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PLO Advanced Math

HI all. First post. I am a PLO pro that is starting from the beginning of the vids to clean up my game. I have a math question that is in regards to a vid that was made in 2014. I thought the thread might be better here than such an old vid. It was Intro to PLO by Don Ding. On hand #3, the board is AsKsJd and one player flops the nuts while another has top set and another has the NFD. Don states that on this flop, the player with the nut straight on the flop will still have the nuts about 50% of the time. I was wondering what is the math to calculate this. I am not looking for the direct answer for this situation but the calculation to all, so that I can do the math on every flop. I think this would be a good matrix to have memorized when calculating bet sizes and pot odds.
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Comments

  • ChaseChase Posts: 182Subscriber
    Welcome to CLP!

    I'm a bit confused about your question. Are you sure you didn't misunderstand Don?

    It seems like asking how often a given hand will hold up is the same question as asking how much "raw"/"hot-and-cold"/"showdown" equity the hand has.

    The equities in PPT are something like:
    board: AsKsJd
    Hand Equity Wins Ties
    QdTc*h*h 33.68% 197,184 9,851
    AA 38.78% 227,757 9,851
    Qs9s8c7c 27.53% 165,208 0

    So I'm not sure how the straight is supposed to hold up 50% of the runouts...
    Seeing only the turn card, top set has 7 outs, and the FD has 8 (we cant count J :s: twice) so the straight has to fade a combined 15 outs on the turn. So for just the turn the math for how often the straight holds is: (22/37 = 0.59)
    Now let's say the turn is the 2
    The two drawing players now have 17 combined outs (10 for the set + 7 for the FD).
    So at this point the straight will hold:
    (19/36 = 0.527)
    So starting on the flop, the straight will hold up (0.59) x (0.527) = 0.31 = 31% of the time, which is close to the result from PPT.
  • NLTOPLOPRONLTOPLOPRO Posts: 17Subscriber
    Chase wrote: »
    Welcome to CLP!

    I'm a bit confused about your question. Are you sure you didn't misunderstand Don?

    I will put down 3 examples to help.

    On a Ax 9x 3x rainbow board where Hero holds AAxx, what % of the time will Hero have the nuts on the river?

    On a As Ks Jd board where Hero holds Qx Tx XX, what % of the time will Hero have the nuts on the river?

    On a Jx Tx 7x board where Hero holds 8x9x2x3x, what % of the time will Hero have the nuts on the river?

    All of these would be independent of any Villain in the hand. Just looking to find out how often Hero will hold the nuts when the river is done. I would guess that in the first example, the odds of AxAx remaining the nuts is very low but I would like to be able to quantify that.

  • ChaseChase Posts: 182Subscriber
    I understand your question. I'm not sure there is much value in solving for a quantitative answer. Usually we can estimate a qualitative answer, which seems sufficient. For example, with the Jx Tx 7x flop the answer is: almost always. With AKJ or A93r, it's probably around one-third of the time.
  • JoneseyJonesey Posts: 151Subscriber
    You want to know how often hero has the nuts??? I’m not sure you mean this. For example, with top set the hero doesn’t have the nuts if a lower card pairs the board (for the potential of quads) but beats all flushes and straights. So are you asking how often one hand beats another hand? Or are you asking how often the board bricks out and makes no flushes, straights, or boats/quads? And if so, I don’t get why I want those numbers instead of knowing my chances to win.
  • JoneseyJonesey Posts: 151Subscriber
    edited January 24
    In terms of calculations I use Lyle Herman’s kill card calculations. I’ll try to attach it here. You’ll have to read up on it to understand how it works, but it’s my way of calculating.
  • JoneseyJonesey Posts: 151Subscriber
    Here it is
    Thanked by 1LatvianMissile
  • NLTOPLOPRONLTOPLOPRO Posts: 17Subscriber
    Jonesey wrote: »
    And if so, I don’t get why I want those numbers instead of knowing my chances to win.
    It is a strange thing to want to know. I suppose it could be used in conjunction of how aggressive we should be with certain hands. Maybe it could quantify how aggressive we should be. We all learn that playing the flopped straight without backup can be a very expensive proposition. This is because a straight can be very vulnerable. Top set on a dry board, on the other hand, is much less vulnerable. I am just seeing if there is a calculation to quantify this vulnerability. I have searched and can't find it anywhere.

    Simply, the question is this.

    What is the equation to determine what % the flopped best hand will be the best hand on the river?

    Sorry for all of the confusion and thanks again.

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