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

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?

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

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.

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.

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

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.