1

I've been looking for the answer to this for a while. I have my lovely Ace-King and I missed the flop. The flop is 9 5 2 rainbow. For several reasons, I put my opponent for a top pair (9 - kicker) or a pocket pair in hand (Jacks or eights...etc.). I know that in order for me to win (in showdown), I'll need to hit the board on the turn or more ironically on the river. What's the percentage for that to happen (hitting A or K on turn or river)? How often do pro players generally draw for this?

  • Please unaccept this accepted answer. Lee Daniel Crocker is correct. – Chris Farmer Oct 15 '15 at 4:40
4

Sometimes during play you want a quicker method that isn't 100% but gives you very close percentages.

The rule of 2 and 4.

If you have 2 cards left to reveal (ie the turn & river) then you multiply your outs by 4.

If you have 1 cards left to reveal (ie just the river) then you multiply your outs by 2.

So in your example, 6 outs with 2 chances left = about 24%.
After the turn your chances are about 12%.

  • 1
    That's pretty close to the actual number of 22.25%. – Lee Daniel Crocker Oct 29 '15 at 21:16
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When facing an "at least one of" problem, you can't just add probabilities. You have to calculate the probability of missing everything, then subtract from one.

Assuming 47 unknown cards, 6 of which are outs, the exact probability of missing both the turn and river is 41/47 * 41/46, or 1681/2162, so the probability of hitting either or both the turn and river is 481/2162, or about 22.25%

  • You're absolutely right. I got what looked like a reasonable answer and didn't really check it afterward. I would happily delete my answer but it won't let me given that it's marked as accepted. – Chris Farmer Oct 15 '15 at 4:39
  • The mods helpfully deleted my previous answer. – Chris Farmer Oct 15 '15 at 20:45

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