Theory: Stack Efficiency in SNGs

[ChrisV]

Disclaimer: The following applies more to higher buyin SNGs, where there are more aggressive players. If you're an experienced player you probably know everything in this post already, but it doesn't hurt to get concepts clear in your mind.

When is the best time to steal from your opponents? Most players understand that in allin steal scenarios, it's better for your opponent to have a smaller stack. If he has a large stack, applying ICM concepts will give him similar results to just using pot odds, and he'll just call whenever he thinks his hand is probably better than yours. The shorter your opponent's stack, the better, all the way down to the point where the blinds start becoming such a large percentage of his stack that he's forced to call loose.

What about non allin steals? Once again, it isn't a good idea to steal from very large stacks which can't be hurt by you. This time though, I don't think it's a linear progression down through smaller stacks.

Consider the typical steal situation:

Hero (1900)
SB (irrelevant)
Villain (???)
Blinds 50/100
Dealt to Hero [ Qh Js ]
(folds to Hero)
Hero raises (300)
SB folds

What stack size would you prefer Villain has? In this situation it's unlikely that he has enough that your 1900 can't seriously hurt him. Let's consider stack sizes from, say, 1200 to 2400. I'm pretty sure everyone agrees that we can't really call a reraise for any of those amounts. Villain calling is outside the scope of this post (as I said at the top, I'm assuming aggressive opponents), but I think everyone will agree it's nowhere near as bad as him reraising.

Pretty clearly, any reraise from the villain will have to be allin. If he has a mediocre hand, say AT suited, the object of his reraise is primary as a resteal, to make you fold. Since we can't call a reraise no matter the amount, villain is better off with the stack of 1200 than with any other amount. It accomplishes his goal while putting much less at risk than if he has a stack of 1900. I refer to this as stack efficiency. Villain has maximum stack efficiency at the point where you will fold steal hands to a reraise. Minimum is at the largest stack size he has where a reraise still has to set him allin. It rises again if his stack is larger than the effective stack (ie when he has more chips than you do).

So the original question: When should you steal from your opponents? You should be more inclined to steal when your opponent has low stack efficiency and less inclined to steal when he has high stack efficiency. This will leave you less vulnerable to resteals.

Also, when you actually have a good hand, if you don't think your opponents will be tipped off by bet size variation, you can change your bet size to give them maximum stack efficiency. For example, if you and your opponent both have a stack size of 1700 at 50/100, you might try a raise to 400 instead of to 300. This also has the effect of looking like a donk attempt to prevent a call, but against an aggressive opponent it will actually encourage them to attack you.

[bawcerelli]

it's interesting, but i don't quite get it yet.

[ChrisV]

Put yourself in villain's shoes. Suppose you have something like A9 suited in the blind at 50/100. It folds to the button with 2000 chips who steal raises you. Do you feel more comfortable playing back at him with 1200 or with 2000?

If you wouldn't consider playing back with A9 suited, increase the hand strength a little.

[Irieguy]

I understand your concept and I think it is actually a pretty valuable one (though I would imagine all good high stakes players already understand it, intuitively.)

The only thing I have to add is that I'm not sure the term "stack efficiency" is the best name for this concept.

Your efficiency decreases as your stack increases which makes you less likely to resteal which makes it better for your opponent to steal against you. There are too many conceptually disparate motions for this terminology to catch on.

I was discussing this concept with another 2+2er just the other night and mentioned how I thought you could use a stack-size disparity as a lever on the bubble. Maybe "leverage" fits this idea a little better than "efficiency."

I don't know, it's your idea so call it whatever you want. But from a marketing standpoint you may be able come up with a better slogan.

Half of the reason why the PVS gets so much notoriety is because the name is cool.

Maybe you can just call stack efficiency "V"

Irieguy

[bawcerelli]

[ QUOTE ]
Maybe you can just call stack efficiency "V"

Irieguy

[/ QUOTE ]

harrington has the single letter concept market already cornered. it'll have to be the CV.

[golfcchs]

Is this basically saying that if a player is in the blinds he would like to have a smaller stack (to a point) for his resteal, because it is -ev for 2 big stacks to clash all in?

