It seems that I have been overly academic in the first article in the series, and for ones who are really interested in playing the game better, it offers little strategic help. The second installment a little bit too casual and may be too trivial to be viewed as helpful advice. Here I would like to jump ahead and offer a casual but nontrivial perspective of what the game is really about. I hope this can setup the stage for me to go back to numbers and be academic again in the subsequent articles, on the various topics I will discuss qualitatively in the following.
In my opinion, there are three stages of the level of play. In the first stage, new players tend to set their price goal at roughly 1/2 of the most possible value. Intuitively (but wrongly), buyer and seller divide their profit, square and fair.
However, in no time the players will find that there will be some of them who are constantly winning. Those are players who are willing to pay more and acquire the majority of the paintings. This is easy to understand: as we discussed in the first article, the buying player can bid at (n-1)/n of the value to break even in a n-player game, even if he makes no profit from his own sale at all. This pretty much sets the baseline for the auction prices.
In the second stage of play, people start to realize that for a painting with definite value, getting a small piece of it is strictly better than getting none. On the pure theoretical analysis for this single auction, the reasoning is sound. Players starts to bid high, sometimes as high as more than 90% of the expected value. At this stage, people usually sell what is currently most valuable, but start to find that in general the winner is simply the player who holds the more valuable paintings. They notice that double auction paintings are really strong, and sometimes they feel the game is somewhat determined on the cards, and the decisions made are secondary.
I cannot say this is entirely untrue. The game is somewhat determined by luck. I would add that the most important luck factor, in my opinion, is the additional cards that come at the end of the first and the second round.
In the third stage, players try harder to make their painting valuable. They do this by delaying the use of double auctions, and try to sell from their long suit. They value the painting on sale also by their holding. The only games I played at this level are all with computers– not that they are doing this terribly well, but it is indeed kind of hard to find that many serious players near you to play that many games to reach this level.
In this stage, players start to face interesting dilemma. In the early rounds, if you have a long suit, you will definitely want to save some of them until later rounds, especially when you have double auctions among them. For your short suits, you worry that selling them benefits your opponent more in the long term. Near the end of the first and the second round you will also experience the situation such that you have no strong desire to end the game (especially since you will be wasting a card worth at least $30 if it places in the subsequent turns), yet other cards you can sell are worthless (or even worse, worthless at the moment, but can potentially harm the value of the paintings you have bought.) It is as if the game mechanics is somehow flawed that the ideal move in the early rounds is to pass but it is forbidden and you are forced to throw your paintings away.
In later rounds, annoying things can happen too. Have you set up your Lite Metal double auction? Your LHO ended the previous round, but when it’s your turn three Lite Metals are already sold. You aim to sell a double Krypto with a $50 price tag already on it? When it’s your turn, two doubles in other suits are already sold and you are forced between biting it yourself or selling it cheap. Both options can be deadly, though; when you sell it, the buyer pushes another double in the same suit and make a fortune; when you bite it yourself, you are forsaken. In this stage, it is hard to say in the first place which paintings are better or worse than one another; it depends on the position, the distribution of your and others’ holdings. From the strategic point of view, the value of the paintings fluctuate in a way which is not determined by the strategy of any single player. It is even random in some sense: a side effect from a play can snowball into unintended directions provided the distributions unseen are right.
The meat of the game occurs at this stage. With the major market deficiency gone, one has to look harder. One cannot play a strategy on his own; instead, he should try to take advantage of the market. There are no guaranteed way to work, but when it is there, one can observe patterns that he can take advantage of.
Here are a few things I observe that one can take advantage of:
- In early rounds, when you have someone selling a painting you hold quite a few, there are two cases you can take advantage of. If the prices is low, you can buy it cheap and sell another in your turn. If there is some competition, while you are still (in some sense) at an advantage to bid higher (since you have more control to make this suit scorer higher), the correct play may be to let others have it. This way they may be forced to push it themselves later in the round, giving you a bigger profit at later rounds. One can view it this way: it is sort of a random gift when someone sells your long suit. There are ways to take advantage of it.
- Early in the round, consider strongly to buy a painting even if it is not your suit as long as it does not cost you a fortune. This way one can avoid (or at least, mitigate) the worst: all the opponents are happily sharing the paintings that you just don’t have. You at least also make some profit, and in some cases without the painting the other player may sell a different painting.
- You need to save for the later rounds, but you don’t need to save your painting all that much. While in the first two rounds it may seem you have all the eternity to sell your paintings, in the third and fourth you are very lucky if you can sell more than two paintings in the same suit. It is better to sell out a few more from your long suit instead of pushing up others’ unwillingly. Keep at least one painting in each suit if possible; this way you won’t waste the single double auction painting you draw later…
- Beware of Krypto and Karl Gitter if you didn’t hold a lot of them. There are 3 doubles for each; and if you don’t have any others must have some. Pushing them in earlier rounds can be fatal for you later. When you have like 2 of them but no doubles, it is best to sell them when other suits already go high. You can even spend a few dollars to buy an insurance.
- it is basically scoring time at round 3 and 4. Try to sell the paintings you saved at the right time, and buy the paintings based on holding/position. One can make a great fortune by buying the paintings that were not expected to place.
One last job 