Odds question

[RaskolnikovX]

Any comments as to when I should fold are welcomed (when CO 3 bets the turn is the earliest I can see myself dropping this normally although I was feeling stubborn and stupid [as usual]), but my major question is what are the odds of three players having pocket pairs and all flopping a set?

PokerStars 1/2 Hold'em (10 handed) converter

Preflop: Hero is MP3 with 3[img]/images/graemlins/club.gif[/img], 3[img]/images/graemlins/spade.gif[/img].
<font color="#666666">2 folds</font>, UTG+2 calls, <font color="#666666">2 folds</font>, Hero calls, <font color="#CC3333">CO raises</font>, Button calls, <font color="#666666">2 folds</font>, UTG+2 calls, Hero calls.

Flop: (9.50 SB) J[img]/images/graemlins/diamond.gif[/img], 3[img]/images/graemlins/diamond.gif[/img], 7[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(4 players)</font>
<font color="#CC3333">UTG+2 bets</font>, <font color="#CC3333">Hero raises</font>, <font color="#CC3333">CO 3-bets</font>, Button folds, <font color="#CC3333">UTG+2 caps</font>, Hero calls, CO calls.

Turn: (9.75 BB) Q[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">UTG+2 bets</font>, <font color="#CC3333">Hero raises</font>, <font color="#CC3333">CO 3-bets</font>, UTG+2 calls, Hero calls.

River: (16.75 BB) A[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
UTG+2 checks, <font color="#CC3333">Hero bets</font>, CO calls, UTG+2 calls.

Final Pot: 19.75 BB

Results in white below: <font color="#FFFFFF">
UTG+2 has 7h 7s (three of a kind, sevens).
Hero has 3c 3s (three of a kind, threes).
CO has Jh Jc (three of a kind, jacks).
Outcome: CO wins 19.75 BB. </font>

[Hybrid_11]

Put simply I'm not folding. Specially since this is 1/2 which belongs in micro by the way but With little straight and no flush possibilites i am not letting this go. I think a call down is in order once the 3 bet hits on the turn. Your river bet is pointless and will not accomplish anything. I think your lucky that it did not end up costing you another BB on that river.

[SeaEagle]

I'm pretty sure it was Lee Jones who said you are probably OK if you never fold a set - and he's considered weak/tight by most here.

I think you played this fine all the way to the river bet, and I certainly wouldn't be folding anywhere.

Welcome to the forums.

[TrippH]

[ QUOTE ]
but my major question is what are the odds of three players having pocket pairs and all flopping a set?


[/ QUOTE ]

I get 2/3795, or .000527 (these are the odds for all three hitting a set on the flop, assuming they already have the pocket pairs)

[W. Deranged]

I'll be approximate because the slight adjustment effects of knowing one extra card and so forth are not that important (though interesting if someone wants to undertake the calculation).

It's about 1 in 17 that any given player has a pocket pair; as you start conditioning this on the fact that others have pairs it goes up slightly, but not much.

Given we know 6 cards now, their are 46 cards outstanding and the probability of each person hitting their cards on A SPECIFIC point in the flop (2nd card on the flop, etc) is 2/46= 1/23. Since there are six orderings of the cards on the flop, the odds they all flop sets is ~6*(1/23)^3.

So the probability is in the neighborhood of (again, this is not exact, but very close):

6*/(23*17)^3

which needless to say is a very small number.

[W. Deranged]

Rounded we're talking .0000001, or 1 in 10 million-ish.

[RaskolnikovX]

Apologies for posting in the wrong forum: I shall make sure I post in the right place in future. Thank you for the replies and the welcome [img]/images/graemlins/laugh.gif[/img]