Suppose your opponent reraises all-in before the flop, and you know that she would do this with 90% probability if she had aa, kk, or qq. if she had any suited connectors, she would do this with 20% probability. with any other hand, the probability that she would reraise all-in is 0. given that she reraises all-in, what is the probability that she has suited connectors?

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17-11-2017
Mathematics

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Suppose your opponent reraises all-in before the flop, and you know that she would do this with 90% probability if she had aa, kk, or qq. if she had any suited connectors, she would do this with 20% probability. with any other hand, the probability that she would reraise all-in is 0. given that she reraises all-in, what is the probability that she has suited connectors?

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nobillionaireNobley nobillionaireNobley · Answer 1 · 2017-11-28T07:53:19+01:00

Let "sc" mean suited connectors and "ai" mean all in.
[tex]P(sc) = \frac{4\times13}{ ^{52}C_2} \\ \\ =\frac{54}{1326}\approx3.922\%[/tex]
[tex]P(AA, KK, or\ QQ) = \frac{3\times{ ^4C_2}}{{ ^{52}C_2}} \\ \\ = \frac{3\times6}{1326} = \frac{18}{1326} \approx1.357\%[/tex]
So,
[tex]P(sc|ai)=\frac{P(ai|sc)P(sc)}{P(ai|sc)P(sc)+P(ai|AA,KK,orQQ)P(AA,KK,o QQ)} \\ \\ =\frac{20\%\times3.922\%}{20\%\times3.922\%+90\%\times1.357\%}= \frac{0.7844\%}{0.7844\%+1.2213\%} = \frac{0.7844\%}{2.0057\%} =39.1\%[/tex]