[Buzz]

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Anybody ever calculate the probability of flopping 0,1,2 or 3 low cards (A-8)? I'm reading Cappelletti's O/8B book and he says that those probabilities, when you hold A24Q, are 5.6%, 33.1%, 46% and 15.3%.

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Domester - We don't exactly want the probability of flopping 0, 1, 2, or 3 low <font color="white">_</font>cards. Of more interest is the probability of flopping 0, 1, 2, or 3 low <font color="white">_</font>ranks

The answer to the number of low cards is very easy:
• 0 low cards on flop: P = 0.0560
• 1 low card on flop: P = 0.2867
• 2 low cards on flop: P = 0.4460
• 3 low cards on flop: P = 0.2113

But this is misleading because when there are two low cards on the flop, the two low cards could be a pair, together amounting to only one rank of low card.
Similarly when there are three low cards on the flop we could have a pair or trips.

The answer to the number of low ranks is more tedious:
• 0 different ranked low cards on flop: P = 969/17296 = 0.0560
• 1 rank of low cards on flop: P = 5723/17296 = 0.3309
• 2 different ranks of low cards on flop: P = 7957/17296 = 0.4600
• 3 different ranks of low cards on flop: P = 2647/17296 = 0.1530

Those are evidently the numbers Cappelletti is using.

But, since you’ve brought it up, aren’t we really interested in knowing when we have two or three low cards on the flop that are of benefit to us?

For example, there are some flops with three different ranks of low cards that don’t make a low for us when we hold A24Q. (eg. 2-4-8).
And there are other flops three different ranks of low cards that make a low, but not the nut low. (eg. 2-7-8).

Does he later somehow make a correction for this?

Buzz