SOME INTERESTING BUT NOT TOO USEFUL MATHEMATICAL FACTS:

In hold'em, with no betting after the flop, all pairs are a favorite over Ace-King oflsuit, by at least 529 to 489. All pairs except Deuces with neither card in the Ace-King's suit are favored over Ace-King suited. If several players lold first, Ace-King suited is a favorite over most pairs. (The exceptions are Aces, Kings, and Jacks, and also lens where one of the lens is the same suit as the Ace-King.) Even Ace-King oflsuit is now a favorite against small pairs. The reason for this is that players are more likely to play hands having an Ace or King than those containing smaller cards. Therelore, as players lold, the probability of an Ace or King coming on the board increases.

The chances of having pocket Aces in hold'em are I in 221. When everyone folds to you and you have the big blind, the probability of having a pair of Aces is approximately 1 in 134, since players are more likely to enter the pot if they have an Ace.

Similarly, but more obviously, when everyone folds to the big blind in lowball, it is likely that the big blind will pick up a hand mainly consisting of low cards.

When playing heads-up triple-draw lowball, it shouldn't be surprising that pat hands gel beat on the third draw much more frequently than in single draw, since some useless cards have been discarded on the first two draws, and the opponent is draw ing to better hands.

Two players play a heads-up session for eight hours. Let's suppose they play 40 hands per hour for a total of 320 hands. If every hand has a 509c chance to be won by one player or the other, what is the average longest winning streak either of them w ill have?

If n is the number of hands, the average longest streak is approxi­mately log, ii_y even for small values of n. VVe should expect, on average, that one player will win eight hands in a row over the course of 320 hands. People tend to expect things to even out sooner than they do, so they are surprised by the streaks that come about. This leads them to believe that other things must be influencing the results: "He's just hot," "That's his lucky dealer," etc.