1. The problem statement, all variables and given/known data Player 1 starts by choosing 0 or 1, then player 2, repeat infinitely many times and stick a decimal point in front and see the bit string as a real number between 0 and 1. If it's rational player 1 wins, irrational player 2 wins. Does either player have a winning strategy? 3. The attempt at a solution Player 2 has a winning strategy. He can simply randomly choose bits, and hence he wins with probability 1 (not hard to show). But my professor does not want a probabilistic algorithm. I'm drawing a blank.