Peter offers to play exactly one St Petersburg game with each of [math] players, Paul [math] , [math] , Paul [math] , whose conceivable pooling strategies are described by all possible probability distributions [math] . Comparing infinite expectations, we characterize among all [math] those admissible strategies for which the pooled winnings, each distributed as [math] , yield a finite added value for each and every one of Paul [math] , [math] , Paul [math] in comparison with their individual winnings [math] , even though their total winnings [math] is the same. We show that the added value of an admissible [math] is just its entropy [math] , and we determine the best admissible strategy [math] . Moreover, for every [math] and [math] we construct semistable approximations to [math] . We show in particular that [math] has a proper semistable asymptotic distribution as [math] along the entire sequence of natural numbers whenever [math] for a sequence [math] of admissible strategies, which is in sharp contrast to Peter offers to play exactly one St Petersburg game with each of [math] players, Paul [math] , ..., Paul [math] , whose conceivable pooling strategies are described by all possible probability distributions [math] . Comparing infinite expectations, we characterize among all [math] those admissible strategies for which the pooled winnings, each distributed as [math] , yield a finite added value for each and every one of Paul [math] , ..., Paul [math] in comparison with their individual winnings [math] , even though their total winnings [math] is the same. We show that the added value of an admissible [math] is just its entropy [math] , and we determine the best admissible strategy [math] . Moreover, for every [math] and [math] we construct semistable approximations to [math] . We show in particular that [math] has a proper semistable asymptotic distribution as [math] along the entire sequence of natural numbers whenever [math] for a sequence [math] of admissible strategies, which is in sharp contrast to [math] , and the rate of convergence is very fast for [math] . , and the rate of convergence is very fast for [math] .