A Probability bet.

[Raiter]

2 players named Aaron and Gary are playing Texas Holdem. Gary offers aaron a even money bet of $200 on the outcome of a particular wager. The wager is that after recieving your 2 down cards and seeing the flop (3 cards face up on the board) Adam has to successfully guess the exact next card to come out on the turn (one of the 47 unseen cards) and if he misses he has to guess the next card (of the 46 unseen cards). Now Aaron get to do this 26 times for a total of 52 seperate guesses. Now the question is who is the favorite to win this even money $200 bet? Aaron (the guy who is guessing) or Gary?

[elitegimp]

[ QUOTE ]
2 players named Aaron and Gary are playing Texas Holdem. Gary offers aaron a even money bet of $200 on the outcome of a particular wager. The wager is that after recieving your 2 down cards and seeing the flop (3 cards face up on the board) Adam has to successfully guess the exact next card to come out on the turn (one of the 47 unseen cards) and if he misses he has to guess the next card (of the 46 unseen cards). Now Aaron get to do this 26 times for a total of 52 seperate guesses. Now the question is who is the favorite to win this even money $200 bet? Aaron (the guy who is guessing) or Gary?

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If the guesser sees 5 cards (two hole cards and the flop), then I get he will be wrong on the turn 46/47 of the time. If he is wrong on the turn, he will also be wrong on the river 45/46 times... so 45/47 times (95.74% of the time) he will be wrong twice. If he gets to try 26 times, then he will be wrong all 26 times (45/47)^26, or about 32.3% of the time. Therefore the guesser wins 1-(45/47)^26 or 67.7% of the time.

Even if the guesser had to pay 2:1 (i.e. he wins $100 if he guesses right and loses $200 if he guesses wrong) he's a favorite in the game. Even money it's not even close!

If the guesser sees the flop, but doesn't see anybody's hand, then he is wrong on the turn 48/49 of the time, and wrong on the river (given wrong on the turn) 47/49 times. Therefore he misses both cards 47/49 or 95.9% of the time... he'll be wrong 26 times in a row (47/49)^26 or 33.8% of the time -- still a favorite (but not quite 2:1 any more).

[TomCollins]

I'll give you 2-1 if you can predict the Powerball jackpot correctly!

[LetYouDown]

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2 players named Aaron and Gary are playing Texas Holdem

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Adam has to successfully guess

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I'm hoping this is a typo and not the dumbest logic question of all time. Only reason I even post this is the fact that you referred so heavily to names.