapter, I will assume that all players abide by these simple guidelines. Some players may play more aggressively, others more peacefully and more cooperatively. Some players may undervalue certain aspects of the game while overemphasizing others (like a player who enjoys hoarding gold but not building prestige buildings with them, or a player who makes his first move on the joust square each turn). Such play is not considered against the spirit of friendly competition (although it is not recommended due to its sub-optimality). However, there are several no-nos, which should not be done in any case.

a. Never make any move which would hurt your own position the most (or benefit you the least). For example, as the last player on the bridge, paying to move the provost forward to enable only other players to receive a benefit (unless doing so achieves a secondary objective, such as ending the phase).
b. Never deliberately decide the winner through your actions, unless it advances your own position. For example, as the player clearly in last position, making a play which would not improve your score relative to any of the other players, but would significantly affect the placing of the other players.
c. Do not make personal attacks on another player for non-game reasons. This is very much frowned upon.
d. Do not sacrifice your position to bring down a single other player, unless it benefits you relative to him. This is an extension of a and c.
e. Try not to hold grudges in-game. Caylus is about advancing your own position and maximizing your score. Try not to “pay back” a denial move several turns ago, or make such destructive moves with the intention of “revenge”. Vengeful players often do not perform well, anyway.

The aim of the game is to maximize your own position, with the secondary objective of maximizing the score difference. It is important to bear this in mind. There are several different guidelines towards making these crucial multiplayer decisions. Let us examine them.

a. Make the move that benefits you most relative to the player with the highest potential score. This may not always be the same player. Sometimes that player will be you, in which case you make the move relative to the closest player. Potential score is very hard to estimate. Beginning players often are unable to estimate a player’s potential. Of course, the player with the highest potential score at one point in time is not always going to be the winner. Hopefully this guide will aid you in maximizing your potential score, and winning.

How should we judge potential score? This is a good guide.

Take each other player’s current score. Count their useful buildings (buildings which will see more than 50% usage, according to the chart in section 6A, and which are currently behind the bailiff). Add/subtract one point for each building they own/don’t own above the average. Multiply this by the expected number of turns left and add it to their score. Next, add points equal to 1 more than what they would get in the castle, for every set of cubes they have. For example, in the 3rd scoring phase, a player with 5 sets of cubes can be valued as having 20 more points. This is because cubes can be converted at a slightly higher rate than the castle. Do this only if the player is reasonably expected to be able to build them in the castle. (Ie. 5 sets of cubes is worth 5 points if the player has them as leftovers, so don’t count them if the player did not play in the castle or will be unable to build due to the castle being full.) For every stone farm they have, add 1.5 points per turn left in the game (this is in addition to potential score for buildings). Stone farms are the most powerful buildings, after all. Add a few bonus points for the player who has SF if 2S is not out. (It is the best of the 3 stone farms, unless 2S is out). If 2C is not out, add a few bonus points for the player who has CF. Comparing these scores should give you a rough idea of who is in the lead.

This style of play is optimal in theory. However it can be very hard to put into practice, and in a 5 player game, the highest potential player tends to change very often.

b. Make the move that benefits you most absolutely. In this method of play, we do not consider the impact our moves have on the other players, but simply make moves that benefit you. This method works best in 5 player, as the move that benefits you the most is usually the optimal move. In a game with fewer players, the impact a move has on one’s opponents is far more relevant than in a 5 player game. Players who play by this rule are generally rather peaceful, and do not like to hurt their own position.

The above are only general guidelines. The rest of this chapter will be more specific on how exactly to go about playing with these guidelines.

B. Passing and the Inn

Briefly, the inn gives the benefit of being able to place a worker for 1 coin, regardless of the number of players who have passed, at the cost of having one less worker. It costs 1 coin to place in the inn, and denies any other player from the benefit of the inn in the subsequent turn. Once a player is in the inn, he may choose to withdraw himself from the inn when the inn space is activated. Since once you are in the inn, you may remain in there for more than 1 turn, it is somewhat like an investment. This section will detail when to undertake the inn investment, and how to maximize its returns.

The total cost of playing in the inn is as follows:
Initial placement cost of playing in the inn (at least 1 coin)
Opportunity cost of playing in the inn as opposed to other spaces
Loss of one worker as long as you remain in the inn

The benefit of playing in the inn is as follows:
Savings on worker placement after other players have passed. This can be significant, depending on how many players have passed. This also allows the inn player to make cheap plays to pass last.
Denying any other players the privilege of the inn. (You should recognize this as a ‘denial’ benefit.)

