Among other skills, a great poker player must have a big heart, a good mathematical basis, and the ability to reason. It is this last ability that the following posers and puzzles are aimed at testing.
1. True(man) and (Liar)ry. Our weekly poker game has a pair of identical twins, Truman and Larry. No one can tell them apart except for a very unusual tell. During, and only during, the game, Larry would lie every time he spoke while Truman would tell the truth every time he spoke. The eventual consequence of these tells was that neither would say anything during the game. One week, one of the brothers arrived late and took a seat without saying anything. The other twin did not show up at all. No one knew which brother was playing and which was absent. A pot over $1,000 developed between Joe and the twin. On the end, Joe was afraid he had a loser. Before he called a final $500 bet, Joe offered the twin $100 if he would look at Joe's hand and answer one question with "yes" or "no." The twin answered the question and collected the $100. However, Joe called the final bet knowing he had won the pot. What was the question? How did he know which brother was playing?
2. Smallest Favorite Puzzle. You are playing heads up Hold'em. Your opponent will let you select any hand you want except for AA. He will then select his hand and give you 5 to 1 odds that he will beat you. Should you take the bet? What selection would make him the smallest favorite if he selected his best two cards?
3. Hold'em vs. Omaha Puzzle. The same two whole cards played in Hold'em and High Omaha can give you substantially different win expectations with the same board. Determine the twocard hand (we will ignore the other two cards in the Omaha hand for purposes of this puzzle) that meets the following conditions: On the flop, this hand is the 2nd nuts and has a positive dollar win potential over 95% of the time in Omaha and even more in Hold'em.
On the turn, the hand in Omaha is the nuts with a 100% win potential. In Hold'em, the hand still has an excellent but diminished dollar win potential of around 90%. On the end, the Omaha hand still has the highest win potential while the Hold'em hand has 0% win potential. Note: Both games are three-handed with all players staying in the pot until the end.
Give the two-card hand, flop, turn, and river cards. SOLUTIONS
No. 1: Joe shows the twin his hand while asking, "If your brother was here and assessed my hand, would he say your hand beats my hand?" The twin said, "Yes" and Joe confidently called. If the twin playing was Larry, then he would lie about what his brother would truthfully say. Thus, you should do the opposite of what he says. A "yes" meant that he should call.
If the twin playing was Truman, then he would truthfully tell you what his lying brother would say; thus, you should do the opposite of what he says. A "yes" meant he should call. He did not know which brother was playing and it did not matter. No. 2: Take the bet. If you select 54 suited, you will only be a 4.4:1 underdog against his best selection of 66 with one of his cards in your suit.
No. 3: The two cards are 8/9 suited. The flop is the 10/J/Q of the same suit. The turn is the King of the same suit. The river is the Ace of the same suit.
