Probability of 2 PP's at 9 handed table?

[AaronBrown]

You have to do this in steps. First consider only three players. If you deal six cards at random, there are C(52,6) = 20,358,520 possible hands, only six of which are AAAAKK (there's only one way to pick four Aces, and six ways to pick two Kings out of four). If you start with AAAAKK, shuffle, and deal three holdem hands, there's 1 chance in 5 that you'll get AA, AA and KK (the first King can pair with any of five cards, one of which is a King, and if it does you get AA, AA, KK; if it doesn't, you don't). So thats 1 chance in 16,965,433 with three players.

With 10 players, there are C(10,3) = 120 ways to pick three players to have this happen. That gets you to 1 chance in 141,379. That's not exactly correct, because on some very rare deals you could get AA, AA, KK and KK; and this method will double count those.

I would not have folded this hand. If both of them do have AA, you still have a 20% chance of winning (basically, the chance of a King showing up on the board, ignoring some four-card straight or flush boards). That's negative EV if played to the river, but since no Ace is going to show up, you should be able to get both of them to fold if any high card shows up.

If neither one has AA, the most likely situation, you have a very strong hand. The worst situation for you is if one has AA and the other has some other strong hand (or one or two of your Kings). But it's still a situation I would play.

[rrrorrim]

Very good advice...

Of course, when I folded, I didn't know they both had aces. I assumed one did and another was a fish with a midrange pocket pair. If I knew they both had Aces, I would have gone in just for the sheer joy of saying I did, brave soul that I am...

Also, I was playing an STT and I have a strategy (still being refined, but definitely working) that maximizes how often I get into the money.

It's based on this concept:
Don't assign so much value to premium hands... Be more concerned with the situation as a whole. Instead of asking myself, "Is my hand valuable?" I should be asking myself, "Is my situation valuable?" In this light, my Kings were more of a regular hand.

... and also based off the fact that in STTs you have an extra avenue of winning - patience (which, when combined with 2-3 well-timed power plays, will usually put you in the money).

... and that's my justification for doing something stupid like folding Kings. [img]/images/graemlins/smile.gif[/img]

[AaronBrown]

You're thinking is right on both counts. You were afraid of one AA, not two. My criticism of the decision is AA is so unlikely that when you suspect it, you're probably wrong.

You're also correct that premium hands don't make you rich. The best hand at the table wins the most, but the second best loses the most. Most of the time when KK wins, it's not the nuts, and it's not beating a good hand, so you can't maximize the value. And KK will generally lose more when it loses than it wins when it wins. In no-limit, you make your money with nuts and near-nuts beating very good hands; and lose most of your money with very good hands that lose to nuts.

Still, folding KK preflop is taking that to an extreme.

[rrrorrim]

Definitely is an extreme...

In an STT in the micros, players overvalue small pocket pairs, so it was likely I was up against 33 and JJ. But I didn't feel like putting my entire stack at risk.

I'd much rather be shortstacked with 4 opponents left in an STT than risk my entire stack on an iffy situation for the sole benefit of becoming chip leader.

In an STT, having a big stack is not nearly worth the 3-4 ranks you gain by being patient...