The benefit conferred by the inn increases the more players there are. In a 3 player game, the maximum cost of a placement is 3, if the two other players have passed. The player in the inn hence saves 2 coins with each placement. On the other hand, in a 5 player game for example, the cost of a placement can go up to 5. The inn player now would save 4 coins on a placement instead, which is quite significant.

The net gain from the inn is hence the savings from placements after players have passed and the denial of the inn to all other players, minus the cost of putting a worker in the inn itself, and the subsequent loss of the worker. One should then place in the inn only if he expects the savings to outweigh the cost of placing in the inn. To fully utilize the inn, you need to utilize the savings as much as possible. This means making as many plays as possible while in the inn, after players have passed. Also, it would help greatly if players pass early, thus maximizing your benefit. To put it in tangible terms, to fully benefit from the inn, you must have a sizeable sum of money, AND at least one player must pass early due to having no money (or whatever other reason). Again, thinking about it differently, if you have money (at least 7 or 8 to start the turn), and one other player will start next turn with a low amount of money, you should probably place in the inn. If one player has 2 or 3 coins to start next turn, he will at most make 2 or 3 plays then pass, giving you at least 2 plays in which you save money. The 2 coin savings hence would have outweighed the 1 coin cost of placement in the inn last turn. If the player with the lowest money has 4 coins, the inn is somewhat less useful as it gives you only one play in which money is saved (unless for some reason that player passes earlier). If all players have at least 5 coins, and nobody passes early, the inn would have lost its benefit entirely.

When to play in the inn?
The answer to this question is the same answer I would give as if the question “When do I play in the XXX?” Play in it if the net benefit from that square is greater than any other available square. Since the inn is a delayed investment, its value is somewhat low, not to mention, negligible if players do not pass early. The value of the inn increases greatly as other players run low on money. You should probably play in the inn if you sense another player starting next turn with 3 coins or less.

The inn sees much greater use in a 5 player game. Passing last is always a strategic advantage, as it potentially saves you money on moving the provost. Having the inn may allow you to make a cheap play after players have passed, for the sole purpose of passing last, even if that worker achieves no real effect.

Minimizing the inn advantage
More often than not, you’ll find yourself NOT in the inn. In such a situation, taking the inn is not necessarily the best option. The largest weakness of the inn player is the worker shortage. This ensures that the inn player is always forced to pass first, due to lack of workers. By exploiting this weakness, you can turn the advantage of the inn into a severe disadvantage, possibly causing the inn player to withdraw his worker from the inn the subsequent turn.

The main way to counter the inn advantage is to not pass. The moment a player not in the inn passes, if the inn player has any remaining workers, he will experience a huge advantage as he will be able to place them at a discount. However, playing all your workers requires at least 6 coins. The solution then is to keep money high (above 8) at the start of each turn, and deny the inn player money, forcing him to pass early and miss out on his advantage.

Sometimes, even if you do not pass, there will be players who might inevitably pass early, giving the inn player an advantage. A workaround would be to build buildings so you are able to play cheaply on them after players have passed. If you are the inn player, consider preferentially playing on buildings of players who have not passed to increase the cost of placement for them, forcing them to pass as well and giving you an advantage.

The third case: No inn player
At the very beginning of the game, and generally by the mid-game, there will no longer be a player in the inn. At this point players will often be tempted to pass first, for the 1 coin. A pass will generally encourage other players to pass. Now we will tackle this question: when should you pass?

Let us do a simple analysis of net benefit from passing:
Increase in placement cost for all other players on non-owned squares
Gain of 1 coin

And the net cost is:
Reduction in opportunity cost for all players who have not passed.
Early passing reduces control over the provost

The cost and benefits, once again, are not very tangible. Lets start with “increase in placement cost”. Naturally, this only takes effect IF players play on non-owned squares after you have passed. If you pass, and all other players pass, this benefit has not been realized. Likewise, if you pass and the other players continue to play for 1 coin on their own buildings, this benefit has not been realized at all.

Next, consider the “reduction in opportunity cost”. The moment you pass, you no longer contest the remaining squares that round. That means each remaining player has greater access to the remaining placements, although at a higher placement cost. This can be a significant benefit, especially if they are not facing the higher placement cost due to owning buildings and/or the inn.

Lastly, early passing reduces control over the provost. Look at the discussion section on the provost to understand exactly what that entails.

