5CD - Low boat.

[MarkGritter]

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B) since you have a boat it will be harder for your opponent to also hold one because he can't make a boat using deuces and is unlikely to make one using eights.



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I'm sure my thinking is flawed, but I'm not sure if this is accurate. Doesn't my having a boat mean that there are more cards of the same rank in the deck? For example, if I had 2222x, wouldn't my opponents chance of getting 4 of a kind actually go up (albeit very small) as I am 'removing' a rank from the deck?
So in this case I'm partially removing ranks, thus making a boat more likely??

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I'm not doing so hot on algebra lately, but this should not be too hard... Just count the number of full houses.

In a full 52-card deck there are 13*12 different full houses. Each one has 4C3 = 4 possible trips and 4C2 = 6 possible pairs. So that's 13*12*4*6 = 3744 full houses out of the total 52C5 = 2598960 distinct hands. Call it .144%.

With your 3 deuces and 2 eights removed now there are only 11 possible trips. There are still eleven possible pairs, but only one way to form 88 instead of 6. So we have 11*4*(10*6+1*1) = 2684 full houses out of 47 cards remaining. 2684 / 47C5 = .175%.

So, yes, you having a boat makes the chance of somebody else having a boat go up slightly.

The same is probably true of having a flush... let's see.

In the 52-card deck there are 4 suits, each of which can form 13C5 flushes. 4*1287 = 5148 hands out of 52C5 = .198%.

After removing five suited cards three of the suits can still form 13C5 flushes, while one can only form 8C5 flushes. 3*13C5 + 8C5 = 3917 hands out of 47C5 = .255%.