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Please Check My EV Math

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  • Please Check My EV Math

    OK, I recently encountered the following scenario and wanted to test my grasp of EV:

    Player A: QhJh - CO
    Player B: Kc7h - SB
    Player C: ???? - BB

    Pot: 450
    Board: 5s 2d 3h 7d

    Player B bets 225 - Pot 675
    Player C calls with ?? - Pot 900
    Player A calls with QhJh (maximum of .13636 equity given all known information)

    So, player A calls and loses 225: 1 - 0.13636 = 86.364% of the time. This is an EV of -194.32.

    However, player A expects that if he hits one of his 6 outs, he will gain an additional 600 chips (approx 1/2 pot bet). So, the other 13.636% of the time he will gain the 900 in the pot on the turn plus 600 more from a river bet = 1500 chips. This works out to an EV of 204.54.

    Assuming all my math above is correct, this is a +EV play, as 204.54 - 194.32 = 10.22.

    Am I missing anything?

    4 Time Bracelet Winner

  • #2
    Hi Jcrondps!

    How tight or loose were the two opps playing? I don't want to use just the cards that they had when looking at the odds, I need to consider their entire range.

    I'll be happy to go thru all the numbers, etc with you... but need players range info in order to do it correctly, as that is what I need to put into pokerstove in order to get the hand equities.

    John (JWK24)

    6 Time Bracelet Winner


    • #3
      Hi jcrondps.
      unfortunately, your entire math set is flawed because the number you start with, 13.36%, is not the true equity of the QJs hand here. That number is the chance QJ has to spike a live out with 1 to come to beat K7o. Because there is an unknown hand still in the mix, that simple chance does not equal player A's equity.

      example: if player C holds a made straight, QJ is drawing dead. He has 0% equity.

      The weighted combination of the likelihood of ALL possible hands that player C might have must be combined to arrive at an estimate of QJ's equity here. This is what JWK means by range info is needed.

      Additionally, you really need info on what amount you might be able to extract if you do make a better hand, and the chance you might have to get both opponent's to fold to a given bet size by you in order to determine your equity with QJs. Afterall, if you bet or raise you might win without making the best hand, and you'd really like to know what you may have to risk versus what you might win if you do make the best hand or try to bluff.
      Double Bracelet Winner



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