Hence, you should pass only when the gain from the 1 coin earned and the penalty to placements for the other players outweighs the benefit gained from your non-contesting the remaining buildings and your loss of control over the provost. In simpler terms, “pass when the 1 coin is the highest benefit you can obtain”.

C. The Castle

The castle is an interesting place. It is unarguably the most complex square of the whole game. For one placement, you may convert multiple sets of cubes into points (as long as there are sections left), although at a pretty low rate. The first section allows direct conversion at 1.66VP a cube, the second section converts at 1.33VP a cube, and the third section converts at 1VP a cube. The first section in each phase of the castle is effectively worth 7VP, giving it the best conversion rate at 2.33VP a cube. Compared to other means of conversion, these are pretty low conversion rates. Considering that a cube has an intrinsic value of 0.33VP, the third section nets only 2VP every 3 cubes. Converting sections is hence not a fantastic way of generating points.

The incentives here are the favors. The person that builds the most each turn gets a favor, and building to a certain threshold gets you another favor. Favors will be discussed in great detail in Chapter 8. The basic idea is that the benefit of receiving a favor is the immediate benefit, as well as making all subsequent favors in the same track better.

Let me summarize the costs and benefits of the castle:
The cost of placing in the castle is the total cost of the placement, and the activation cost, which are the cubes you plan to turn into castle sections.

The benefit of playing in the castle is the gain in points from converting those cubes, and the potential of getting an immediate favor (if you built the most), as well as the guaranteed favors at the end of each phase.

D. The Provost

Some regard control of the provost as the most important aspect of Caylus. Control of the provost involves two separate aspects, namely, when you need to control the provost, and how to avoid being controlled by the provost.

(Author's Note: It's been almost two years since I have stopped writing this guide, and picking it up again will be a little challenging, so pardon me if I repeat myself or contradict existing points.)

As a quick recap: playing anywhere, including on the provost, takes up a full action, and hence causes you to give up the opportunity to play anywhere else. As mentioned many times before, only do so if the benefits of doing so outweighs the cost.

The benefits of the provost are somewhat different from the benefits of other locations, in that its benefit is the ability to control benefits and/or losses from other squares, both to yourself and to other players. When you use the provost to move it back on another player, the benefit to yourself is the denial of the benefit of the square(s) played on by the other player, or the denial of money to the other player who has to pay it forward to protect his benefit. When you use the provost to move it forward for yourself, the benefit to yourself is the reduced opportunity for your opponents to deny you the benefit to squares you have played on near the front by seizing the provost square first, and a deterrence to them in paying money to push the provost back on you.

Briefly then, here are some rough guidelines to when you should, or shouldnt use the provost, from most compelling to least compelling:

1. Deny multiple spaces with no benefit to yourself
Almost always attempt to deny multiple spaces played on by an opponent. The most vulnerable spots to denial are the space the provost is on and the two spaces immediately behind. Occasionally, there may be buildings (such as the gold mine) after the provost which are played on, which are especially vulnerable to denial.

Bear in mind the discussion in section 7A about players and potential score. It is more valuable to deny players with a higher potential score, and hence chance of winning, than someone who is behind.

Friday, December 07, 2007

Weaknesses


Today, I will attempt to answer the following question:

To what extent should one try to improve on the areas one falls short on?

At first sight, it seems like the answer should be “always”. It is a common paradigm to learn and identify one’s weaknesses, and using this knowledge, to work on one’s weaknesses, such that it no longer is such a weakness. However, this view relies on the common notion that weaknesses are absolute. I would like to place this notion into contention, and in doing so, perhaps obtain a more concrete answer to the original problem.

There appears to be two types of weaknesses in a person’s skill set or character, inherent weaknesses, which are actual weaknesses which arise from physical factors or past background, and perceived weaknesses, which are weaknesses which arise as a result of one’s or others’ perception of one’s self. Here, we take weakness to be the opposite of strength: a weakness is something that can cause one to perform worse in a certain situation. For example, a lack of psychomotor coordination can be seen as a weakness, so far as it affects one in situations where dexterity is required. A lack of ability to obtain knowledge via visual means can be seen as a weakness, so far as it lowers the ability to learn from visual stimuli. A lack of social graces can be seen as a weakness, so far as it lowers the ability for one to interact well with others in a social situation. As they are all weaknesses arising in different circumstances, none of these should be seen as a greater weakness than another.

