Generalizations of bold play in red and black

The strategy of bold play in the game of red and black leads to a number of interesting mathematical properties: the player's fortune follows a determ inistic map, before the transition that ends the game; the bold strategy ca n be "re-scaled" to produce new strategies with the same win probability; t he will probability is a continuous function of the initial fortune, and in the fair case, equals the initial fortune. We consider several Markov chai ns in more general settings and study the extent to which the properties ar e preserved. In particular, we study two "k-player" models. (C) 2001 Elsevi er Science B.V. All rights reserved.