![]() Even if the dealer had stacked the deck to deal himself favorable cards, the randomness of the cut will necessarily ruin his efforts. Assuming the two players are not colluding and there is no sleight of hand, this ritual absolves the dealer of any guilt. One of the most common such rituals is “cutting the deck.” The player who shuffles the deck passes the deck to a second player, who cuts the deck in half, placing the bottom half above the top half. ![]() Instead, we incorporate rituals into standard play that assure fairness. In card games, especially gambling games, trust is rarely given freely. For the sake of this post, the betting rules will not matter. And we found quite a bit more than we expected! But first, let’s recap the ideas from our original post.įor a reminder of the rules of Texas Hold ‘Em, here’s a silly tutorial video from. And so months later, after traversing the homotopic hills of topology and projective plains of algebra, we’ve finally found time to solve the problem. In the mean time, we’ve gotten distracted with graduate school, preliminary exams, and the host of other interesting projects that have been going on here at Math ∩ Programming. It’s been quite a while since we first formulated the idea of an optimal stacking. ![]() Main Theorem: There exist optimal stackings for standard two-player Texas Hold ‘Em. ![]()
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