Re: odd s calculations
Here is my own explanation .
Lets say that you have AhKh and the flop is 2h 6h Qs . You're up against two random hands .
Solution 1: The probability that you hit another heart on the turn is 9/47 . Pretty easy .
Solution 2 : This one is a bit more involving but the answer is the same . The deck contains 43 cards of which may or may not contain 9 hearts .
The probability that there are no hearts amongst the 4 cards and 9 hearts in the stock pile of 43 cards is 38c4/47c4*9/43
The probability there is only one heart amongst the 4 cards and 8 hearts amongst the 43 cards is 9*38c3/47c4 .
The probability there are two hearts amongst the 4 cards and 7 hearts amongst the 43 cards . 9c2*38c2/47c4
Likewise we have 9c3*38c1/47c4 and 9c4/47c4 for three hearts and 4 hearts respectively .
Now we use conditional probability to compute the probability that the turn is a heart given the additional information of your opponents cards .
1)38c4/47c4*9/43
2)9*38c3/47c4*8/43
3)9c2*38c2/47c4*7/43
4)9c3*38c1/47c4*6/43
5)9c4/47c4*5/43
Now if we add all these mutually exclusive events , we get the probability is equivalent to 9/47 !!
This is no coincidence .
Which method do you like better ?
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