what are the odds?

[riverboatking]

just curious what the odds of flopping set over set are.

was playing the 20-40NL last night and was on the ass end of set over set 4 times in 8 hours.

and no i didn't get away from any of them.

[Jeebus]

better than the odds of flopping AA vs AA preflop and KK vs. KK preflop in the space of an hour.

[mgsimpleton]

well if two people have pocket pairs it's 12% times 8% or something, right?

and if 3 people have pocket pairs it's 12% times 16%? is this math right at all?

so just take the conditional probability of a pocket pair in each spot (1/17) times the prob. of them flopping a set given you flop a set (and thus there are only 2 cards for them to do it in) so (8%) and multiply that by 9 in a full ring... so if you flop a set, the odds of someone else flopping a set are 72% (1/17) or a little under 5%.

that sound right?

of course that's purely based on random cards in every spot, so if more people call pre flop raises, what's the likely hood they have a pocket pair? more than 1/17. so let's say people call preflop raises with pocket pairs 1/3 of the time, 2/3 it is suited connectors or AK, AQ hands... then it's more like 1/3 times 8 percent for every preflop caller which is significantly more...

[freemoney]

thats pretty wrong if one person flops a set then its only 2 cards left to flop a set for the other person.

[mgsimpleton]

wtf are you talking about?

[freemoney]

lol if you dont understand that...wow. Alright I will make it veryyy simple you have a pair of aces i have a pair of 10s now for you to flop a set over me we BOTH have to set, so now if you flop an ace on the flop that only leaves 2 cards left on the flop (because 3-1=2). so the odds of set over set isnt simply the odds of both setting because we are sharing the board, thats wtf im talking about. got it?

[Garland]

Let's see. Let's take two random pocket pairs: T[img]/images/graemlins/heart.gif[/img]T[img]/images/graemlins/diamond.gif[/img] and 6[img]/images/graemlins/heart.gif[/img]6[img]/images/graemlins/diamond.gif[/img]

I'll work on the denominator (total possibilities) first: There are (52-4) 48 remaining cards, so there are 48c3 (48 choose 3) total hand combinations, which means 48*47*46/3*2*1 possible flops or 17,296 possible flops with the remaining cards.

Now there are four ways to flop exactly one T and one 6:

T[img]/images/graemlins/club.gif[/img]6[img]/images/graemlins/club.gif[/img] + one of 44 other possible cards
T[img]/images/graemlins/club.gif[/img]6[img]/images/graemlins/spade.gif[/img] + one of 44 other possible cards
T[img]/images/graemlins/spade.gif[/img]6[img]/images/graemlins/club.gif[/img] + one of 44 other possible cards
T[img]/images/graemlins/spade.gif[/img]6[img]/images/graemlins/spade.gif[/img] + one of 44 other possible cards

That makes 176 possible hands that have exactly one T and one 6. So the probability of flopping set over set is:

176/17296 or 0.01017576...

Translating that into odds, it's 17120:176 against, which reduces to 97.27:1 against. In short, it'll happen about 1 in 98 times when both opponents hold pocket pairs.

The answer changes slightly if you want to include the possibility of flopping quads as well.

I assume the above logic holds true for any two random pairs. Someone check my math/logic.

Garland

[riverboatking]

[ QUOTE ]
Translating that into odds, it's 17120:176 against, which reduces to 97.27:1 against. In short, it'll happen about 1 in 98 times when both opponents hold pocket pairs.

[/ QUOTE ]

thats [censored] sick.

[mgsimpleton]

[ QUOTE ]
lol if you dont understand that...wow. Alright I will make it veryyy simple you have a pair of aces i have a pair of 10s now for you to flop a set over me we BOTH have to set, so now if you flop an ace on the flop that only leaves 2 cards left on the flop (because 3-1=2). so the odds of set over set isnt simply the odds of both setting because we are sharing the board, thats wtf im talking about. got it?

[/ QUOTE ]

ok jerkface if you read my post i already said that and if you actually took the time to look at my math i said 12% times 8% now if you don't understand why flopping a set in 3 cards making it 12% makes hitting it in 2 makes it 8% then it seems you're the [censored].

now go post something useful. and maybe with some correct grammar, while you're at it.

[rid.br]

I think that's the probability IF there are only two players with pocket pairs in the hand.

If there are more people with pocket pairs, the probability of set over set is bigger.