From Fox and Harker's NL book

[1969Cowboy]

From Chapter 7, p. 88 in Mastering No-Limit Hold'em by Russell Fox and Scott T. Harker

The authors state:

"Assume you know the button holds A [img]/images/graemlins/club.gif[/img]A [img]/images/graemlins/heart.gif[/img]. You have A [img]/images/graemlins/diamond.gif[/img]Q [img]/images/graemlins/diamond.gif[/img] in the small blind. The flop comes T [img]/images/graemlins/diamond.gif[/img]8 [img]/images/graemlins/diamond.gif[/img]4 [img]/images/graemlins/heart.gif[/img]. Assuming you didn't know your opponent's cards, you would have a 35% chance of making the flush. With this "divine" knowledge, you now have a 36.4% chance of making the flush. Your chances of winning the hand are a bit higher, because of running cards, at 38.2%."

My questions: Aren't the odds of making a flush 4.2 to 1? (52-5=47 cards left. 9 "good cards" and 38 "bad cards". 38/9 = 4.2). How were the percentages derived? Why did the percent chance of making the flush increase when you knew your opponents hole cards? You had 9 outs to make the flush before and after you knew what your opponent's hole cards were, right? Nothing changed. I don't understand that point.

Then, in a footnote on page 89 the authors state "the odds of making your hand are 2.6 to 1" Where did that come from? How was that calculated and why is it not 4.2 to 1?

Thank you for your explanations.

Cowboy

[sopoRific]

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Aren't the odds of making a flush 4.2 to 1? (52-5=47 cards left. 9 "good cards" and 38 "bad cards". 38/9 = 4.2). How were the percentages derived?

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That's only the odds that your flush will come in on the turn. You'll make a flush on the turn 9 times out of 48. In addition, on the 37 of the 48 turns you miss your flush, you'll hit it on the river 9 times out of 47. So the probability of making a flush is (9/48) + (37/48) * (9/47) = .350, or the odds would be (1 / .350) - 1 = 1.86:1.

[ QUOTE ]
Why did the percent chance of making the flush increase when you knew your opponents hole cards? You had 9 outs to make the flush before and after you knew what your opponent's hole cards were, right? Nothing changed. I don't understand that point.

[/ QUOTE ]

Something did change. We now know 2 more cards that cannot come on the turn and river. With only 45 unknown cards, the probability that you will make your flush is now (9/45) + (35/44) * (9/44) = .364

[ QUOTE ]
Then, in a footnote on page 89 the authors state "the odds of making your hand are 2.6 to 1" Where did that come from? How was that calculated and why is it not 4.2 to 1?

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I'm not sure.

I hope this helps.