Below is a question I found in old statistics book of mine, that I really would like to know how to solve: Suppose two players, A and B, play a game. If we assume that A has probability pA og winning and B has probability pB=1-pA of winning, the number of wins and losses for player A will be binomially distributed. Now let us assume that we a priori don't know pA and pB. Player A and player B play 50 games and it is found that player A wins 30 games. Can he then claim that he is the better player?