chances your opponent won't have a pair on the flop or turn

[Wynton]

Say you're headsup on the flop, and fail to flop a pair. And say the flop itself does not contain a pair. What would the odds be that our opponent neither has a pocket pair nor has flopped a pair?

And what would those odds be if you still fail to make a pair on the turn?

[warlockjd]

Disclaimer: I am a probability ultranoob and will start answering many questions including this one (many incorrectly) in the hopes of improving. My goal is a super in-depth excel workbook with detailed preflop and postflop analyses to help me improve in superaggressive NL SH games.)

Opponent starts with pair (1/52 + 3/51) = 7.805%

Opponent does not start with pair = 1 - 7.805% = 92.195%

-Opponent pairs his nonpaired combination = 6/50 + 6/49 + 6/48 = 36.745 %

Opponent has a pocket pair or has flopped a pair 7.805% + (92.195% * 36.745%) = 41.682%


I hope this much is right, but do not know how to combine this with the assumptions that the flop contains no pair and/or that I fail to flop a pair.

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.

Why do you calculate 'opponent starts with pair' as ( 1/52 + 3/51 )? I don't get the 1/52 part, shouldn't it just be 3/51? It shouldn't matter what the first card delt is, the odds of pairing the second card with the first card should be 3/51, right?

Damn, I was out-posted.