[HesseJam]

[ QUOTE ]
Put yourself in villain's shoes. Suppose you have something like A9 suited in the blind at 50/100. It folds to the button with 2000 chips who steal raises you. Do you feel more comfortable playing back at him with 1200 or with 2000?

If you wouldn't consider playing back with A9 suited, increase the hand strength a little.

[/ QUOTE ]

If i understood you correctly, you would prefer playing back with 1200, because if you get called and lose you lost only 1200 whereas if you resteal the pot the result would be the same.

I would be more happy to play with 2000 because if I get called and I win, I win 2000. If I lose the result would be the same (bust).

OTH, with A9s , I would be somewhat less likely to play back with 2000 than with 1200. But if I do as you propose and increase hand strength so that I would play back no matter what, I sure preferred playing with as much as possible up to the amount of villain's stack.

[curtains]

I'd like to know how many players are left and other things before attempting to answer this question, as I believe these are important factors that may affect the villians play.

[ChrisV]

[ QUOTE ]
If i understood you correctly, you would prefer playing back with 1200, because if you get called and lose you lost only 1200 whereas if you resteal the pot the result would be the same.

I would be more happy to play with 2000 because if I get called and I win, I win 2000. If I lose the result would be the same (bust).

[/ QUOTE ]

This has much the same flaw as taking coinflips for big stacks: it hurts you more to lose than it helps you to double up.

In the situation where it's you and the villain with 2000 chips each and 5 other stacks with 1200, here's your fold, successful resteal, and double through equities:

Fold: 0.1825
Resteal: 0.2169
Double through: 0.3163

A successful resteal increases your equity by 18.85%. Doubling through increases your equity by 73.32%.

Same stacks, except you have 1200 and it's one of the other stacks with 2000:

Fold: 0.115
Resteal: 0.1499
Double through: 0.2197

Here restealing increases equity by 30.35% and doubling through by a gigantic 91.04%. Therefore you should be much more willing to resteal with 1200 (making percentage comparisons is correct, since this takes into account what is being put at risk to achieve the gain).

[ QUOTE ]
OTH, with A9s , I would be somewhat less likely to play back with 2000 than with 1200. But if I do as you propose and increase hand strength so that I would play back no matter what, I sure preferred playing with as much as possible up to the amount of villain's stack.

[/ QUOTE ]

That's not quite what I meant. I meant if you aren't willing to play back with A9s at all, ever, then pick a better example for yourself.

There comes a point at which you'd actually prefer them to call than fold to your reraise. At that point, it's a value raise rather than a resteal. But that point comes later for 2000 chips than for 1200 chips (because of the reduced equity gain of a double through). And at all points before that, when it's a true resteal, you should be preferring to resteal with the smaller stack.

EDIT: Just a couple more things:

[ QUOTE ]
If I lose the result would be the same (bust).

[/ QUOTE ]

This is your mistake. The result "bust" isn't the same each time any more than the result "double up" is the same each time. You lose more equity when you bust with a bigger stack.

Also, in the maths above I'm ignoring the fact that a bigger reraise causes your opponent to fold a bit more often. I don't believe this affects the conclusion for a couple of reasons.

Firstly the subset of hands which your opponent might do different things on is small compared to the subset of true steal hands (like QJ) where he always folds.

Secondly, if you do get called, doubling up gives you a bigger equity gain with the small stack than the big one. This cushions the blow of getting called a bit more often.

[ChrisV]

[ QUOTE ]
I'd like to know how many players are left and other things before attempting to answer this question, as I believe these are important factors that may affect the villians play.

[/ QUOTE ]

Can you give an example of a situation in which my theory wouldn't hold?

[curtains]

Well your opponent would be less willing to make a move in some spots and more willing in others, if there were 4-5 players left. Also it seems like with about 4000-4500 in combined chips between these two players, there could be some other game conditions that apply. Give me an exact example (# of players, stack sizes etc) and I'll give my answer /images/graemlins/smile.gif Hurry though, gotta go in 10 minutes.

[curtains]

Oh I didnt read your theory btw, because I wanted to answer on my own before seeing it. Don't like to read too much so I can be unbiased. In my opinion you want to steal most often from mediumish stacks as opposed to small and large ones. I thought this was a reasonably basic concept, but you seem to have given it a different name.

