JJ v. QQ, KK, and AA

[Filmore Slim]

I think this is the way to calculate the chances of someone else having a pocket kings, queens or aces when you have pocket jacks:

The chances of you hitting pair of jacks is 1/221

The total number of 2-card combinations with the remaining 50 cards is: 50 choose 2 or 50*49/2*1 = 1,225

There are 6 ways to have a pair of anything. Since there are 3 remaining ranks that can beat your pocket jacks (queens, kings, aces), the total number of pocket combinations that can beat you are: 6*3 = 18

So 18/1,225 is the chance that someone else will have either pocket queens, kings, or jacks when there are 50 cards left

The chance that you have pocket jacks while another person have a higher pair is therefore:

1/221 * 18/1,225 = 1/15,040 or .0065%

Anyway, it’s infinitesimal, even though it occurs somewhat frequently on party poker.

But this reinforces my belief that if you held pocket jacks, it doesn’t matter how the other person’s betting (given that you don't think they might somehow have made a draw or set or flopped a higher pair) you don’t have to worry about them having a higher hole pair.

[Michael_C]

You're missing something there.. You've already hit that 1/221 chance of hitting the jacks. So, you don't count that in the chance that someone else has a higher pair.

Also, you're playing against 9 other people. The chance that none of them has a higher pocket pair is (approximately) (1207/1225)^9 = 87.5%.

So the chance someone has a higher pair is about 12.5%. Maybe that's why it seems to happen more often =)

[Nottom]

Dont forget to add in the 16 instances of AK that although you might be a slight favorite, you really don't want to see and there is an over 20% chance someone has a hand that can beat you rather easily when you have JJ (this isn't even counting AQ and KQ). I hope this shows why JJ is not a hand you really want to go all-in with in a NL game.

[Louie Landale]

Yes, your .0065% number is the chances that, on the very next deal, YOU have JJ and I have a bigger pair.

You know the chances that someone, as we speak, is wearing the exact make of shoes, socks, pants and shirt that I'm wearing right now? Its astronomical if you start counting the number of such shoes in cirulation etc., except, as it happens, its 100%.

Now read the other responses.

- Louie

[Filmore Slim]

Can you just answer the question without being condescending? Why do you need to show superiority? You must be really insecure.

[Louie Landale]

Your original post was so many orders of magnitude out-of-whack that I thought you needed an analogy, and exagerated one, to see the light. That was neither condescending nor insecure.

- Louie

[Filmore Slim]

The analogy was not condescending but your tone was

[luckycharms]

AAAh. I did that the other day. I was getting totally crap cards for over an hour, and suddenly i get JJ. Someone raises 5 pre-flop, I reraise all in (18) and get called by KQ suited. Of course, I got beat.