What is the correct number of cards to play poker? According to a new mathematical discovery, the traditional answer is 52. Approximately.
In Texas Hold’em poker, players bet on the best five cards of the two cards in their hand and the community cards on the table. Hands are ranked based on their probability of occurring. A full house, for example, three cards of the same value (for example fives or kings) and two cards of another, is less likely than a flush with any five cards of the same suit. That’s why a full house is full of clutter. In short-deck poker, a variant that removes cards numbered 2 to 5 (called “Rank 2-5”), there are fewer cards of each suit and the probability of a flush is reduced compared to a full house. In a recent paper Posted on preprint server arXiv.orgComputer scientist Christopher Williamson investigates how the game of poker changes as the number of cards per suit increases or decreases. Depending on that number, an interesting paradox can arise, Williamson found – a paradox that is almost always avoided in games with 52-card decks, in which each suit has 13 cards.
After the bidding process, poker players will declare their best performance in a “showdown”. Consider two hands: a pair, containing a pair of cards of the same value, and a two pair, containing two pairs of such cards. In short-deck poker, although two pair is less likely to appear than one pair, its showdown probability – the probability that it will be someone who has the best hand – is actually higher than that of one pair. If the hand rankings are adjusted accordingly, no one will ever play two pairs against one pair, changing the probability of a showdown once again.
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Regarding how many cards in each suit a deck should contain, Williamson says, “Thirteen is kind of the sweet spot.” This is the smallest number for which the showdown ranking actually matches the standard ranking for all hands except one high card (the lowest ranking hand). Although the general number of cards in the deck is entirely historical – it is said to symbolize the 52 weeks of the year and the four seasons – Williamson was pleased to find a more mathematical justification. There is only one better setup, which will keep all rankings, including high cards, in line with their showdown possibilities: You will need 23 cards in each suit, which is almost twice as many as in a traditional deck.
Top professional poker player Nikita Luther finds the result fascinating. ”It’s very complex,” she says, ‘the way the variables interact with each other.” Luther says she hasn’t explored the variants in depth beyond Texas Hold’em; There, too, “I could spend the rest of my life trying to figure out this game.”
Try a related math puzzle here,
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