Straight
Join Date: Dec 2004
Posts: 236
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Originally Posted by DaNutsInYoEye
Where did you get these? I only glanced at a few and they were wrong...
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All of these numbers were confirmed from external sources save the numbers of flopping 8 out straight draws. If you feel a number is incorrect, I invite you to point it out and we can walk through the math and the references. Errors are always possible. But, save for the 8 out straight draws, it would mean that lots of sources are making the same error or I mistyped an entry.
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Originally Posted by dwarfman
They look wrong to me.
Odds of flopping one pair on unpaired hole cards is 41%, I am sure.
I'm certain that it is over 27%.
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The 41% number is a common misconception. It is true that if your hole cards are unpaired then you have a 40.408% chance of having a pair after the flop. But that percentage includes pairs from the board that completely miss your hole cards. This is why I tried to be explicit and describe that you have a 26.939% chance of hitting a pair by pairing one of your hole cards. Again, while the numbers are easy to compute and available from multiple sources, I will quote Ken Warren from his guide:
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Originally Posted by Winner's Guide to Texas Hold'em Poker, Ken Warren
When your hand is not a pair, you will flop one pair 40.408% of the time. However, 1/3 of these pairs will be on the board and not pair one of your hole cards. That means you will flop one of your hole cards 26.939% of the time.
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To see where the numbers come from, you can compute them fairly quickly. You are looking for 6 possible cards (the 3 of each of your hole cards), then you are looking for a card that is not one of your hole cards (44 remaining), then you are looking for a card that is not one of your hole cards AND is not a match to the card that just flopped which would give you two pair using the board. Then there are three ways for that to fall (think of it as your pair falling on the first, second, or third card of the flop). All divided by the number of possible cards in each case, 50 * 49 * 48. The comes to ((6 * 44 * 40) / ( 50 * 49 * 48 )) * 3 which equals 26.939%.
Most of these numbers I computed myself and then confirmed from various sources. The primary source was Winner's Guide To Texas Hold'em Poker, Ken Warren. Though the numbers were available in multiple locations and are fairly easy to compute. The 8 out straight draws are tricky due to double barrelled gut shots. I think I found all the possible ways of making them for the various connectors but I may have missed some. I invite discussion.
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