Anyone know...

[DonkBox]

How you go about calculating the odds that pocket jacks, pocket queens, pocket kings and pocket aces will all be dealt out in the same hand?

I have a starting point the odds of getting dealt AA, KK, QQ or JJ pre-flop are 1 in 56.

But i'm buggered if i've got the maths brain to work it out. anyone point me in the direction of a program that has?

[FirePhil]

I make it 0.005% on a 9 handed table.

I did:

(16/52)*(3/51)*9 = .1629 (Chance of any player getting any of AA, KK, QQ, JJ)
(12/50)*(3/49)*8 = .1176 (Chance of another player getting any of one of the other 3)
(8/48 )*(3/47)*7 = .0745 (Chance of another player getting any of one of the other 2)
(4/46)*(3/45)*6 = .0348 (Chance of another player getting the 4th one)

Multiply those numbers together to get 0.005%. I don't know if this is right but it seems to make sense to me.

[Hedonist]

I calculate that the odds of this happening on a 4 seat table are 1 in 60,693,646
On a 10 seater table the odds of these 4 hands being dealt are 1 in 274,632.

This is based on the odds of being dealt AA as being 1 in 221 so the odds of having one of the top 4 pairs are a quarter of that 1 in 55.25
For the second pair there are only 50 cards so the odds are 1 in 204/3 which is 1 in 68
The third pair is 1 in 188/2 (2 possible pairs remaining) which is 1 in 94
The last pair has on 46 cards but only one pair which is 1 in 172.5

[ratboy01]

you are too clever you should be out saving the world or something

[FirePhil]

Those odds for each pair are right but how do you end up with 1 in 274,632?

[FirePhil]

WARNING: Don't click this link if the maths may destroy your brain, it's pretty nuts.

Basically it says this:
.0000768 chance that a player holding J-J is facing at least one pocket pair of each of the ranks of queens, kings and aces at a 10 handed table.

Working it out for 10 handed the way I did it gives .00008266, which seems about right as that only includes there being exactly one of each higher pair rather than at least one. That is 1 in 12,098.

[neildowse]

Basically, You just need to know the probability of one person holding aces, one with kings, one qith queens and one with jacks, and then multiply by the number of permutations.

The probability of it happening is:

(probability aces) X (probability kings) x (probability queens) x (probability jacks)

So this is (4/52*3/51)*(4/50*3/49)*(4/48*3/47)*(4/46*3/45)
= 4/(13*17*50*49*47*46*5)
= 1/ 1463268625

Then the number of permutations depends on the number of people at the table, for example it is 210 on a 10 seat table.

So for a 4 seat table the answer is as above and for other sizes as follows:

5 seats : 1/ 292653725
6 seats: 1/ 97551242
7 seats: 1/ 41807675
8 seats: 1/ 20903838
9 seats: 1/ 11613243
10 seats: 1/ 6967946

All-in all, the chance of it happening on a 9 seat table is approaching your odds of winning the lottery, but then, you don't play the lottery several hundred times a night.

[neildowse]

Thinking about it again, thats the odds of them being dealt in that order, so you have to multipy each answer by 24, meaning you are now far less likely to win the lottery, disappointing i must say.

[Hedonist]

Thinking about it again, thats the odds of them being dealt in that order, so you have to multipy each answer by 24, meaning you are now far less likely to win the lottery, disappointing i must say.

To get the odds of them being dealt in any order you have to DIVIDE by 24.

This brings your answer to almost the same as mine!

[Haggis]

My brain is now hurting.........


But seeing how you all seem to love this kind of thing......

In a live league game last week, i am big blind and serious short stack.

Five handed, I get dealt JJ, two players go all in in front of me but seeing as i have only 1.5BB left I decided to follow and the out come is.......

Player 1: KK

Player 2: QQ

And as no-one hit the K's took the pot.

So my little Math monkeys....What are the odds of that happening?

Ps. I hate JJ's, give me 72 anytime (this would have won the hand btw!)

PPs. really should have heeded Phils warning!