In a pub poker game recently a hand developed where 4 players got all in pre flop.

The first player showed 2 red aces. the second player showed 2 black kings. the third player showed 2 red kings and the last player showed 2 black aces.

This is an actual hand that happened in a live game.

What are the odds of this happening? the 2 pocket aces against the 2 pocket kings let alone everyone only having one suit colour?

Need to know how many players were dealt in.

The probability of one of those hands, say AcAd, is dealt to a player is 1/1326 = 0.075%. With four players, the probability of those four hands being dealt is to 4!*1/(1326*1225*1128*1035), virtually zero. With 9 players there are C(9,4) = 126 ways to select 4 players out of 9. Multiplying the near zero value by 126 still gives almost 0 probability. Doing the calculation, the odds against these four hands in a nine player game are about 125 million to 1. With less than 9 players, the odds against are even greater.

Still, one must remember, that with millions of hands played daily, events as rare as this are likely to happen every once in a while. It’s when it happens in a game that you are playing or watching that makes it seem so remarkable.

amazing.

Thanks

Minor point but what is the maths behind this please

edit Perhaps duh moment and it's C(9,4) but I don't know what that means!!

That's the combination function. It means from 9 things how many ways can you pick 4.

The combination function can be done in Excel as
=combin(number,pick)
and some calculators can do it.

To do it longhand you have to do factorials.
C(n,r) = n! / r!(n-r)!

So C(9,4) = 9! / 4!(5!)
which can then be reduced by dividing both sides by 5! leaving

(9*8*7*6) / (4*3*2*1) = 126

Notice that the numerator gives you the number of permutations in the last step (3024), and the denominator gives the permutations per combination (24). Permutations is all the ordered sets, and combinations is without regard for order (so 4-3-2-1 is the same as 1-2-3-4).

Wow - thanks. A lot more complicated than I realised. Just when you think you are getting a handle on things you realise theres even more depth to just about every level of the game.