#1
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Back door etc
2 q's 1 What is the probability of flopping a straight w/ JT or an open ender? 2. What is the probability of a backdoor stright if Q-7-2 or 9-2-3 flops to that same hand? I tried to calculate it but my answer didn't seem right as it just about equalled the prob of a backdoor flush. Thanx Joe |
#2
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Re: Back door etc
P(flopping a straight if you hold JT)= P( AKQ)+ P(KQ9) +P( Q98) +P(987)= 4(64)/ 50C3 P(making a straight if you hold JT and the board is Q-7-2)= P(AK) +P(K9) +P(98) = 3(16)/47C2 Note P(back door flush)= 10C2/47C2= 45/47C2 so it should be close. Ill do openended later (its more of a hassle). |
#3
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Re: Back door etc
what is C? I hope this isn't a retarded question. Joe |
#4
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C = choose
like... 50 choose 3... number of ways to choose 3 things from 50. formula is something like n!/k!(n-k)!... I believe... it's been a long time since I did any math and didn't just look up an answer. k is the number you are choosing, 3 in this case, and n is the total number... 50 in this case. ~D |
#5
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Re: C = choose
Right, or combinations. C(50,3) = 50!/[(47!)(3!)] = 50*49*48/3! That is, there are 50 ways to choose the first, 49 ways to choose the 2nd, and 48 ways to choose the 3rd, then we divide by 3! = 6 since there are 3! ways to get the same 3 in a different order. If we didn't divide by 3! we would have P(50,3) or "permutations of 50 things taken 3 at a time". |
#6
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open ended
P(openend w/a paired board)= P(KKQ) +P(QQK) +P( QQ 9) + P99Q) +P(998) +P(889) =48(3)/50C3 P(openended w/o a paired board)= P(KQ X (Xnot K, Q, A or 9)+ P(Q9X) +(P98X) =16(34) + 16(34) +16(34)/50C3= 48(34)/50C3 Finally we can also compute the probability of a double gutter ball. P(K97) +P(AQ8) =2(64)/50C3. SO P(openended or double gutter)=48(3) +37(48)+ 2(64) / 50C3= about 10% and also P(straight or openended)= 48(40)+2(64)+ 6(64)/ 50C3= 2304/ 19600=about 12%. Oh yeah pCk is the number of ways to pick k objects out of p of them. (Ex 50C3 is the number of flops if you hold 2 particular cards, so the number of flops is (50 49 48)/ 3!). Also P(A) means the probability of event A happening. |
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