One of the interesting features of this heads-up poker duel between a computer and a human is that it is designed to eliminate luck as a factor. In one room Polaris will play Laak and in another room Polaris will play Eslami, and Polaris will get Laak’s cards when playing Eslami and Eslami’s cards when playing Laak.
Jonathan Schaeffer, the Polaris team leader, claims that the set up will eliminate most, not all, of the luck. This raises the question, “In what way can luck still play a factor in this match?” And of course this question raises the more fundamental conceptual question of what luck means, a question I’ve touched upon in previous posts (here and here).
I still don’t know what it means to say that someone is lucky in Hold’em. If there were no betting in the game, then luck would simply be a question of what cards were dealt. And the Polaris experiment would rule this sort of luck out, for if Laak would get lucky, then Eslami would be unlucky. However, Hold’em has betting, and this means that there is a certain amount of skill involved in the game.
Suppose your opponent in a heads-up match gets dealt pocket aces five times in a row. And suppose during this streak your hole cards are 2 and 7 off-suit. Does this mean that within these five hands your opponent was lucky and you weren’t?
I think the answer is “It depends”. It depends on whether your opponent wins with his starting cards and how much he wins if he does win. Of course, it is more likely that he will have the winning hand in the end than you. But getting to the “end” of a hand is not one’s primary goal when playing hold’em. One’s primary goal as a rational gambler is to maximize winnings, and how one does this is what makes the difference between great players and not-so great players.
Now let’s turn to the Polaris match. Suppose in the first five hands between Polaris and Laak, Polaris gets pocket rockets for its hole cards and Laak gets dealt 2 and 7 offsuit as his hole cards. This means that between Polaris and Eslami, Polaris will have been dealt 2 and 7 as its first five hole cards and Eslami will have been dealt pocket rockets. Isn’t it still possible that beteween Eslami and Polaris in this first hand luck can still play a big role in who makes the most profit? Consider the following.
Suppose in the first hand before the flop Polaris bets X amount of money and Laak folds. Suppose that before the flop Eslami bets X amount of money but Polaris doesn’t fold. Polaris may, of course, still win the pot against Eslami with his horrible hole cards. He/It may eventually outdraw Eslami, which indicates that he/it got lucky or he/it may win by bluffing, which again may be a result of luck.
So intuitively it seems to me that the Polaris experiment doesn’t eliminate as much luck as the designers of the experiment would like us to believe. Perhaps I’m incorrect. But I think that in order to show me why I’m incorrect, one needs to explain what “luck” means in Hold’em. I’m waiting.