Now, I would like to consider the viewpoint that weaknesses are absolute. This viewpoint would assert that all weaknesses are actual weaknesses, which means that two people with exactly the same lack of ability in a certain situation would possess the same weakness. For example, the inability to draw lifelike portraits can be seen as a weakness. Someone who believes in absolute weaknesses would agree that this inability would count as a weakness in all people who possess this inability. Now, perhaps some will begin to disagree with me. Some would claim that the ability to draw lifelike portraits is a very specialized skill and the lack thereof should therefore not be considered a weakness. Yet, if you looked within the community of artists, especially the community which specializes in the painting of portraits, such a lack of ability should certainly be considered a weakness. Therein lies my contention with the notion of the absolute weakness.

Consider then, a more general weakness, such as the lack of empathy leading to one often making inappropriate comments in social situations. As the social situation is a lot more common than the artistic situation pictured above, one would be far more ready to admit that if one often makes inappropriate comments in social situations, he possesses the actual character flaw or weakness of a lack of social awareness. Now, I would like one to consider, wherein lies the difference between the two situations? Does the fact that one weakness arises in situations that are a lot more common make it more of an absolute weakness than one which appears less frequently? Upon further reflection one might realize that there is nothing which makes that evident. Although it may not be possible to imagine a human situation where that weakness may not be called into play, save the remote one of a person who spends his entire life on a solitary island, people will still readily call that weakness a character flaw far more readily than the inability to draw life-like portraits.

As can be seen, the distinction between what should or should not be called an absolute weakness is blurred, which leads one to feel that this notion of an absolute weakness is in fact, perceived.

Now, I would like to refer to the other end of the spectrum, perceived weaknesses, and put forth the notion that all weaknesses are perceived. To achieve that, I would first like to discuss the various ways in which a weakness can come to be perceived.

1. Perceived weaknesses arise as a result of expectations.

Where there are no expectations, there can be no weaknesses. Imagine if we captured an alien that landed on Earth, and put it in a social situation such as a party or a formal dinner, and noted that the alien failed to put on any social graces at all, or displayed any interest in any conversation. If a human were in that very same position, one would probably conclude that the human lacks social awareness, or social graces, and attribute to him or her the respective character flaw. However, due to a lack of preconceived notions or expectations about the social abilities of aliens, one will be less willing to impose these same expectations on the alien. In fact, if the alien nodded his head while we were speaking to it, we might consider it to be incredibly polite!

2. Perceived weaknesses arise from experience

Weaknesses can only arise through an observation of behavior. If weaknesses were absolute, it would be possible to deduce one’s weaknesses just through a thorough examination of the person’s physical and mental state. But as is empirically evident, any measure of strength or weakness has to arise from a series of measurements, which in itself requires experience with a person. And the more experience one has with a person, the more easily perceived these weaknesses are. That being said, it is likewise impossible to deduce the weaknesses of a total stranger. Hence, to you, that stranger has no weaknesses.

3. Perceived weaknesses arise from comparison

It is pretty much self-evident that a weakness arises from comparison. After all, how can there be a weakness without a corresponding strength? What I am saying though is that the weakness which arises in this way is perceived and not actual. If there was a skill which everyone could do to the same degree, there would be no notion of strength or weakness in that field. For example, no one would say “I can breathe better than you”, because breathing is an activity that everyone can do to the same degree. Likewise, it is important to realize this distinction, that the weakness which arises from comparison is perceived.

(Apart from the above, there are probably other reasons from which weaknesses can arise. Please feel free to let me know and I will be glad to consider them.)

As I have pointed out above, many of the ways in which we come to believe that a person, whether one’s self or others, has a weakness is through an act of perception rather than an act of matching an actual physical/mental state with a fixed map of states to weaknesses. As such, it is quite clear that a person may be perceived to have certain weaknesses in one society and a different set of weaknesses in another. We find this to be empirically demonstrable as well.

Having established that a wide variety of weaknesses, if not all, are perceived rather than absolute, I would like to return to the original issue, which is the way by which we should come to obtain a heuristic as to which areas of one’s character or skill set that one should improve on. First of all I would like to note that the italicization of the word “should” is a means of emphasizing that this heuristic is normative and relies very much on opinion. That being said, anything which I am about to suggest is and will remain only a suggestion.

Since weaknesses are perceived, the only way to eliminate a weakness is to eliminate the perception of the weakness. While changing one’s self by improving one’s character or practicing the weak skill serves to eliminate the weakness, it is crucial to note that the weakness can also be eliminated by changing the perception directly. This can occur if one convinces the perceiver(s) not to perceive the weakness as such, or if one changes his environment such that the new perceivers do not perceive that particular weakness. For example, moving to China will most likely eliminate the perception of one’s weakness at speaking English (although it may reveal a new weakness at speaking Mandarin). Hence, addressing the weakness directly is not the only way of eliminating it, contrary to what supporters of the absolute notion of weaknesses believe.

