A post for Ed Miller

[Mikey]

this is where I'm confused, I'm working these out myself now...... why am I using (8/47) x (8/46)..... shouldn't it be 8/47 x 7/46 ?

I don't understand.

[Ed Miller]

this is where I'm confused, I'm working these out myself now...... why am I using (8/47) x (8/46)..... shouldn't it be 8/47 x 7/46 ?

(8/47)(8/46) represents:

Eight cards on the turn give you an open-ended straight draw. Eight cards on the river complete that open-ended straight draw.

When two terms are summed, it indicates that they are mutually exclusive.

[Mikey]

thanks Ed, I got it now.

[Dooner]

If the turn is a Queen or a 8, you will have either four Kings and four 8's or four Queens and four 7's to make your backdoor straight. Which is 8 outs on the turn and 8 outs on the river.

If the turn is a King or a 7, you will have either four Queens or four 8's to make you backdoor straight. Which is 8 outs on the turn and 4 outs on the river.

This can then be broken down into:
(8/47)(8/46) + (8/47)(4/46) = 96/2162 = 4.4%

To break that into odds:
100 - 4.4 = 95.6 95.6/4.4 = 21.72 or 21.7 to 1 odds

If I did the calculations correctly, you will catch two runners to make a backdoor straight a little more than 4% of the time or 21.7 to 1 odds.

Hope this helped and I hope it is correct, it's awfully late and I'm a wee bit tired.

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[Dooner]

LOL, should have read farther down the thread before I did the calculations AGAIN for ya. Sorry about that did not know Ed had done them for you already.

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