# Why Are There Antes in Poker?

Consider the following simple game of poker. Each player has a 13 card deck, with one of each rank, ace through 2. At the beginning of the game, each player draws a card randomly from the deck. They then simultaneously choose whether to bet \$1 or fold. If either folds, no money exchanges hands. If both bet, then there is a showdown. Whoever has the highest rank wins the \$1 from the opponent. In the event of a draw, no money changes hands.

How should the players strategize in this game? You might suspect that a player should bet if he or she has a higher than average card. But Bayesian Nash equilibrium makes a different prediction.

Takeaway Points

1. A type with the highest rank card (ace) has a weakly dominant strategy to bet. At worst, they draw. And against any opponent who bets with a card worse than ace, the ace type makes money.
2. A type with the lowest card rank (2) has a weakly dominant strategy to fold. At best, they draw against another 2. At worst, any opponent that bets with any other card rank will cause the 2 type to lose.
3. The previous point alters how a type with a 3 would want to play. The only way he or she can win is if a 2 bets. But if a 2 does not bet, then the best a 3 can do is draw. Thus, in the remaining game, the 3 type has a weakly dominant strategy to fold.
4. The previous two points alters how a type with a 4 would want to play. The only way he or she can win is if a 2 or 3 bets. But if a 2 or 3 does not want to bet, then the best a 4 can do is draw. Thus, in the remaining game, the 4 type has a weakly dominant strategy to fold.
5. This logic works all the way up to the rank of king. Despite being the second-highest rank, the king type anticipates that everyone other than an ace or king should fold. Thus, the king type also folds.
6. The unwillingness for all types other than the best hand to fold is why poker games require players to place an ante before the start of a hand. That existing money in the pot gives weaker hands a temptation to bet so they can acquire the money up for grabs.
7. The general effect described here is known as the unraveling principle. It arises in many other situations, and we will discuss it further later in this course.

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