How then, should one go about deciding which weaknesses require the most attention? I would like to suggest three factors which may aid one in reaching this decision. The first I will call frequency, which refers to the frequency in which this weakness would cause one to perform less than optimally in any situation. A more frequent weakness would therefore cause one to incur disutility more often (but not necessarily to a larger degree). For example, the weakness of speaking broken English would be a more frequent weakness than the weakness of speaking broken Swahili for a person living in America. It could also be a more frequent weakness than the weakness of having a poor constitution, although having a poor constitution can cause disutility of a larger degree. It is also readily apparent that the frequency of a weakness differs from individual to individual, even when the weaknesses being compared are identical.

The second factor I will call the dependency factor. The dependency factor of a weakness is a measure of the number of people who perceive this weakness in one’s self, weighted according to how dependent one is on these people. If one’s employer or spouse perceives this weakness in one’s self, the dependency factor of the weakness is likely to be very high, but a lot less so if this weakness was only perceived by some people that one has met only once. The dependency factor is entirely subjective, perhaps even more so than the frequency, because it relies on one’s perception of how dependent he or she is on the people perceiving this weakness. The number of people who perceive this weakness is likewise adjusted by how dependent the person is on each one of these people. When calculating this heuristic, one should bear in mind that even people whom one does not regard one’s self to be dependent upon should still contribute to the dependency factor, even if only marginally, because it may be needed to break ties otherwise.

The third factor I will call ease of change. By this I refer not only to the ease of directly changing the weakness, but also to the ease of changing the perception, for example, by changing one’s living or working environment. It is clear that some weaknesses cannot be directly changed, such as those arising from a physical condition. Other weaknesses, especially those requiring the obtaining of a difficult skill set, can be considered to be very hard to change directly. Yet, in this factor allows one to take into account actions which would change the perceivers of the weakness and hence eliminate the weakness. For example, a person who has the weakness of being color-blind can change the weakness by taking up an occupation that does not require the unique identification of colors. A person who has the weakness of speaking with a lisp can take up an occupation that does not require much speech (or go for speech therapy courses, but for the sake of computing this factor, we will select what the person considers to be the easier change).

With these three factors in hand, one can then approach the original question with a certain level of confidence. I will propose several methods which one can go about deciding which weaknesses need to be improved upon the most urgently.

Frequency-based approach: Target the weaknesses which are the most frequent. As frequent weaknesses generate disutility in one’s self the most often, correcting them will lead to a significant improvement in one’s life and disposition, and hopefully increase the motivation one has to work on the other less frequent weaknesses.

Dependency-based approach: Target the weaknesses which have the highest dependency factor. As dependent weaknesses generate disutility in others, which one considers to indirectly result in the most disutility to one’s self, correcting them will lead to better relationships with the people one is most dependent on. This in turn will lead to a happier life, and hopefully more motivation to work on the less dependent weaknesses.

Breadth-first approach: Target the weaknesses which are the easiest to change. That way, one can eliminate the most weaknesses in the shortest amount of time. Those weaknesses may or may not be the most frequent or dependent weaknesses, but as people commonly believe, eliminating a weakness is always for the better, never for the worse.

Combined approach: Using a combination of the three factors, weighted according to one’s personal preference, target the weakness which scores highest on the weighted average of the factors. Needless to say, this approach has all the benefits of the previous three approaches. It also has the disadvantage of being the most inaccurate, because it is rather hard to identify a proper weighting that takes all factors into account.

Regardless of which approach one chooses to use, the hardest part is still the actual overcoming of the weakness itself. I have no suggestions regarding this, and how each individual goes about achieving this is entirely up to effort and determination. Nonetheless, I hope that the above discussion has helped one in obtaining a way to prioritize one’s weaknesses, and will certainly welcome any criticisms or suggestions.

Monday, October 15, 2007

The Summoner

Wendy looked around her. Her house, with all its sky blue furnishings, its beautiful ocean view, and its Victorian furniture, used to be a pleasure to go home to each day. Now, it all seemed like a joke. She felt like a fool, like she had been fooled through her fifteen years of marriage.

Thomas looked down sadly. He had not wished for this. All his life, he had only wanted to please her.

