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  • Probability Question

    Could someone please confirm or otherwise that the probability that overcards will flop when you hold the following pairs are:

    KK - 23%
    QQ - 41%
    JJ - 57%

    etc....

    If i'm wrong can u show me why please.

    Thanks

  • #2
    This was a bunch of flawed math (I never said I was a rocket scientist).

    Hazy

    Comment


    • #3
      Thanks for you time on this hazy. The way i worked out, say, the probability that overcards would flop for QQ was as follows:

      P(overcards will flop) = 1 - P(no overcards flop)
      = 1 - P(no ov/ca on first flop card)*P(no
      ov/ca on 2nd flop card)*P(no overcard
      on 3rd flop card)
      = 1 - (42/50)*(41/49)*(40/48)
      = 41%

      So we get different numbers... I'm too tired to concentrate (marathon WPO warmup that takes about 10 hours to knock the 16th person out) but when i wake up i'll have a good look at the way you do it. In particular, the thing you said about AK looks very interesting.

      Thanks again

      James

      Comment


      • #4
        That way works, and is more mathematically correct, but for figuring on the fly, and since the 3 cards are coming regardless, I use my method (it's a lot easier to divide once than three times in your head).

        Comment


        • #5
          Your absolutely right that its quicker hazy - but i've got to put my maths (notice the 's', we do more of it this side of the pond ) degree to some use... thanks for pointing out how the calcs change when you can confidently put someone on a hand like AK, hadn't really thought about that

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          • #6
            Re: Probability Question

            Originally posted by jb7643
            Could someone please confirm or otherwise that the probability that overcards will flop when you hold the following pairs are:

            KK - 23%
            QQ - 41%
            JJ - 57%

            etc....
            Absolutely right. (Always happy for a chance to put my degree in statistics to good use. )

            Chris

            Comment


            • #7
              yes, he is, I just like doing the simpler version because I don't have a degree in statistics (but I can do simple division in my head) and can't calculate 10/49*10/48*10/47 in my head - thought this would be the easiest way for someone to use it in a tourney (unless you are like some people I know, who have charts for these odds).

              Comment


              • #8
                Originally posted by thehazyone
                That way works, and is more mathematically correct, but for figuring on the fly, and since the 3 cards are coming regardless, I use my method (it's a lot easier to divide once than three times in your head).
                True, but it's also important when approximating to come up with a method that approximates the actual figure well. For example, in your calculation of probability of overcards to JJ, your approximation of 72% is way off the actual figure (57%), and will lead to a player making mistakes in calculating odds. It's not as easy as it seems to figure out odds of things hitting on the flop on the fly; that's why it's usually easier to memorize the odds for the most common situations.

                Also, I noticed that you had the odds of overcards to JJ on the entire board being over 100% 8O ...while this would confirm what I've always thought about JJ (namely, THEY NEVER WIN), I suspect this may not be quite accurate.

                Chris

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                • #9
                  Yes, you're right. It's really -

                  1 - (38/50)*(37/49)*(36/48)*(35/47)*(34/46) = 76.3%

                  still enough to warrant JJ as always being a loser LOL.

                  I knew my logic was flawed, but it's still easy for me to think of it as, OK there are 12 overcards to JJ, 5 cards are gonna come, so there is 5 opportunities for one of those 12 to hit, so that's 60, and there are 50 possible cards out there besides the 2 I have so by God that's 60/50 or 120%, yep I better be careful with these Jacks.

                  So I'll delete my math - because it is somewhat flawed (it's just how my mind works at a table on the fly).

                  Hazy

                  Comment


                  • #10
                    I won't tell you how my mind works at the table on the fly, very strange... Chris, i put another post in Rolf's forum. Could you have a look at it if you can please. I think you probably need to use the binomial theorem etc etc...

                    Comment


                    • #11
                      Dang, I missed hazy's original post.

                      I did a statistics module as part of my degree. I still can't do the calculations. Don't know whether that says more about me or the degree

                      Comment


                      • #12
                        I deleted it before you made fun of me.

                        Comment


                        • #13
                          Re: Probability Question

                          Originally posted by jb7643
                          Could someone please confirm or otherwise that the probability that overcards will flop when you hold the following pairs are:

                          KK - 23%
                          QQ - 41%
                          JJ - 57%
                          Now that you've got the statistics covered, let's look at the strategic implications. These numbers are precisely why it is so important that you make it three bets if you are holding a pair of queens and someone raises in front of you. Because queens, and of course jacks, are so vulnerable to overcards, three betting is a mandatory action to discourage anyone with a lone ace or king from entering the pot after you've acted.

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