Both players flopping a set

[aliensyndm]

As mentioned in a previous thread it can be a bit of a piggy if two players in a pot both flop a set. Now it doesn't really serve any useful purpose but I thought I would go through the process of working out how often this occurs.
There's really no getting away from putting all your chips in when this happens but at least you'll know just how many times this is likely to happen.

OK I'm going to skip the probability of both people being dealt a pocket pair as we're primarily only interested in the chances of them both flopping a set when they both have one.
For this we shall say one player has pocket kings and the other has pocket aces, a definite stack buster methinks !


OK first of all we have to work out how many different possible flops there are. OK well we know what four of the 52 cards available are, AA and KK so that leaves us 48 unknown cards. How many possible three card flops are there with 48 cards ?

The formula to work out how many possible combinations of anything being selected from anything is...

N!/ ( (N-S)! * S! )

Where N is the number of things, S is the number of things being selected.
The ! is factorial. 5! = 5*4*3*2*1 , 7! = 7*6*5*4*3*2*1 etc
Scientific calculators have a factorial button usually denoted x! or n!


OK so from a 3 card flop of 48 cards we get....

48! / ( (48 - 3)! * 3! ) = 17 296


Ok so 17 296 possible flops there.


Right we now need to work out how many of those flops will have both an ace and a king. So our flop must be of the form A-K-X where A is any ace, K is any king and X is any of the other remaining cards.
We have a choice of 2 of the remaining aces or 2 of the remaining kings of course and then that leaves 44 remaining cards. Note that I have left out flops where one person flops quads and the other a full house.

OK so we have 2 * 2 * 44 = 176

So 176 of those flops will contain both a king and an ace with another card(whch isn't the other king or ace).



So 176 of 17 296 flops will see both players flopping a set.

176 / 17 296 = 0.01017576

I will round up and that makes for a probability of 0.0102

To get this as a percentage we multiply by 100% ie

0.0102 * 100% = 1.02% chance of this happening.

There's the answer, it's a 1.02% chance of both players flopping a set.
If you don't like things expressed in percentages we can take the figure in traditional odds style

100 / 1.02 = 98.039

So approximately a 1 in 98 chance of it happening. Or 97/1 shot if you prefer traditional fractional odds.


OK so not very often really so you can't be worrying about it too much.
The one time you do go bust is more than made up for by the numerous times the raiser cannot throw his AA or KK as an overpair to the board and you bust him.

[mrmuzeman]

Nice work Alien

Alien - is this just the chances of both players flopping a set or you losing to a set over set?

If its just 2 players flopping a set then presumably youd benefit from this half the time and its actually 200/1ish that youd lose to a set over set am I right?

[aliensyndm]

This is just both people flopping a set if both have pocket pairs.
Sometimes you will be the higher set, sometimes you will be the lower set.
This calculation is just for two players having any 2 pocket pairs and both flopping the sets of these pocket pairs.
You can't just double the figure and say it's 200/1 you would lose to an over set. If you have pocket kings and the other guy has a random pocket pair you will both flop sets 1.02% of the time. Of that 1.02% 11 sets will be undersets and one set is the overset ie AAA set hence it should be obvious it's not simply 200/1 to lose to an overset. It does of course depend on your cards. It's simply 1.02 % chance that both players will flop a set if they both have pocket pairs.

If you had KK and you KNEW your opponent had AA it's a 1.02% obviously that you both flop a set, but to a random pocket pair you then of course have to take into account the chances of him having KK.
That of course would be 1 chance in 12(assuming he had to have a pocket pair of course) ie there are pocket 2,3,4,5,6,7,8,9,T,J,Q he could have or pocket A.
So it would be a 1/12 chance followed by a 1/98 chance hence a 1 in 1176 or 0.085% chance that if you had pocket kings that you flop a set of them and are behind to a set of aces. Bear in mind this behind is only taking into account a pocket pair flopping a set and not any possible straights etc.
It should be obvious how to work out the chances for any other pocket pair being behind from that.

[aliensyndm]

Also bear in mind this figure is assumes the person has a pocket pair. It is of course different if your opponent has a random hand.

[mrmuzeman]

Basically its bloody rare

I seen 3 people ALL flop sets before KK, QQ and 22. The chances of that have gota be HUGE.

