Odds: set over set

After being stacked when my set ran into a bigger set I decided to do a little math and see what are the chances of being that 'lucky'.

For the sake of simplicity we'll assume that every PP will pay to see the flop.
Also note that when I say Full Ring (FR), I mean 9 opponents and accordingly 6max means 5 OPPs.

1) Chances to get PP:
there are (52*51)/2=1326 theoretically possible holdings, 13 PPs and 6 ways to be dealt each which leads to 13*6/1326=0.058823 or 5.88% or (1-to-17) 1/17.

2) Chances that at least one of your opponents has different PP himself:
first we must take 2 (your hole) cards out of the deck so there are (50*49)/2=1225 possible holdings and remaining 12 PPs, 6 ways to be dealt each -> 12*6/1225=0.058775 or 1/17.01 AGAINST 1 OPPONENT (HU).
With 9 OPPs (FR): (1 - (16/17)^9) = 1/2.38
With 5 OPPs (6m): (1 - (16/17)^5) = 1/3.82

By now we have two different PPs preflop. Since we want to know how often will our OPP have the better one (OBV half of the time), we need to divide these with 2 ->

HU: (1/2)*(1/17.01)= 1/34.02
6m: (1/2)*(1/3.82)= 1/7.64
FR: (1/2)*(1/2.38)= 1/4.76

3) Chances of you flopping a set:
first we must take 4 known (hole) cards out of the deck -> 1-((46/48)*(45/47)*(44/46))=0.12234 or 1/8.17

4) Chances of your OPP flopping a set:
now we must take 5 known cards out of the deck: 4 hole cards and one flop card that brought us a set which also means there are 2 remaining flop cards that OPP might hit set with -> 1-((45/47)*(44/46))=0.084181 or 1/11.88

5) Putting it all together:
now we just have to multiply all of the above:
(HU) (1/17)*(1/34.02)*(1/8.17)*(1/11.88)= 1/56133
(6m) (1/17)*(1/7.64)*(1/8.17)*(1/11.88)= 1/12606
(FR) (1/17)*(1/4.76)*(1/8.17)*(1/11.88)= 1/7854

************************************************** *************

SYNOPSIS:

On average, how often will it happen that you flop a set AND your opponent flops a bigger set?

Roughly about ...

HU: once in 56.1K hands
6m: once in 12.6K hands
FR: once in 7.8K hands

HU: once in 56.1K hands
6m: once in 11.2K hands
FR: once in 6.2K hands

= doesn't matter, won't happen too much for you to care

Originally Posted by badape

HU: once in 56.1K hands
6m: once in 11.2K hands
FR: once in 6.2K hands

= doesn't matter, won't happen too much for you to care

Yeah, but I didn't know that before all the hard work was done. Somehow I had a feeling that it was way more often.

Originally Posted by Sheetah

Originally Posted by badape

HU: once in 56.1K hands
6m: once in 11.2K hands
FR: once in 6.2K hands

= doesn't matter, won't happen too much for you to care

Yeah, but I didn't know that before all the hard work was done. Somehow I had a feeling that it was way more often.

That's interesting, I also would have thought it would happen much more often than that.

This very thing happened to me yesterday in a full ring game. (Played for about 6 hrs. yesterday.) I had pocket 8's, one before the button, bet 4x BB. Button called, everyone else folded. Flop came 89K rainbow. I put in a smallish bet, one-third pot size, trying to disguise my hand. He bet me all in. I jumped on it, putting him on maybe TT or 2 pair. Showed it down and he had the set of 9's. Impossible to get away from this after only the flop.

Also, during that long session, this happened to me TWICE: I flopped a full house, bet all in and got called, and got beat by a bigger house on the river. Painful.

This is my first post on the site, though I've enjoyed reading your advice. Just started playing this past summer, trying to get better....

Originally Posted by deacon_bluez

This very thing happened to me yesterday in a full ring game. (Played for about 6 hrs. yesterday.) I had pocket 8's, one before the button, bet 4x BB. Button called, everyone else folded. Flop came 89K rainbow. I put in a smallish bet, one-third pot size, trying to disguise my hand. He bet me all in. I jumped on it, putting him on maybe TT or 2 pair. Showed it down and he had the set of 9's. Impossible to get away from this after only the flop.

Also, during that long session, this happened to me TWICE: I flopped a full house, bet all in and got called, and got beat by a bigger house on the river. Painful.

This is my first post on the site, though I've enjoyed reading your advice. Just started playing this past summer, trying to get better....

welcome

^^^
Welcome to FTR!

Be careful there, I was calculating odds of only FLOPPED set vs FLOPPED set (disregarding turn and river)

Yeah, I had pocket 8's and he had pocket 9's. (Unless I'm misreading you, in which case disregard.)

