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Math Help - The probability of flopping a set in holdem

  1. #1
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    The probability of flopping a set in holdem

    Hi

    I was just trying to work out the probability of flopping a set on the flop in texas holdem but don't know if its exactly. I'm assuming only a set and not four of a kind.

    My workings:

    P(Flopping a Set)=[(2/50)*(48/49)*(47/48)]+[(48/50)*(2/49)*(47/48)]+[(48/50)*(47/49)*(2/48)]

    = 0.11510204 or about odds of 8.688:1

    Does that seem correct?
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  2. #2
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    Quote Originally Posted by fobster View Post
    Hi

    I was just trying to work out the probability of flopping a set on the flop in texas holdem but don't know if its exactly. I'm assuming only a set and not four of a kind.

    My workings:

    P(Flopping a Set)=[(2/50)*(48/49)*(47/48)]+[(48/50)*(2/49)*(47/48)]+[(48/50)*(47/49)*(2/48)]

    = 0.11510204 or about odds of 8.688:1

    Does that seem correct?
    You mean 3 cards in consecutive order?

    I do not think there is a numerical answer to your question. I might depend on how many players are in the game.

    However, I can compute it for you assuming you deal those first.
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  3. #3
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    Quote Originally Posted by fobster View Post
    Hi

    I was just trying to work out the probability of flopping a set on the flop in texas holdem but don't know if its exactly. I'm assuming only a set and not four of a kind.

    My workings:

    P(Flopping a Set)=[(2/50)*(48/49)*(47/48)]+[(48/50)*(2/49)*(47/48)]+[(48/50)*(47/49)*(2/48)]

    = 0.11510204 or about odds of 8.688:1

    Does that seem correct?
    Looks good to me. You assumed you have a pair and calculated the probability of catching exactly one of the two remaining cards of the pair in the 3 cards of the flop.
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  4. #4
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    Do you mean everyone playing flops a set?

    Wouldnt it be more interesting to see the probability of flopping a set given a pocket pair?

    *Ooops I get it thats exactly what you did*
    Last edited by MathGuru; December 19th 2006 at 12:45 PM.
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  5. #5
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    what about after the river?

    What about hiting a set after the final fifth card?

    In other words if I go all in preflop with a pocket pair . . . what are my chances of hitting my set after all cards are on the table?
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  6. #6
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    Quote Originally Posted by Shmuel View Post
    What about flopping a set after the final fifth card?

    In other words if I go all in preflop with a pocket pair . . . what are my chances of hitting my set?
    is a set three-of-a-kind or three in a row?
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  7. #7
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    A set is 3 of the same card (different suits)

    In texas hold'em each player is dealt 2 cards and then 5 community cards (first 3 (called flop) then 1 (called turn) then 1 (called river)). The best 5 card hand (each player makes a 5 card hand from 7 available cards) wins.
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    The probability of a Royal Flush is 1 in 50,000.
    But for some reason when I deal the cards it is much much much more common, hmm, did I do something wrong in my calculation .
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  9. #9
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    Quote Originally Posted by Shmuel View Post
    What about hiting a set after the final fifth card?

    In other words if I go all in preflop with a pocket pair . . . what are my chances of hitting my set after all cards are on the table?
    First, I assume no one else is playing.

    You have a pair, the odds that the third card isn't in the first four flips is: \frac{48}{50}\times\frac{47}{49}\times\frac{46}{48  }\times\frac{45}{47}=\frac{207}{245}
    (that number is according to excel)

    Then the odds of a match in the last flip is: \frac{2}{46}=\frac{1}{23}

    So you multiply that together to get: \frac{1}{23}\times\frac{207}{245}=\frac{9}{245}\ap  prox3.67\%

    So it's very low.

    But what if you're playing with n amount of people (including yourself, also this assumes they don't have your needed card). Then the equation would be:
    \frac{50-2n}{52-2n}\times\frac{49-2n}{51-2n}\times\frac{48-2n}{50-2n}\times\frac{47-2n}{49-2n}\times\frac{2}{48-2n}
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  10. #10
    Site Founder MathGuru's Avatar
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    I think Shmuel was asking what are the chances that any of the 5 community cards are the same as his 2 cards.

    Please calculate that.
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  11. #11
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    Quote Originally Posted by MathGuru View Post
    I think Shmuel was asking what are the chances that any of the 5 community cards are the same as his 2 cards.

    Please calculate that.
    It's the same odds (remember the commutative property)
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  12. #12
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    I dont think so.

    If the odds of hitting 3 of a kind with 3 community cards is 0.11510204
    then how could it be lower with 5 community cards?
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  13. #13
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    Quote Originally Posted by MathGuru View Post
    I dont think so.

    If the odds of hitting 3 of a kind with 3 community cards is 0.11510204
    then how could it be lower with 5 community cards?
    Maybe excel is doing something wrong...
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    Quote Originally Posted by fobster View Post
    Hi

    I was just trying to work out the probability of flopping a set on the flop in texas holdem but don't know if its exactly. I'm assuming only a set and not four of a kind.

    My workings:

    P(Flopping a Set)=[(2/50)*(48/49)*(47/48)]+[(48/50)*(2/49)*(47/48)]+[(48/50)*(47/49)*(2/48)]

    = 0.11510204 or about odds of 8.688:1

    Does that seem correct?
    Quote Originally Posted by Shmuel View Post
    What about hiting a set after the final fifth card?

    In other words if I go all in preflop with a pocket pair . . . what are my chances of hitting my set after all cards are on the table?
    Extending (and simplifying) fobster's calculation to 5 cards:

    P = 5 *\frac{2*48*47*46*45}{50*49*48*47*46} = .1837.
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  15. #15
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    How does other people playing lower your odds? You hold a pocket pair and are seeking one of two cards left in the starting deck to appear on the flop.
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