no-limit hold’em, from first principles

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A deck has fifty-two cards.

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Pot odds & equityWhat a call costs as a share of the final pot, and why you call when your chance to win is higher.Expected valueWeight each result by how often it happens and add them up: the way to compare any two poker decisions.CombinatoricsWhy there are 1,326 starting hands, how many ways each can be dealt, and how the cards you can see remove combinations.Range vs rangeList every hand they could hold, weight each by its combinations, and see how often you’re ahead.Bet sizingEvery bet sets two prices: how often they need to win to call, and how often your bluff must work.Bluffing & MDFHow often a bluff has to work, and how often you must defend so they can’t bet any two cards: minimum defence frequency.Nash equilibriumA bluffing game solved on one square: best replies, the point where neither player can gain, and why a third of bets are bluffs.Variance & bankrollWhy a winning player can lose for thousands of hands, and how big a bankroll has to be to survive the swings.How computers solved pokerHow poker programs taught themselves by self-play and regret matching, from a toy bluffing game to Libratus and Pluribus.ICMWhy tournament chips aren’t money: the Independent Chip Model, prize equity, and why calls get tighter near the money.The rakePoker is zero-sum until the house takes a cut. How the rake makes it negative-sum, and how good you need to be to break even.BlockersHow the cards in your hand change what they can hold: counting flush combinations, and why holding the ace matters.

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