Especially when a 2 came at the river as well

[aliensyndm]

You could work it out by following the calculation with a little bit of alteration here and there. Yeah I think jezza told me about a similar hand where all three flopped a set and then rivered quads, mental stuff.

Also remember the probabilities I've done there are the chances if both people already have pocket pairs etc, the chances of it happening in an actual game require you to work out probability of people having pocket pairs in and X seater game etc etc. Can get a bit messy.

The all three is simple really ......

Say AA, KK and QQ


17,296 flops as already worked out.

Flop must be AKQ

2 Aces * 2 Kings * 2 Queens = 8 flops


8 / 17,296 * 100% = 0.04625%

[GaNgStA kEeKs]

Very nice stuff Alien. Enjoyed reading that

[aliensyndm]

This happened to me today, I had 99 and the flop was AJ9
Had two other people in the pot whom I thought were on aces, the turn was an ace and I hence went all in so an ace could not fill up. One player had AK and and called and didn't fill up but there was of course the other person who had JJ and did me,
Ah well that's the first one for a looooooooooooooooooooong time, not to panic

[mrmuzeman]

Hard lines Alien

Ive only had it once ever actually in cash so I must be running good on avoiding it. Ive done other people on it at least 3 times

I was holding JJ today and there was this dude with 99 and....

[christianu]

I had AA the other day, and I raised pre flop and a short stack went all in, then a medium stack went all in and so obviously I called.

I had AA
Short stack had 44
Medium stack had 10 10

Flop: A 4 7
Turn: 10
River: cant remember

Sick!

[mrmuzeman]

At least there wasnt a 10 or 4 on river!

I seen set over set over set all in on the flop before. KK v JJ v 22 on a KJ2

Needless to say the river was a 2

[crowie]

I was playing at a mates house on Saturday night. 2 people pulled out late on so that left 4 of us playing, a bit shorthanded but we gave it a go.

Playing our 3rd tourney of the night, I get dealt 10-10, raised it a fair bit, called by one lad, 3rd (SB) player folds, 4th player raises. I call the raise as does other player.

Flop comes 10-4-2 rainbow.

I went all in, as does player to my immediate left. Player who re-raised my raise also goes all in.

Player to my left turns 4-4, player who re-raised turns A-A!

Turn came with A!!

So 4 handed game we have 3 players with sets by the turn. If that had happened online I would have been shouting "Fixed" but it does happen.

The player with 4-4 also had quads twice in approx first 15 hands of the night!

[aliensyndm]

That's the thing, if a ridiculous outdraw happens online people often say see it's fixed bla la la la. They happen in live games too !
I've seen just as bad if not worse outdraws in live games as online.
Do you ever hear a long term winning poker playing complaining it's fixed ?
To people what still say it's fixed I just say "Well I must be lucky cos they fixed it in my favour"

Although I had been stuffed when both players flopped a set I forgot I was actually the right side of it the same night. Funny how you always remember your beats but not always your wins.
One guy raised 10 BBs and another called, I had JJ. Quite a large pre-flop raise but if I hit my set I'm getting the whole lot so I called.
Flop came 3 10 J , perfect. Normally I would lead this flop but I checked it being pretty certain the other guy would stick in a large bet, the first guy goes all in *rubs hands*, can't even remember what the second guy did
Turns out the all in guy had 10 10 and had also flopped a set, ouch !
Twice in one night both players flop a set, I'm on the right end of it one time and the wrong end of it another. I might not see it again for weeks, months or years. Just hope I am on right end of it if I am !

[mrmuzeman]

Just gona vent a bit of frustration, not set over set. My KK all in v QQ on a Jack hi flop, bloody rivers a Queen. Massive pot it was, this Kings nonsense is taking the piss now

[raisin man]

Just had a crazy hand. I limped in in early position with 22. The guy in my left limped in too. 7 people to the flop. Flop comes 2 Q 8.

I raise 3 times the pot. Guy on my left just calls. Everyone else folds. Turn is a 4. The bosrd is all different suits so no flush possible.

I raise another 3 times the pot. The guy on my left pushes all in. I call after a long think. I don't think he would have pocket 4s as he called my big raise after flop. No flush or possible staights out yet. My best guess is two pair.

He turns over pocket 8s. We both hit a set on the flop. But he's clearly in the lead.

Last card: 2!!!!!!!

I hit my only out and took down a $120 pot at a 25c/50c table. Loved it.