question

[thechainsaw]

what is the probability of flopping top pair

if this is not specific enough, perhaps a rough estimate or for AKQ or J would help

thanks!

[AlienBoy]

???

If you hold what, for instance?

Or are you saying if you hold Ax (or Kx), that the flop is Ayy or Kyy?

If I am not mistaken, that varies CONSIDERABLY depending on the value of the cards you hold.

For instance, if you hold 67, you could flop 457 for top pair, but this would be a different probability of "top pair" since it is more likely for the flop to contain a higher card, than if you held QJ, and the flop was Q45.


If you hold 2 non-pair cards, the probability that you will flop one pair using one of your pocket cards is about 29%.

Which is why your trash holdings flop a pair a little less than every third time.

Which is also why that pair is mostly useless.



AB

[AaronBrown]

Assuming you don't hold a pair, 68% of the time you won't flop a pair at all and 3% of the time you'll flop better than a pair. 2% of the time you'll flop a pair, but there will be another pair on board.

The remaining 27% of the time, you'll flop exactly one pair on an unpaired board. Exactly one-third of that, 9%, you'll be top pair.

However, 9% is an average figure. Obviously you have a better chance with AK than 32. With AK if you flop a pair, it has to be top pair, so the chance is 27%. With 32, it can't be top pair, so it's 0%.

Let X and Y be the number of ranks smaller than your first and second cards. If you hold Q9, for example, there are 9 ranks smaller than Q (not counting 9 since you hold it) and 7 smaller than 9. Half the time you pair the queen and the chances are (9*8)/(11*10) = 72/110 that Q is the top pair. The other half of the time you pair the 9 and the chances are (7*6)/(11*10) that 9 is the top pair. On average, your chance is ((72+42)/2)/110 = 57/110 of having top pair. 29% x 57/100 = 14%.