The present paper has as starting point the results of S. Csörgö and G. Simons (2002–2006) on the classical St. Petersburg(1/2) game, played by two gamblers with an unbiased coin. The author considers the generalized St. Petersburg(

$p$) game with

$p\in (0,1)$ as the probability of the “heads” at each throw of a possibly biased coin. An interesting result is that, while the stochastic dominance is preserved for the case of two players and an arbitrary parameter

$p\in (0,1)$, for three or more players, the admissibly pooled winning strategies generally fail to stochastically dominate the individual strategies. The main result of the article consists in determining the best admissible pooling strategies for a rational value of

$p$, illustrating also the algebraic depth of the problem for an irrational value of the parameter

$p$.