risk matching in gambling

An argument for playing a game such as poker with “real” money is that it forces people to play with true risk-reward calculations. While this is certainly better than playing without risk, there exists the question of how to match risk profiles among players. With enough players (large liquid market), they can self-sort by stake size, and this seems fair. With only few people though, the situation is turned around, where a stake size has to be agreed upon at some clearing size (so that enough people agree to play the game) rather than chosen individually, and that same amount of money may be considered as very different values by different people. A pauper and a millionaire do not see $100 as the same value, and will adjust their utilities accordingly, and this will materially affect wagering. Since risk is measured in utility units, it is desirable to match utilities rather than dollar amounts. But there isn’t an agreed-upon utility currency. Or is there?
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some propositions on the game of go

I’ve been meaning to learn the game of “Go” (weiqi) for quite a while now, and finally got around to it now that there are some people at Harvard at beginner’s levels to play with.

The usual adage is that the rules of “Go” are simple, but the strategies are difficult. Sometimes they cite the fact that computers can’t play “Go” very well (compared to, say, chess). I’m not in a position to defend or refute this sentiment yet, but I think this stuff is easier than it first appeared to me years ago, if you think about it the right way. “Go” seems a very mathematical game, almost a counting and topological reasoning game. And all the difficulties arise out of the fact that the counting and reasoning is done in 2D (rather than 1D, which would be simple).

So there is this list of terminology like “liberties,” “eyes,” “false eyes,” “alive and dead regions,” etc., but sometimes they greatly confuse the matter, so I found it easier to recast these basic concepts in more general terms.

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on 80 points (bashifen), aka tractor (tuolaji), aka double rise (shuangsheng)

This is a popular card game of the 5-10-K class played in China, the rules of which are described in English here, but not in a generalizable way. Another version on Wikipedia makes logical sense but isn’t how I’ve seen it in practice. In any case, like for many card and board games, the rules are not described in a proper way for the new player and that’s annoying (some rules are not important or obvious, other rules are important but obscure, etc.). I remember in the help files of say, MS Hearts, they follow a four-section template of: (0) basics, (1) goal of the game, (2) playing the game, and (3) strategy; in that order, which I think is the perfect logic that should be used for describing all games. Why nobody wants to explain a relatively simple game as this except by enumeration of examples is a mystery to me, so here goes:

The game is played with two joker-included decks of cards. 5, 10, and K are point cards worth face value, except K is worth 10 points. It is a standard 4-player partnership game, so a person and his cross is a team. It is played in multiple rounds and each round there is a dealer (hence a “dealer” team and an opposing “grabber” team). Each team keeps a “level” represented by a card rank (i.e. 2,3,…,A), and each round is associated with the dealer’s level, whose corresponding rank cards are called the level cards.
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resolving the St. Petersburg paradox

The St. Petersburg paradox is based on one of those gambling games where the usual model of using expected gain to decide whether to play the game gives a counter-intuitive result.

In the simplest of examples, you pay some entry fee to play the game, $1 is put in a pot by a counterparty, then a coin is repeatedly flipped and the pot is doubled on every coin flip by the counterparty, until “tail” comes up. You receive the money in the pot. The expected gain of this game is infinite, regardless of the initial entry fee. So it would seem that one should always play the game, regardless of the amount demanded as entry fee. But, as the article points out, “few of us would pay even $25 to enter such a game.”
(Read the article)