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How do these odds make sense?

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  • How do these odds make sense?

    Hero has Ac Jd. Villain has 7s 3s. Flop is 6s Ks 2h. Software says Villain is ahead, 54.5% to 45.5. Why? If a flush draw has approximately 36% chance to hit, doesn't that mean there is a 64% chance it doesn't hit? And if it doesn't hit hero should win. True, villain has additional outs if he pairs, but hero has those same outs, with higher pairs. They both have backdoor straights, but hero's is higher. The other outs are even, except that hero has a greater chance of winning when the flush misses. I'm confused.

  • #2
    Hi - as a fellow new member, found this an interesting question as it feels counter-intuitive to me too.

    I can't run the numbers at present, but been trying to think it through.

    Hero's hand is obv ahead in that if the hand ends there they have won - so if the turn and river are blanks for both players they win. However, how likely is this? If either player improves to one pair they win (hero is already winning) - there are 12 outs to hit one pair across the two players, so that's around 48%. Villain obv has half of these, so their outs mean they have close to a 25% chance to hit one pair and they win - assuming that the other card doesn't give hero a pair.

    Would the odds of that be about .25 * .25? , ie overall there is a 6% chance that both players improve to one pair (not sure if I have the maths right). Certainly, if villain does get to one pair, it is unlikely hero also does.

    On top of this you have the flush, which is 36% as you say, and then assorted less likely improvements across both hands.

    So villain would be - very roughly - 36% + 25% - 6% which would come to 55%. I've ignored the less likely draws to straights etc as I imagine they only move it by a % or two.

    By all means rip my maths to shreds - I am also here to learn.


    • #3
      Hi Bruce

      I think what you're missing is that a lot of Hero's outs are actually dead.

      Ace of spades gives the hero top pair but gives the villain a flush etc so the chance of villain improving is far higher than hero.

      Villain has roughly 16 outs (assuming 1 extra out for backdoor straight draw) so is going to improve to a better hand approximately 56% of the time by my calculation.

      Also, a lot of the time when the hero does improve, the villain is also going to improve to a better hand, for example turn is Jc and river is Ts.

      I must admit that I woould never have thought off the top of my head that villain would actually be ahead here so a good learning opportunity.