REU Project

We examined a combinatorial game called Division game. There are 2n coins and two players, Alice and Bob, who want to split the coins so that each player has exactly n coins. In the first turn, Alice picks a coin and Bob decides who gets it. Then, the roles swap and the game continues until one of the players gets n coins. The other player then obtains the remaining coins and the player with the larger sum of coins wins the game. We conjecture that Bob always has a non-losing strategy which we proved for a small number of coins and for special classes of games.