Sometimes in a game of poker you feel compelled to throw more chips into the middle of the table even when you know you’re likely to lose the hand. Usually, it’s a psychological trick you’ve played on yourself. It’s the sunk-cost fallacy. You’ve already invested so much on the opening bet, then more on the subsequent flop, and more still on the turn, that your pride or your fear moves your hand forward at the end. You’re just hoping to get lucky.
But sometimes, throwing more chips in at that point is the mathematically correct decision. The combination of your own and others’ circumstances conspire to make throwing good money after bad the most rational decision. Perhaps you’re running low on chips altogether, and a number of players acted irrationally at the start of the hand, over-betting at first but folding once they suspected that another player had drawn the top possible hand. You didn’t make your straight and are stuck with something no better than a high pair. But the pot has grown to a size 30 times larger than your remaining stack of chips. Nothing can be undone. You suspect the last remaining player has a full house. All that’s left is your small remaining bet and the potential large prize. This is what’s known as “pot commitment.” You have every reason to believe that you’re going into the final card well behind in the hand, and your chance of “sucking out” at the end is small. But the pot is too large now. Mathematically, your small chance of winning is overwhelmed by the prize itself. You can’t turn away now. You just have to push your chips in and hope it works out.
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