"I know you were different all along. I knew you had special talents, that you used to make me happy. But I didn't think you would lie to me in this way." Wendy was almost in tears now.

"I'm sorry..." was all he could offer in response.

"I should have expected this, marrying a magician." Wendy sat down firmly on a sturdy wooden chair, which looked like it had been crafted in the early 19th century.

"If I had not asked you to let me see Sharon again, I never would have found out." she continued, adopting an accusatory tone.

"Maybe I should have said no. But she was your best friend before you met me. I had to." Thomas said regretfully.

"Then? You would have me continue living this lie?"

"We were happy." Thomas offered, the tone of melancholy apparent in his voice.

"Yes. We were." Wendy said now. She heaved a great sigh. Her past fifteen years had been the most wonderful time of her life. Though they did not have children, they had spent every moment bathing in each other's love and concern. Hardly a moment passed when she wasn't thinking of the next time she would see Thomas, of what they would do together next. Yet, she hadn't realized that her life as of now had been a construct, bent solely by Thomas' will and imagination.

For she had known all along that Thomas had the gift of magic. Powers one would call other-worldly. She had seen him produce flowers from thin air. She had been taken on flights through the air on nothing but a wisp of cloud. He was special in that sense. And he loved her more than anything else.

But what she did not know, until recently, was that Thomas was not a magician in an ordinary sense of the word. Through history there have been many different types of magicians. Mentalists, who could cause things to move with the power of their mind. Illusionists, who could conjure images of things and people and create stunning visual effects, and psychics, who could read minds and find out one's deepest emotions and dreams. Thomas, on the other hand, was a Summoner. He did not summon things, nor creatures, but worlds.

And it was with this talent that he attempted to create the perfect world for their union. He created a world around the both of them, a world free of dangers and sorrow, a world filled only with warmth and joy. He had never let Wendy out of this world once it had formed around them. Slowly, she had lost contact with all her former friends, and had made new ones within his creation.

"But I still cannot come to terms with this... " Wendy said, a tear escaping her right eye. She raised a hand to wipe it off. "My job, all my friends at work. All your friends at your supposed IT firm. They're all figments of your imagination?"

Thomas nodded sadly. It was no easy task, of course, creating this world for his beloved wife to live in. But he had no choice but to do this to protect her. Magicians never had an easy time in society. There were those who hated his kind and hunted them and their loved ones to the end of the earth.

Thomas had thus painstakingly crafted this world for both of them. He had covered every aspect, like the job at the clothing designer's store for Wendy, her boss, colleagues and even clients were all his constructs. Daily he would plan the next surprise for Wendy at work, be it designing clothes for princes, to clothes for orphans in Third World countries. (What third world? Wendy thought.) And he enjoyed seeing her ideas and products very much. In fact, in the guise of his IT firm job, he actually spent a lot of time simply admiring his wife's work. Such were the lengths of his devotion.

In a way, Wendy's artistic talent had drawn Thomas so closely to her. They were both artists, and in their ideas they had found a similarity from which their love blossomed. Thomas appreciated Wendy's creations, and too felt happy when Wendy praised the world she lived in: his creation. That, was when she was still living in blissful ignorance.

"Thomas," she demanded, "why did you do this?"

"To protect you," he replied.

"But why did you have to create all this? Did you think that I would not have been able to handle the world on my own?"

"Dear, you do not understand. A magician has many enemies, some of which would not think twice about destroying you. I loved you so much that I had to do this."

"Its all a lie. Its all fake." Wendy moaned, cupping her face with her hands. Tears still trailing from her eyes, she swiped out with her left hand, and the wooden chair toppled over with a crash.

They stood together, just four feet apart, but in a very uncomfortable silence.

"Its all fake." she whispered softly again.

Thomas stepped towards her.

"No. Its not."

"We're real." He put his arms around her. "We're real, dear, our love is real. I love you. I always will." She gazed back at him, speechless for a moment.

"I love you too, Tom," Wendy said, unable to hold back the tears as she buried her face in his chest.

Slowly, the world begun to melt away around them as Thomas and Wendy stood locked in a fierce embrace. The house and its furnishings dissolved into dust. The wooden furniture, beautifully crafted in Thomas' mind, vanished into a thousand specks of virtual ash. The beautiful sea which used to lap on the rocks of the beach through the night dried up in seconds. Slowly, their surroundings became visible to them. They were in a bare, off-white room, cobwebs being the only decorations on the grubby walls, as they had been the past fifteen years of their life.

