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  1. #1
    Fish
    Join Date
    Jan 2006
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    59

    Default Math for two overcards vs pockets heads up

    I've been reading in the probabilities section and I'm looking at the problem of the pocket pair vs. over cards.

    Maybe I shouldn't admit this but when I get big slick in a late position, especially with limpers and maybe even with a small raise on a generally passive table, I try to buy or get heads up before the flop. Now I don't really worry about the straight of flush preflop, I kinda figure those odds at 50-50, it either happens or it doesn't. (nod to Beavis's "too many possibilities)

    I find myself trying to figure the percentage chance of hitting on of those 6 outs that are left over the course of the entire board if someone calls and this is where I'm at...
    _________________________________________

    If after the flop


    1 - (47-x)/47*(46-x(/46) = % chance of hitting either the turn or river

    Then before the flop

    1 - (50-x)/50*(49-x)/49*(48-x)/48*(47-x)/47*(46-x)/46 = % chance of hitting one of the five board cards
    _____________________________________________

    See, I'm not really working on an exact percentage as a rule of thumb and I have this horrible obsession with proving things to myself, anyway, after reading and figuring and pointing and scratching and scribbling away my whole Friday night at this I thought I'd post it and see what anybody else had to say about it.

    It's something I'm trying to figure for a rough base to work from and modify on the fly with the extra information I have that hand, suited overcards would pick up a little edge with the flush possibility, if 7 out of nine people had been in before the push I'd assume one or a couple or more of my outs were/are in their hands and so it had to be adjusted accordingly. That sort of thing.

    anyway there it is for what it's worth.
    Last edited by thinTim; 02-11-2006 at 03:23 AM. Reason: 6 outs not 4, why the hell I can't keep that straight I do not know

  2. #2
    Fish
    Join Date
    Jan 2006
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    59

    Default

    Oh and I apologize for the headache. If it makes anyoone feel better it's given me one too.

  3. #3
    Check Raiser Aces-o-8s's Avatar
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    Sep 2005
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    778

    Default

    try www.homepokergames.com/odds.php

    No headaches -

  4. #4
    PokerForums God Marm's Avatar
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    Oct 2004
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    Cleveland
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    Default

    Better yet: http://www.pokerforums.org/probabilities

    But through all of that..... I'm not sure what you want? there is an odds chart posted somewhere on here, and I posted one (do a search) that is an Xcel sheet that actually shows the math in the formulas in the background.
    Marm is back, maybe. Been off for 3 years. Rusty as Hell.

    Luck is a Residue of Design.

  5. #5
    Fish
    Join Date
    Oct 2005
    Location
    Norman, OK
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    90

    Default

    I think he's asking what's the chance you'll hit either hole card on the community.

    I'll roughly estimate it to be 60%. 6 outs, 5 cards, roughly 2% per card.

  6. #6
    (Formerly Steve-O) Steve Ruddock's Avatar
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    Dec 2004
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    Default

    the easiest way to figure it out is the chance you will not hit, turns multiple possibilities into 1
    Read my musings on poker and life at Online Poker Examiner, Poker Examiner, PokerNewsBoy.com, and My Poker Blog

  7. #7
    Check Raiser ypsieast's Avatar
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    Default

    Holding AK:
    probability that A or K hits board (5 cards) = 49%
    but the probability that pp will hit his set (5 cards) is 20%
    AK has slight edge for the flush (if suited - or if suit is shared with pp)
    AK has slight edge to make a str8.
    AK has edge if board pairs twice with overcards to pocket pair.

    Your formula looks right to me.

    If you are obsessed with the math/statistices, check out this website. Good reading if you are a stats geek.
    http://www.math.sfu.ca/~alspach/pokerdigest.html

  8. #8
    (Formerly Steve-O) Steve Ruddock's Avatar
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    out of curiousity, why not just run it through pokerstove or some other sim and memorize the percentages? Makes it much easier
    Read my musings on poker and life at Online Poker Examiner, Poker Examiner, PokerNewsBoy.com, and My Poker Blog

  9. #9
    Fish
    Join Date
    Jan 2006
    Posts
    59

    Default

    Quote Originally Posted by Steve-O
    out of curiousity, why not just run it through pokerstove or some other sim and memorize the percentages? Makes it much easier

    Lol, sorry guys, wsn't really asking a question. I had just sat and figured on it until I had the formulas figured out and was posting them for general consumption by anyone who was interested. It was all just the result of proving to myself how to do it.

    Yeah, A LOT easier to just memorize the results from someone else's figures or charts, I was just proving it to myself. Unfortunately, by the time I had done so my brain was pretty well fried I guess I didn't compose my post very well, sorry.

    Thanks for the replies guys.

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