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Re: Odds of open-ended straight improving
First of all, 41% is incorrect, indeed.
Although your calculations are mostly incorrect, you have reached a result pretty close to real odds. Your event "hitting on river" is ambiguously defined. You should consider "hitting on river if not hit on turn". So, even if applied formula is correct, the entire calculation becomes incorrect. Here is the correct result, obtained by using combinations: Let C and D be the expected cards (as value). 4 outs each. The favorable combinations of turn+river cards are: (Cx) - 4*(47-8) (Dx) - 4*(47-8) (CD) - 4*4 (CC) - C(4,2) (DD) - C(4,2) (x different from C and D) Totally, we have 340 favorable combinations from C(47,2)=1081 possible, so the odds of hitting the straight by river are 31.45%. |
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