Fundamental Theorem of Poker - An Example

An Example

Suppose Alice is playing limit Texas hold 'em and is dealt 9♣ 9♠ under the gun before the flop. She calls, and everyone else folds to the big blind who checks. The flop comes A♣ K♦ 10♦, and the big blind bets.

She now has a decision to make based upon incomplete information. In this particular circumstance, the correct decision is almost certainly to fold. There are too many turn and river cards that could kill her hand. Even if the big blind does not have an A or a K, there are 3 cards to a straight and 2 cards to a flush on the flop, and he could easily be on a straight or flush draw. She is essentially drawing to 2 outs (another 9), and even if she catches one of these outs, her set may not hold up.

However, suppose she knew (with 100% certainty) the big blind held 8♦ 7♦. In this case, it would be correct to raise. Even though the big blind would still be getting the correct pot odds to call, the best decision is to raise. (Calling would be giving the big blind infinite pot odds, and this decision makes less money in the long run than raising.) Therefore, by folding (or even calling), she has played her hand differently from the way she would have played it if she could see her opponent's cards, and so by the Fundamental Theorem of Poker, her opponent has gained. She has made a "mistake", in the sense that she has played differently from the way she would have played if she knew the big blind held 8♦ 7♦, even though this "mistake" is almost certainly the best decision given the incomplete information available to her.

This example also illustrates that one of the most important goals in poker is to induce the opponents to make mistakes. In this particular hand, the big blind has practised deception by employing a semi-bluff — he has bet a hand, hoping she will fold, but he still has outs even if she calls or raises. He has induced her to make a mistake.