But it didn't matter anymore, for once again, while Wendy's eyes were still closed tightly and her head rested firmly on Thomas' chest, the world formed around them once more. The Eiffel Tower rose in front of them, and all of them the dark sky began filling with Paris' evening lights.

"Look where we are, dear."

"Paris. Where we had our honeymoon." Wendy smiled happily, her anguish entirely forgotten.

"Yes, dear. Shall we go up the Eiffel Tower?"

Together, they stepped into the laden elevator, filled with fellow tourists from all over the world, and once again, the world, and everything, seemed right once more.

Sunday, September 09, 2007

Why I believe in God

This post is largely in response to recent developments in school. A friend of mine has been reading the work of one Richard Dawkins, who has gone to great lengths to undermine God, organised religion, and much of what I hold dear in this world and the next. I have read part of Dawkins' book myself. It's called "The God Delusion", but this is certainly not an advertisement advising anyone to read it. The only benefit I have derived from reading Dawkins' anti-God rant is the opportunity to take a closer look at my faith and deal with some of the theological questions which I have largely ignored. So thank you, Richard Dawkins, for helping me understand my faith better.

I have, and have had, a multitude of reasons for believing in God. Some of them are poor reasons, but I will state and acknowledge them anyway. Two caveats before I begin:

1) The God I believe in is the Christian God; Yahweh; the holy triune God, one with Jesus Christ and the Holy Spirit. I do not believe in a pantheon of gods, nor do I believe in demi-gods or immortals.

2) These are my personal reasons for believing in God. They are not necessarily my church's reasons, my parents' reasons, or the reasons of the guy sitting next to me now in property law tutorial. They do not need to be your (the reader's) reasons either. There is a personal realm, a private sphere in which religion exists, and this holds a different experience for each of us. My religion is a proselytist one (and it must be) but this post is not meant to convince you to believe in God too, though that would be a happy consequence.

Let's start off with some poor reasons for my belief in God:

1) I was born into a Christian family.

Although it is my fortune to be born into a Christian family, this is such an inadequate reason to believe in God that I will say little on it. There comes a period of time when one must make important personal decisions in life which may or may not conflict with one's upbringing. Though my family has undoubtedly influenced me, my decision to believe in Christianity is independent of them. (Though I am glad I was not born into a cannibalistic or child-sacrificing family)

2) Christians are nice to me.

The one thing that differentiates many Christian groups from their secular counterparts is the genuine warmth and affection they display to people in their midst. And I, persecuted soul that I am, have sought solace in their company many a time. Insofar as Christians are God's representatives here on earth, this may seem like a satisfactory reason to believe in God. However, there are other people who have treated me well -- Buddhists, Muslims, Hindus, atheists. Indeed, many people who do not believe in Christianity may have exhibited Christian-like values to me before, yet I do not share in their belief systems. So reason number 2 by itself is a poor reason to believe in God.

Let's move on to some slightly better reasons:

3) God has blessed me.

I have been bountifully blessed in life thus far. Sufficient wealth, adequate health, academic success (though mine pales in comparison to some of my readers) are mine to claim. Yet the times I am most grateful for are those where I have recovered from a potentially disastrous state of affairs. To cite a few examples -- my relationship with my family; the A levels; the first half of my army experience; law school; women in general, etc.

The non-Christians will dismiss this as a fallacious argument; how do I know blessings come from God? Maybe I'm genuinely gifted (as the government would have me think). Maybe I made it through army on my own perseverance. Maybe I'm irresistible to women (just maybe). I am wary of attributing every new occurrence to the hand of God. I don't think that I had a good sleep last night due to God's interference. I don't think that I missed the 156 bus this morning due to an act of God (more likely, it was an act of the malicious driver).

However, when an improbable situation resolves itself in my favour when I specifically petition God for it -- i.e. my prayers are answered -- I tend to chalk it down as an instance of divine intervention. (NB Dawkins and I agree that it is impossible to conclusively prove / disprove the existence of God logically. The best we can do is look at the probability of God's existence.) Several prayers of mine -- the examples I gave included -- have been answered positively even when the odds have seem stacked against me. Several times, when I look back after something has not gone my way, I realise that I hadn't prayed about it.

"Inconclusive," I hear Dawkins say. I know that the effects of prayer do not constitute definitive proof of the existence of God. But ceteris paribus, the fact that my acts of prayer repeatedly coincide with my good 'fortune' increase the probability, in my mind, that God exists. It's a personal phenomenon. Only I know what I prayed for, and whether the state of events prayed for ultimately occurred. This is why this post consists of MY personal reasons for believing in God. If you wish to test out my reasons, try praying yourself ;)

4) Humans are fallible.

