Monday, January 11, 2010

Chinese Blackjack (Ban-luck)

Chinese Blackjack, otherwise known as "Ban-Luck" to some Singaporeans, is interesting in that it is an almost symmetric game between the player(s) and the dealer. This is because the payouts and scoring rules are identical for both player and dealer, which contributes to the simplicity of the game. In fact, if the dealer chooses to play in a particular fashion, namely hitting his cards before revealing the players' hands, then it does become a perfectly symmetric game.

Conversely, a dealer's house advantage comes solely from being able to selectively reveal some players' hands before hitting. In other words, the dealer has an advantage in that he is able to first beat hands which are likely to be weaker (by being busted), and that he is able to further build up his hand to confront stronger hands.

Out of a pure curiosity, I was considering some potential strategies for Chinese Blackjack. However, most player strategies are likely to have a minimal impact, due to the inherently limited strategic nature of the game. Chinese Blackjack forces the player to draw til at least 16, in which case it is (by statistical reasoning) unwise to draw further. The only exception to this rule is when one has a 'soft' hand, comprising of one Ace. Though I have yet to perform a through analysis of the mathematics, I believe that it is better to hit in this case. There is a small chance of improving one's hand, but the main issue is to confound the dealer's opponent model by tricking him into believing that you have a busted hand.

As a dealer, there is much more room for strategic analysis. It is quite possible to compute, via extended Monte Carlo simulation, the probability of a 4, 3 card hand being busted (assuming the basic opponent model given by the hit-til-16 rule). Furthermore, with some computing power or pre-computed tables, it is possible to obtain the precise odds of a player's hand being superior to yours, and the odds of a drawn card improving your hand, given the already exposed hands. However, I have my doubts regarding the feasibility of such implementations.

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