When you steal from a small stack they are pretty desperate, and will move allin a lot, whereas if they are a medium stack the risk/reward just isn't there a lot of the time. A large stack can reraise a lot for other reasons....as the chips they are raising often don't mean so much to them (although when you have 1900 in chips, its almost impossible for them to reraise on a bluff with the idea of folding, so theoretically its not that big a deal)

[HesseJam]

[ QUOTE ]


(making percentage comparisons is correct, since this takes into account what is being put at risk to achieve the gain).

...

Me: If I lose the result would be the same (bust).

You: This is your mistake. The result "bust" isn't the same each time any more than the result "double up" is the same each time. You lose more equity when you bust with a bigger stack.


[/ QUOTE ]

Those are very good points and I will have to think about them....

I probably looked at it from a wrong perspective. Of course it is better if you call if you have 2000 then if you had 1200 because, well, it is better to have 2000 chips than 1200 in first place. But, well, you have what you have and you cannot chose how many chips you have. /images/graemlins/laugh.gif

The mere fact that I said that I would be more likely to call with 1200 than with 2000 in some way says that it is better to call with 1200 than with 2000 in terms of return on equity.

[tigerite]

Yep, good post. I do kind of instinctively follow it, you're right.

[pooh74]

Great post chris!

I just wanted to add a couple of things (and I play lower limits than you so: Disclaimer).

First, at lower limits obviously a lot of game thoery goes out the window as players are playing their cards much more than the situation. But, I would be more apt to give the smaller stack more respect than the larger stack. Where stacks are roughly 1:2:2:3. If you guage the risk of a reraise all-in from the smaller stack at a "1 risk" then, I think the risk of reraise from the large stack is lower...maybe a .75 or less. This might be part psychology, but when at the table, I like to think it by doing simple subtraction.

For example:

4 left:

A: 2000
Hero: 3000
C: 1000
D: 3800

If blinds are 100-200, I would much rather steal from D than C. I like to think D is thinking that a resteal that is called brings him into 4th intead of 3rd so he more apt to respect a raise, whereas:

Same scenario but hero has 2700 and villain has 4100, here, those extra chips still put villain within the top 3 on a loss so you are risking much more by stealing in this case.

In any regard, assessing threat level is difficult because often the absract is not even being contemplated at low buy-ins...but, I think on some intuitive level, most players are aware of these things.

[pergesu]

It seems to me like, at least in this post, you're ignoring one player's "stack efficiency" - your own. Why'd you make that raise in the first place? Your stack is too big to just open push, looks like, so you throw in a raise and hope BB is either very weak, or is multi-tabling and has the check/fold button clicked.

YOU made a mistake with that raise, imo, because you put yourself in an extremely exploitable situation. If the BB is aware of your stack efficiency concept (and it seems we've established that most solid players intuitively do), then he'll use it against you here. If I'm the BB, my thought process is something like, "That could very easily be nothing more than a steal attempt...and he's got a lot of chips behind him, so he'll almost certainly fold if I push." Then I push.

I get what you're saying, and it makes sense, but I don't like your example hand. It seems like you're raising because you have position and it feels like the correct play. But it's hugely exploitable...so I think you could only do it a % of the time you have hands that you'd fold to a push, and have that balance in some way with the times you do that with AA-QQ, AKs, that way your opponents can't resteal knowing that most of the time you're going to have a bad hand.

Anyway to answer your question, I think the most preferable opponent to steal from is a medium-stacked opponent, because they're not feeling tremendous pressure from the blinds (often waiting for the shorty to bust out), and are willing to fold too many hands.

[tigerite]

Indeed it can be used to great effect with a hand you would normally push with at 10bb, but you have 13bb and a stack comes over the top. Something like JJ say, even under some circumstances TT and 99. It's so often they will have A-rag or even worse, and yet they wouldn't have called a push. That's another facet of the theory I guess.

For me, the more intuitive concept (worded in more traditional terms) is a resteal is bad if you don't have fold equity (your stack is too small), or if you'd be making too large of an overbet to pull it off (your effective stack is too large). The flipside being that stealing -from- a midstack will leave you in a tough spot if they resteal allin.

That being said, the candidate villians most ripe for a resteal are also the ones most ripe to be stolen from for the same reasons (chips not worth too much or too little to them)--enough so to negate this resteal risk hero-as-raiser side.

Am I missing the point?