Nice review, but an error

On Amazon.com, a review was written by Mr. Andrew G. Moore dated July 23, 2005. Amazon link

It was a nice review and he gave Weighing the Odds in Hold'em Poker 5 stars out of 5. I really appreciate that and Mr. Moore, if you are reading this, thank you! However, there is one error in his review that I wanted to point out. Near the end of his review, he writes:

"The only possible mistake that I've seen in the book is on page 87, when Yao says that if you have a four-flush, the odds of hitting the fifth card are 9/47 on the turn and 9/46 on the river = 35 % or 16 outs. I calculate 9/47 + 9/46 = 38.71 or 18 outs. He states the 35% figure again later in the book, so maybe he is doing something statisically that I don't understand. Two other sources quote the figure as 39%.


I don't know where his other two sources are, but they are wrong and I am right. If you have a four-flush on the Flop, the odds of you hitting the Flush on the Turn is 9/47 (9 flush cards left, 47 unknown cards left). If you do not hit the Flush on the Turn, which you won't 38/47 of the time, then the odds on the River is 9/46 (now only 46 unknonw cards for the River). So the total probability of hitting the flush is the probablity of hitting it on the Turn, and the probability of hitting it on the River given you haven't hit it on the Turn. The math:

9/47 + (38/47 x 9/46) = 34.97% or 35% after rounding.

9/47 = Probability of hitting the flush on the Turn
38/47 = Probability of not hitting the flush on the Turn
9/46 = Probability of hitting the flush on the River given you don't hit it on the Turn.

It would be nice if this error was corrected on Amazon but I'm not sure their reviews can be edited.