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  1. #1
    Elite PokerOwned Member GottImHimmel's Avatar
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    Combinatorics expanded

    For this example, you shove in the SB

    You have AK, what are the odds your opponent has AA or KK?

    -There are 1225 possible combinations of hands your opponent could have

    -There are 3 possible combinations of AA and 3 of KK (6\1225x100)=.48%

    For this example, you raise in the Cutoff

    -You have A-10, what are the odds your opponent has, Pocket Pairs AA-10-10 and AK-AJ?

    There are 6 combos of AA and 10-10, and 18 combos of KK-JJ, There are 36 combos of AK-AJ

    - That gives us a total of 60 combos out of 1225 (60/1225x100)=4.9% FOR A SINGLE OPPONENT, since we're in the Cutoff, there are 3 opponents to act after us. We'll round 4.9% to 5%, multiply by 3=15% chance your in bad shape.

    -You have 10-10 in Middle Position

    What are the odds your opponent has JJ-AA?

    6 combos for each, so 6x4=24 out of 1225=About 2%. There are 5 opponents to act after you. So 10% chance.

    -------Remember, There are 16 unpaired combination of any starting hand, 12 unsuited amd 4 suited

    -------There are 6 combinations per paired hand.

    --------If you have a "blocker" or a card such as an ace in YOUR hand, that drops the combinations of your opponent down. 12 unpaired Combinations and 3 paired.

    ---------Try and memorize as much as you can.


    ---------quick note on drawing hands.

    example 1: the flop is 7-8-A Rainbow, you have AK, and are HU after the flop, what are the odds your opponent has an open-ended Straight draw?Gutshot?

    16 combos of 5-6
    16 combos of 9-10
    16 combos of 6-9
    16 combos of 6-10
    16 combos of 10-J
    16 combos of 5-9

    Now, things are a little different than before, we've already seen 5 out of the 52 cards. Thus, our oppponent has now a possible 1081 combinations total.

    So, 48/1081=4.44% for an open-ender

    If we include 48 more draws for gutoshot. . . 96\1081=About 9%

    Now, we included some hands like 5-9 for mathematical purposes, however, we could assume a player would not play this hand.

    So in conclusion, to use rounded numbers, on a 2 runner flop, there is about a 5% chance your opponent has an OESD, and 10% for gutshot and OE.

    If you were interested in finding out the odds of you being beat on the last example, you'd figure out the # of combos for Trips, and Two pair.

    ----i'll do more examples in a future thread. HAVE A GODO DAY EVERYONE!
    Last edited by GottImHimmel; 05-29-2012 at 10:39 AM.
    "Power is my mistress. I have worked too hard at her conquest to allow anyone to take her away from me." - Napoléon Bonaparte

  2. #2
    Elite PokerOwned Member MrPokerVerse's Avatar
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    Cool, thanks for posting. Looking forward to the next one.
    "When a man with money meets a man with experience, the man with experience leaves with money and the man with money leaves with experience." anonymous quote

  3. #3
    Experienced Member
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    good post thank you very much, I hope that I may have something to play poker at PokerStars! gl

  4. #4
    Elite PokerOwned Member GottImHimmel's Avatar
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    This is important stuff people! don't just throw it under the bus, please!
    "Power is my mistress. I have worked too hard at her conquest to allow anyone to take her away from me." - Napoléon Bonaparte

  5. #5
    Seasoned Veteren
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    This is good stuff. and its all fore free!! lol

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