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Old 10-20-2005, 07:05 PM
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Default Re: chances your opponent won\'t have a pair on the flop or turn

warlockjd I think you're making some errors here. But I get corrected for my math all the time so this is by no means definitive:

Whatever the first card you are dealt, there are 3 remaining cards in the deck of 51 left to pair you. So, probability of getting a pair is (52/52) * (3/51), or 5.88 %.

To account for the times you are dealt the pair, you need to make sure not to double-count the times you get two pair, or trips or whatever. Easiest way to avoid this error is to flip the equation. So instead of 6/50 it's (44/50)*(43/49)*(42/48) = 67.5 % of the time your opponent does NOT hit a pair by the flop. Take one and subtract this number and you get 32.42 %, add the preflop pairing percentage to this and you get 38.31 %. If you want to include the turn just multiply the 44/43/42 equation by another number, (41/47), which adds almost 9 percent to your figure for a total of 46.93 %.

That work? Whether you make a pair or not has little bearing on whether your opponent does, and I, like yourself, have no idea how to calculate this.
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