set over set probability

[RedSoxFan]

Ok- probably not a new question so I'll pollute the forum more.

What's the probability of only 2 players (6m and FR- assuming tables full) being dealt pocket pairs?

Given that probability, what is the probability that both flop a set? My intuition is that it's rather small.

So if my intuition is correct, why do I read so many posts about people worrying about being beat by an over set (both flopped)? I just read an idea that playing pocket pairs 55 and down is -EV because your set can beat by an over set too often. This is BS IMO. If I have 44 and flop is A94, I'm focused on stacking the Ax person and not worried about the chance that someone has 99. Is this wrong? Don't you think we're paid off way more than enough with hitting a low set compared to the infrequent times we're busted by a flopped over set?

I've played 20K hands (2 months Pokerstars) and have busted a guy with an over set once (but were both all in pre-flop AA vs QQ) and had my middle set beat once by an over set.

[PantsOnFire]

An overset is rare enough (i.e. less than 1%) that it does not figure in your equity for a hand. Anybody who folds a set fearing an overset (or plays the hand like it is possible) is really quite daft.

If Dan Harrington can say, "If I am beat by an overset, it's not my day", well then so can I.

[jay_shark]

The exact probability that only two players are dealt pocket pairs at a n handed table involves the principle of inclusion/ exclusion . Fortunately , there are better methods to arrive at a fairly accurate answer without evaluating all the insignificant terms .

The approximate probability that at least one of n players is dealt a pocket pair is ~ 1-(1248/1326)^n ; ie , if we plug n=10 then we get ~ 45.46%

The approximate probability that exactly two players are dealt pocket pairs is ~ nC2*(78/1326)^2*(1248/1326)^(n-2)

So if we plug n=10 we get ~9.587%

The probability exactly two random players are dealt pocket pairs and that they flop sets assuming they always see the flop is ~ 0.09587*(2*2*44/48c3) ~ 0.0009755

[AFCBeer]

The time when set over set does become a slight concern is in multi-way limped pots.

Say the flop comes 9 6 3 and you hold pocket 3's. On such a dry board, if stacks go in, you do need to consider why someone else is willing to put such an amount into the pot. This is not a major concern but something you do at least need to be aware of with the low pairs.

Because I'm never going to fold a set to a higher set this is why I believe you should be raising all pocket pairs from all positions. In a raised pot, when villains put stacks in it is far more likely to be with a top pair/overpair then if the pot was limped.

There is an arguement for folding 22-55 in EP, but really set over set is a very rare occurance and not something we should be overly concerned by.

[thrasher789]

the other day I had pocket nines on the button and called a modest raise from the guy to my right, flop came 39J and he bet out, I raised a few dollars putting him on AJ and he didn't call right away, he then called and he only had 2 dollars left so he pushed on the turn and I figured he had AJ, ends up he had JJ and it hurt

[Red_Diamond]

[ QUOTE ]
An overset is rare enough (i.e. less than 1%) that it does not figure in your equity for a hand. Anybody who folds a set fearing an overset (or plays the hand like it is possible) is really quite daft.

[/ QUOTE ]

Then you accuse both Greenstein & Caro of being daft?

[PantsOnFire]

[ QUOTE ]
[ QUOTE ]
An overset is rare enough (i.e. less than 1%) that it does not figure in your equity for a hand. Anybody who folds a set fearing an overset (or plays the hand like it is possible) is really quite daft.

[/ QUOTE ]

Then you accuse both Greenstein & Caro of being daft?

[/ QUOTE ]
When I said anybody, I didn't mean just anybody. Those guys are expert hand readers. If you are exnper then, yes, you can lay down a set to a possible overset or KK preflop to AA. If you're not an expert, then I would say you are daft to make these laydowns.