Thanks. We conducted here similar simulation for all |A|,|B|<11 In case you are interested: arielrubinstein.tau.ac.il/simulation.pdf

To Patrick: Note, that the direction of transfer between any two players is indepedent from the directions in other "matches".

Thanks. We do need the result for small values as well (and not just for large numbers). Note that for general |A| and |B| (not for the case that |A|=|B|) we need the condition that $2>$1: Consider the case that the transfer between a member of A and a member of B (which is now $1) is very very high then if |A|>|B|, the probability of a member of B to win will be larger (the transfers inside B will be negligible).