Cutting Off Set Equity
 

Hey guys, I'm crunching some numbers tonight, and have hit a wall. This SHOULD be simple math, but for some reason my brain just can't wrap my head around this after 30 minutes of thought. I'm sure you guys can clear it up real quick.


My question involves cutting off set equity- how big a 3 bet must be pre flop that a smaller pocket pair is -EV to call even if they KNEW you'd stack off every time they hit a set. I'm coming to two figures, one which seems to make sense mathematically, and one that seems to make sense intuitively. Can ignore any set over sets or spiking a set on turn or river, if that makes it easier. Assume $200 stacks, 1/2 NL with neither player A or B in the blinds.

Which line is correct?

Player A raises to $8 with a small pocket pair. Player B has AA on the button. He wishes to raise an amount that makes player B neutral EV to call (ie the amount he wins when he hits exactly matches the amount he loses the 7.1 or so times he misses). Does player A:

1) Raise exactly 1/8.1 the effective stack Player B can win ($200 + $3 blinds), ie $25.06?

OR

2) Since Player B's implied odds decision begins once Player A re-raises, Player A must raise

211 = (x-8) 7.1
211= 7.1x-56.8
267.8=7.1x

x= $37.72?

This feels like it should be straight forward, but my brain is on vacation tonight. Thanks for any and all help.

Re: Cutting Off Set Equity
 

The simplest way to do that is to see what is equity of AA IF you hit a set. It is about 80% (you can stove it.. AA vs 33 with one 3 on the board will do the trick).
So for 100BB stacks you win 60BB for every allin if you hit. You hit 2 times in 17. The rest is simple.
In practice it has little meaning because :
-you have more hands in your range, some of them won't stack off so implied odds for the pair decrease
-you will sometimes stack off with top pair (for example AK hitting Kxx) when you have less equity than overpair

I did some analysis of those situations here

Re: Cutting Off Set Equity
 

When he wins he'll get his raise + blinds + your stack, which is $211. He'll do this ~11.76% of the time. It will cost him X to call your reraise.

EV(of calling reraise) = -X*(0.8824) + $211*(0.1176)

Since you want to make him indifferent set this equal to 0 and solve for X. X = $28.12. He should have to call $28.12 which means you need to make it $36.12.

You actually have to raise to an amount slightly less than this because sometimes you'll crack his set.

Re: Cutting Off Set Equity
 

[ QUOTE ]
ometimes you'll crack his set.

[/ QUOTE ]

That "sometimes" is huge. You win 60% of his stack on average instead of 100% because of that "sometimes".

Re: Cutting Off Set Equity
 

Hi,

I did this analisys considering set over set and quands vs set in this thread:
http://forumserver.twoplustwo.com/showth...e=2#Post9343754

It comes down that for the call to be EV+, the small pp needs to be able to win more than 9.5 times the bet he is facing.

So in your case, small pp lead for $8, AA on button raises to 8+X, sb folds, bb folds.

Pot will be 8+1+2+8+X=19+X

And the reward is: 19+X+(200-X)=219+X

219+X=9.5*X
219=8.5X
X=219/8.5=$25.76

That is the break even point.

If you want to simplify the math, the reward is 219+X aproximated to 220, so the reaise that the small pp can call is around $22 ($22 is the raise, so he has to put $30 on the pot).

Regards ...

Re: Cutting Off Set Equity
 

Thanks for the responses guys, good to see a consensus on the 2nd method. A lot of useful info presented here.

Re: Cutting Off Set Equity
 

[ QUOTE ]
The simplest way to do that is to see what is equity of AA IF you hit a set. It is about 80% (you can stove it.. AA vs 33 with one 3 on the board will do the trick).
So for 100BB stacks you win 60BB for every allin if you hit. You hit 2 times in 17. The rest is simple.
In practice it has little meaning because :
-you have more hands in your range, some of them won't stack off so implied odds for the pair decrease
-you will sometimes stack off with top pair (for example AK hitting Kxx) when you have less equity than overpair

I did some analysis of those situations here

[/ QUOTE ]

Hey... Why IS AA 20%-ish vs 33 on a flop with a 3? Shouldn't 2 outs twice be in the 8-10% neighborhood?

Re: Cutting Off Set Equity
 

[ QUOTE ]
Hey... Why IS AA 20%-ish vs 33 on a flop with a 3? Shouldn't 2 outs twice be in the 8-10% neighborhood?

[/ QUOTE ]
It's possible to flop set over set. We're interested in your equity when villian flops a set, not your equity when villian flops a set and you don't. The probability that an Ace will be on the board given that villian flopped a set is:

1 -(45/47)*(44/46)*(43/45)*(42/44) ~ 0.165

There's also a small chance you'll make a straight or flush or three of a kind on the board will counterfeit villian's boat.

Re: Cutting Off Set Equity
 

[ QUOTE ]
It's possible to flop set over set. We're interested in your equity when villian flops a set, not your equity when villian flops a set and you don't.

[/ QUOTE ]

Yes. Unless you are mind reader and you will fold a set if he flops the higher one but who you are kidding [img]/images/graemlins/wink.gif[/img]

Re: Cutting Off Set Equity
 

[ QUOTE ]
[ QUOTE ]
Hey... Why IS AA 20%-ish vs 33 on a flop with a 3? Shouldn't 2 outs twice be in the 8-10% neighborhood?

[/ QUOTE ]
It's possible to flop set over set. We're interested in your equity when villian flops a set, not your equity when villian flops a set and you don't. The probability that an Ace will be on the board given that villian flopped a set is:

1 -(45/47)*(44/46)*(43/45)*(42/44) ~ 0.165

There's also a small chance you'll make a straight or flush or three of a kind on the board will counterfeit villian's boat.

[/ QUOTE ]

Ahh yes, it's the equity when they flop a set in general, not when they flop a set and you don't.