View Full Version : Starting hand probabilities

09-22-2005, 10:50 PM
In the probability tables in Brunson's Super System (page 572), it shows the probability of being dealt 2 aces is 0.45% with odds against as 220:1. 2 kings through 2 jacks 1.36% and 72.7:1 etc. (actually, I have another source somewhere that shows kings at 110:1 and Queens at 55:1 as I recall). My question is this: Why are the odds of getting two aces different from getting two kings (or any other pair) different?

The table does show, towards the bottom that any pair is 16:1 against- this makes sense since there are 4*4 possibilities, but what's with the 220:1? Thanks--

09-23-2005, 12:47 AM
Umm this is the way I think about getting dealt a pair of anything, and then more specifically one unique pair.

For any pair...

First card is arbitrary.
Second card needs to match first card. (3 remaining in a deck of 51)
odds are 3/51 = 1/17 or 16:1 against to be dealt a matching card (any pair)

Since there are 13 possible pairs, the odds of getting dealt a specific pair would be...

(1/13)*(1/17) = 1/221 or 220:1 against.

Therefore the chance of getting dealt ANY specific pair is 1 in 221.

09-23-2005, 03:17 AM
I'm guessing you misread that and the real numbers are Kings or better, and then Queens or better...

Each individual pair is the same at 220:1.