LAST ROUND BETTING

THOMAS S. FERGUSON and C. MELOLIDAKIS

Abstract:

Two players with differing amounts of money simultaneously choose an amount to bet on an even-money win-or-lose bet. The outcomes of the bets may be dependent and the player who has the larger amount of money after the outcomes are decided is the winner. This game is completely analyzed. In nearly all cases, the value exists and optimal strategies for the two players that give weight to a finite number of bets are explicitly exhibited. In a few situations, the value does not exist. These results are useful for analyzing Final Jeopardy and the last round of certain casino gambling tournaments.