That's interesting, I also would have thought it would happen much more often than that.

Those numbers sound high, but most set-over-set pots are pretty spectacular so they stick in the memory longer.

Now tell me how often the following situation happens: two people make quads and two others makes straight-flushes. i bet THATs rare, and a good reason to never fold quads.

I think like hit set over sets and not set under sets... not sure why but I just do.

With 9 OPPs (FR) there is 9 times more chance of someone getting PP thus 9*(1/17.01)= 1/1.89
With 5 OPPs (6m): 5*(1/17.01)= 1/3.4

Your math is wrong here, but not VERY wrong. Odds of you being dealt pp: 1/17
Odds of any one OR more of other 9 players dealt pp = 1 minus odds NO ONE ELSE has a pair = ~(1 - (16/17)^9) = 42% or 1/2.37

So you odds will be lower. But mostly you only care about what the odds are that someone else flops a set when you ALREADY HAVE ONE, which would be about 1/2.37 * 1/12 or 3% of the time (full ring). Odds of higher or lower are hard to determine unless you know what set you have (222 vs TTT for example), and obviously if you flop top set then opp. can't have a higher one.

Originally Posted by deacon_bluez

I flopped a full house, bet all in and got called, and got beat by a bigger house on the river.

Originally Posted by deacon_bluez

Yeah, I had pocket 8's and he had pocket 9's. (Unless I'm misreading you, in which case disregard.)

I took into consideration only FLOPPED. If you add turn and river than it's obviously more often.

Originally Posted by zenbitz

But mostly you only care about what the odds are that someone else flops a set when you ALREADY HAVE ONE, which would be about 1/2.37 * 1/12 or 3% of the time (full ring). Odds of higher or lower are hard to determine unless you know what set you have (222 vs TTT for example), and obviously if you flop top set then opp. can't have a higher one.

I wanted to do math for that as well, but there were to many IF-s: should we take into consideration paired boards i.e. sets vs quads; top, middle, bottom set scenarious ...
I think your 3% are about fine for middle sets (average)

Originally Posted by zenbitz

Your math is wrong here, but not VERY wrong. Odds of you being dealt pp: 1/17
Odds of any one OR more of other 9 players dealt pp = 1 minus odds NO ONE ELSE has a pair = ~(1 - (16/17)^9) = 42% or 1/2.37

The reason I posted the whole process is that I wanted someone to check my math/logic so we can have accurate results and YES this is a clear mistake. DAMN! How could I miss that? After checking several times every single step?

And now excuse me I have a homework to do: fix OP

Fixed

Right afer reading this thread it happened to me!!!

Flopped a set and lost to another player who had flopped a bigger set - good thing he was short stacked.

Pocket pairs that turn into sets are your best friend in small stakes NL and I usually play them agressively. They are a huge portion of my overall winnings.

Prima Poker skin
No Limit Holdem Ring game
Blinds: $0.10/$0.20
10 players
Converter

Stack sizes:
UTG: $28.30
Unlucky Me: $20.20
UTG+2: $9.85
MP1: $15.90
MP2: $7.70
MP3: $19.60
CO: $58.39
Button: $20.15
SB: $23.60
BB: $19.80

Pre-flop: (10 players) Unlucky Me is UTG+1 with 8 8
UTG folds, Unlucky Me calls, UTG+2 raises to $0.6, 7 folds, Unlucky Me calls.

Flop: 8 K 7 ($1.5, 2 players)
Unlucky Me checks, UTG+2 bets $0.4, Unlucky Me raises to $1, UTG+2 raises to $2.4, Unlucky Me raises to $9, UTG+2 calls all-in $6.85, Unlucky Me calls.

Turn: 4 ($20, 1 player + 1 all-in - Main pot: $20)


River: 7 ($20, 1 player + 1 all-in - Main pot: $20)


Results:
Final pot: $20
UTG+2 shows Kd Kh

bonus question:

what are the odds of flopped set over set over set?




FullTiltPoker Game #1346101257: Table Washington - $0.25/$0.50 - No Limit Hold'em - 11:36:40 ET - 2006/12/03
Seat 1: DireEmblem ($79.95)
Seat 2: Hero ($49.75)
Seat 3: VillianOne($40.75)
Seat 4: hetmect ($32.85)
Seat 5: VillianTwo ($15.75)
Seat 6: lucid001 ($50)
Seat 7: DormieBear ($11.45)
Seat 8: yugor ($14.05)
Seat 9: HaakonS ($32)
DormieBear posts the small blind of $0.25
yugor posts the big blind of $0.50
The button is in seat #6
*** HOLE CARDS ***
Dealt to Hero [6d 6s]
HaakonS folds
DireEmblem calls $0.50
Hero calls $0.50
VillianOne raises to $2.75
hetmect folds
VillianTwo calls $2.75
4 folds
Hero calls $2.25
*** FLOP *** [Td Qc 6c]
Hero checks
VillianOne bets $6
VillianTwo calls $6
Hero calls $6
*** TURN *** [Td Qc 6c] [5d]
Hero checks
VillianOne bets $16
Villian calls $7, and is all in
Hero raises to $32
VillianOne calls $16, and is all in
Hero shows [6d 6s]
VillianOne shows [Qh Qs]
VillianTwo shows [Th Ts]
*** RIVER *** [Td Qc 6c 5d] [Jh]