Most of the people I've met over my 22 years (and I apologise if you're reading this post now) have reinforced my perception that mankind is indeed a fallible race. Wonderfully talented at times, supremely resourceful at others, but ultimately fallible. I've seen it all -- the scholar whose IQ is off the charts, but goes to bed lonely every night because he is friendless; the beauty queen whom all little girls aspire to be, but is deeply unhappy because she knows she will no longer be beautiful one day; the sports jock who is popular with the 'in' crowd at school but is insecure because he worries that his girlfriend will fall for his best friend.

Humans are inherently imperfect. In my mind's eye, one of the most imperfect examples of humankind is myself. I shall not rant about my own shortcomings on this public blog, but if you have known me, and have thought about me in your spare time, it was probably something unpleasant. Let's not degrade this blog post by talking about me.

Now, Christianity is a religion which recognises and maybe even embraces human fallibility. The creator God -- recognising that His creation of mankind is too imperfect and too deep in sin to save itself -- gave us a free gift of salvation through the sacrifice of Jesus Christ on the cross (that's all I'll say about Christianity here lest the non-Christians think I'm a religious zealot out to convert them). This is what sets Christianity apart from many other religions. Most religions preach salvation through human effort; their acolytes must constantly do good deeds, observe certain rituals or say certain prayers to get to heaven (or achieve a better state of being). While Christianity encourages the doing of good works too, this is merely tangential; at the heart of Christianity is the idea that man is saved by the simple act of confessing his sins and believing in God.

How can man, with all his imperfections, be expected to achieve salvation by himself? If the pathway to heaven was strewn with good works, I'd be worrying myself sick every night -- I've quite a lot to catch up compared to my peers. It is precisely because the Christian God is one who acknowledges my frailty, yet can still assure me that I'm not beyond hope, that I seek comfort in the shelter of His wings.

This is not the best argument yet. Perhaps Dawkins would say humanity is still in the process of evolution; maybe we are becoming more perfect with each passing generation. Yet the human condition since the time of the Bible does not seem to have changed much. Man is still plagued by the same unfortunate problems that have plagued him since his birth. To me, one of the keys to understanding Christianity is humility. There has to be a realisation that man cannot do it all alone. That is how human fallibility ties in with my belief in God -- it is precisely because of our inability to save ourselves that we have such a desperate need for God.

Let's move on to my best reasons for my belief in God:

5) God has changed me.

Perhaps this reason is similar to reason (3), in that it is empirical proof of the existence of God. The major difference lies in the fact that I ask for prayers to be answered, whereas I do not always ask to be changed.

I must begin by defining my terms. When I say God has changed me, I do not mean that He has made me taller, or stronger, or more manly. Rather, it is a more subtle change from within; a changing of personality, of character. Let me attempt to illustrate this point with a few examples.

I used to curse and swear everytime something unfortunate happened to me; now I accept it as part of God's larger plan for me. I used to enjoy telling off-colour jokes; now I still tell them, but with much lesser frequency. Perhaps most strikingly, I used to adopt a terribly individualistic approach to work and material wealth; the fruits of my labour or my money belonged to me and only me, and no person in heaven or hell was going to take it away. As I have come to see myself more and more as a steward of God's riches, I have no problem sharing my notes or my cash. (For those people who are reading this and going "Aha, aha, Jerry the miser is lying through his teeth!" let me tell you that my parsimony is reserved for buying items for myself and I do spend on other people when required.)

If I had actually prayed for God to change me in these ways, then this argument would be part of (3). But the opposite is true. I have been resistant to change (especially when it comes to money). I used to enjoy counting my piles of $2 notes in secondary school and JC. I told myself I was not going to part with my money without a struggle. Yet now, somehow, I am comfortable with giving my money to complete strangers (I just gave 500k vis to someone I didn't know on GE!!)

I know what the counter-argument is. God doesn't exist, I know that Christianity expects me to behave in a certain way, I am subconsciously trying to move myself towards that Christian ideal, either that or the changes are those that come with the gradual maturing of the body and mind. And I have to admit that from the point of the objective bystander, that is perfectly plausible. Yet I must reiterate that these are my personal reasons for believing in God. The person most amazed at my willingness to part with my allowance is myself. To me (and perhaps only to me), my change of character is proof that God exists. (Post paused -- DotA time.)