2851：No Fold'em Hold'em

The recent Texas Hold'em craze has spawned a bunch of on-line Poker sites. These sites tend to breed a group of poor players whose primary strategy is to never fold or throw away a hand. These players will always play and bet on every card on every hand no matter what the cost or what cards they have. You have decided to take advantage of these stupid players by developing your own poker site that allows you to always beat these players.

The way your site will work is: there are only two players in each game: you and your opponent (this is called a heads-up game). Each of the two players will get two “hole cards”; these cards are dealt face down so, presumably, only the player can see them. Four of the five community cards (cards shared by both players) will be dealt face up on the table. We will dispense with any betting for the purpose of this problem: it is irrelevant since each player will always call every bet right to the “river” (the fifth and final community card). You will always be seated at position 1, and your opponent at position 2. The program knows what seat you are sitting at and the hole cards for both players, therefore, it can compute all the cards that remain in the deck that will maximize the amount of money you would get playing the hand – folding is not an option. In the event there is no card that would allow you to win or tie the hand, you will be forced to take a loss on that hand (after all, it looks good if you lose sometimes).