[kgr]

What is the probability with 5 card to start with a double pair?...Looking for an easy explation of the calculation.

Thanks,
Koen

[fred]

kgr, on May 16 2009, 07:41 PM, said:

What is the probability with 5 card to start with a double pair?...Looking for an easy explation of the calculation.

Thanks,
Koen

The way I would do it is to calculate A/B where:

A=number of 5-card hands that contain a double pair
B=number of 5-card hands

A=Cx44 where:

C=number of ways that 4 cards can form 2 pairs
44=the number of ways you can select a 5th card that is not of the same rank as the cards in either of the 2 pairs. I am assuming you don't want full houses to count.

C=(13x6)x(12x6)/2 where:

(13x6)=13 ways to select a card for the first pair and 6 possible pairs (SH, SD, SC, HD, HC, DC)
(12x6)=12 ways to select a card for the second pair and 6 possible pairs

You divide by 2 because there are 2 way you can select the 2 ranks (for example, if the 2 ranks are Ace and King you could select Ace-King or King-Ace).

B=52!/47!5!

So the answer is:

(44x13x6x12x6/2)/(52x51x50x49x48/120)

It is entirely possible I made a mistake in the above, but if the above is right and if I used my fancy calculator properly, the answer is about 4.75%

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[kgr]

Thank you!