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There are five players and ten rounds. During each round every player picks a number between 1 and 5, This choice is secret, no player knows what the others picked. After all players have chosen the numbers are revealed. The player with the highest unmatched number wins the round and is awarded points equal to his number. A number if matched if another player has written the same number i.e if 5, 5, 5, 4, 3 were written then 4 would win since the fives are matched. The points are added each round and after ten rounds the player with the most points wins.

So is there an optimal strategy to guarantee a win? If not is there a certain strategy where the probability of winning is >50%, and finally if this cannot be achieved is there a strategy which guarantees a draw?