Does the math figure in the possibility that multiple opponents may see the flop with you and any one of the several will hit an overset to you?

GUYS please stop flopping set under set and start flopping set over set. that is all.

PokerStars No-Limit Hold'em, $0.25 BB (5 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

saw flop|saw showdown

BB ($26.85)
UTG ($13.80)
MP ($44.15)
Button ($61.95)
Hero ($34.50)

Preflop: Hero is SB with A, A.
1 fold, MP calls $0.25, Button raises to $1, Hero raises to $3.25, 1 fold, MP folds, Button calls $2.25.

Flop: ($7) A, 5, 8 (2 players)
Hero bets $4.5, Button raises to $9, Hero calls $4.50.

Turn: ($25) J (2 players)
Hero checks, Button bets $19.7, Hero raises to $22.25, Button calls $2.55.

River: ($69.50) 4 (2 players)

Final Pot: $69.50

Hero has As Ad (three of a kind, aces).
Button has 8d 8c (three of a kind, eights).
Outcome: Hero wins $69.50.


PokerStars No-Limit Hold'em, $0.25 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

saw flop|saw showdown

SB ($26.15)
BB ($14.75)
Hero ($29.30)
MP ($53.90)
CO ($25)
Button ($22.50)

Preflop: Hero is UTG with T, T. CO posts a blind of $0.25.
Hero raises to $1, 1 fold, CO (poster) calls $0.75, 2 folds, BB calls $0.75.

Flop: ($3.10) 2, T, 6 (3 players)
BB checks, Hero bets $2.5, CO calls $2.50, BB folds.

Turn: ($8.10) 6 (2 players)
Hero checks, CO bets $5.25, Hero raises to $25.8, CO calls $16.25 (All-In).

River: ($55.40) K (2 players, 1 all-in)

Final Pot: $55.40

Hero has Tc Td (full house, tens full of sixes).
CO has 2c 2h (full house, twos full of sixes).
Outcome: Hero wins $55.40.

You can even turn set over set if that works for you.

PokerStars No-Limit Hold'em, $0.25 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

saw flop|saw showdown

MP ($27.75)
Hero ($25)
Button ($8.75)
SB ($50.10)
BB ($24.65)
UTG ($13.50)

Preflop: Hero is CO with 7, 7.
UTG raises to $1, 1 fold, Hero calls $1, Button calls $1, 1 fold, BB calls $0.75.

Flop: ($4.10) 5, 6, 9 (4 players)
BB bets $1.5, UTG calls $1.50, Hero calls $1.50, Button folds.

Turn: ($8.60) 7 (3 players)
BB checks, UTG bets $3, Hero raises to $8.75, BB raises to $22.15, UTG folds, Hero calls $13.40.

River: ($55.90) 4 (2 players)

Final Pot: $55.90

BB has 6h 6d (three of a kind, sixes).
Hero has 7s 7h (three of a kind, sevens).
Outcome: Hero wins $55.90.

I actually haven't had a set under set in about 20k hands now - it should come soon I guess.

Originally Posted by Nova442

Does the math figure in the possibility that multiple opponents may see the flop with you and any one of the several will hit an overset to you?

Math is for AT LEAST one opponent hitting an overset. On some of these occasions (though very rare), there'll be 3 flopped sets

Originally Posted by givememyleg

GUYS please stop flopping set under set and start flopping set over set. that is all.

hmmm, maybe there´s a huge leak in my game

if set over set is a problem for you playing less than 100nl on a poker site, you're playing on the wrong site.

Yeah, im serious.

I don't know if this has been asked, and excuse me if it has but this math only factors in how often set over set will occur but it doesn't take into account if you will have the best set or lower set, right? So I was wondering how you would figure out the odds of having the losing set, because obviously there is no worries if you have top set.

Originally Posted by garveya1

I don't know if this has been asked, and excuse me if it has but this math only factors in how often set over set will occur but it doesn't take into account if you will have the best set or lower set, right? So I was wondering how you would figure out the odds of having the losing set, because obviously there is no worries if you have top set.

This math DOES take into account exactly that: odds of having lower set ( tip:Reread step 2) )