odds question

[fishyak]

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The absence of aces might be the same problem as the absence of Kings?

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It is because the we have the same number of each, 4. And I think the math can be altered to search for 2 cards in a deck of 47 post flop.

[fishyak]

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I get about a 57% chance that a king was dealt to one of the eight people. Here is the calculation for the odds of no one getting dealt a king:

0.434 =(1-2/47)*(1-2/46)*(1-2/45)*(1-2/44)*(1-2/43)*(1-2/42)*(1-2/41)*(1-2/40)*(1-2/39)*(1-2/38)*(1-2/37)*(1-2/37)*(1-2/36)*(1-2/35)*(1-2/34)*(1-2/33)

Have I made an error somewhere?

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You were correct.

1 - c(45,16)/c(47,16) = 1 - 6.46626423E11/1.503232609E12 =~ 0.57

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Note that this answer makes irrelevant whether you face 4 limpers or 5 limpers. What matters is the number of total cards dealt out.

To try and sum up, the above number represents a worst case scenario of the liklihood of at least one King being out against you. Decreasing the number of limpers DOES NOT DECREASE this number.

At the "non-random" level, where folds come into play, there may be some math we could use that is beyond my skill level. As the number of limpers decrease, you can fudge and lower the odds of a king still being out against you. A King could have been folded PF. But I wouldn't take much off the first #.

This work for you Count & Outer?

[Hamlet]

Any calculation that includes the odds of your opponents folding a King are going to depend heavily on everyone's playing tendencies.

If you are playing in a reasonably tight aggressive game, I would expect limping hands that include Kings to be much less frequent than in a very loose passive game. TAGs don't limp many hands with Kings in them, they raise or fold them.

If your opponents are very loose and passive, though, you are going to have to expect more rag Kings to get limped.

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At the "non-random" level, where folds come into play, there may be some math we could use that is beyond my skill level. As the number of limpers decrease, you can fudge and lower the odds of a king still being out against you. A King could have been folded PF. But I wouldn't take much off the first #.

This work for you Count & Outer?

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[TheCount212]

This works fine for me, fish. Thanks very much for your diligent research and effort. Mighty neighborly of ya!