The Kelly Betting System for Favorable Games.
Thomas Ferguson, Statistics Department, UCLA
A Simple Example. Suppose that each day you are oered a gamble with probability
2/3 of winning and probability 1/3 of losing. You may bet any positive amount you li
one should bet (rk /(rk + bk ) on red, while if bk rk one should bet (bk /(rk + bk ) on
black.
A practical example of the use of this type of information gathering occurs in the
game of blackjack. At the start of this game with a well-shued deck, the game
7. Innite Games.
In this Chapter, we treat innite two-person, zero-sum games. These are games
(X, Y, A), in which at least one of the strategy sets, X and Y , is an innite set. The
famous example of Exercise 4.7.3, he-who-chooses-the-larger-integer-wins,
4.7 Approximating the Solution: Fictitious Play.
The method of ctitious play may be used to approximate the value and optimal
strategies of a nite game. It is a sequential procedure that approximates the value as
closely as desired, giving upper and lower