NLHTP#18 The Sklansky-Chubukov Rankings&When and When Not to Use Them

[wallenborn]

The Sklansky-Chubukov Rankings

You are in the small blind in a $1-$2 game. It is folded to you. Your opponent plays statistically perfect poker. Accidentally, you reveal your hand to your opponent. What do you do now? Well, with aces you'd raise, picking up the blinds almost always. With kings, you could still raise, but your opponent would call you with aces and win most of these hands. Since he can bluff you here, if you raise, you might as well raise all-in. That leads to a different formulation of the question: What is the largest stack you could move all-in with, even if your opponent knew your hand. Or even differently: How large does the effective stack size have to be to make folding better than pushing? This size is called your hand's Sklansky-Chubukov number.

(The number is occasionally called the Sklansky-Karlson number, karlson being Viktor Chubukov's user name on 2+2. Here is the original thread.)

As it turns out, some of these numbers are surprisingly large. Of course it is no surprise that you can move in with AK and an M of 110, but for example JTs has a SC-number of $36. So if your M is 12, shoving is better than folding.

There are two major types of hands:

[img]/images/graemlins/spade.gif[/img] Robust hands can be called profitably by a large number of hands, but they don't fare too badly against those hands on the whole.
[img]/images/graemlins/spade.gif[/img] Vulnerable hands can't be called very often, but when they are called, they are significant underdogs.

At the table, your opponent of course does not know your actual hand, he has to put you on a range. The correct calling range against a vulnerable hand is tight and rather well defined, so it is easier for your opponent to call or fold correctly if you move in with a vulnerable hand. If you move in with a robust hand, it is more difficult for your opponent make the correct decision.

For example, A3o and 22 both have a S-C-number of $48. Against A3o your opponent should call with AKo and fold T7s. Against 22 your opponent should fold AKo and call with T7s. Of course your opponent doesn't know your cards, he has to put you on a range and adjust his calling range accordingly. His calling range will much more likely include AKo than T7s. So against an all-in with 22, your opponent might fold T7s incorrectly or call with AKo incorrectly.

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Sklansky-Chubukov numbers always underestimate the real move-in power of a hand. But they underestimate the power of robust hands more than vulnerable ones.

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Robust hands include

[img]/images/graemlins/heart.gif[/img] Suited connectors
[img]/images/graemlins/heart.gif[/img] Pocket pairs


When to (and When Not to) Use the Sklansky-Chubukov Rankings

Adjusting for an Ante: if you divide the S-C number by three, you convert them into numbers in terms of whats in the pot initially.

The best hands for moving in: Moving in is most attractive when S-C proves that doing so is better than folding and you don't have a good reason to play your hand a different way. For example, if you are out of position, against a good, aggressive opponent, and you are looking at a hand that is weak except for its showdown value, say K4o. Then you shouldn't try to play poker. If stacks are deep, fold. If stacks are shallow, move all-in.

Exceptions: There are cases where you should fold despite S-C telling you not to. In a tournament with a very weak and and a very short stack, for example, you should not shove a weak hand if you can see the next couple of hands for free.

Moving in with "Too Many" Chips: With a robust hand, you can move in with more than the S-C number of chips, because your opponent is likey to call or fold incorrectly.

Don't move in with hands that "Play Well" S-C tells you when moving in is better than folding. But it doesn't tell you when moving in is the best move. With a hand that plays well, especially in position, you should play normal poker instead.

[wallenborn]

I'm not sure i got all this robust/vulnerable stuff right. First, robust hands are better hands to push since your opponent is more prone to make mistakes against them. But robust hands are also hands that "play well", so then he says, you'd rather push K4o instead and try to play poker with 22. What gives?

[Jurrr]

Is this all even that relevant for deep-stack cash games?

[wallenborn]

Not sure. The strategic situation is symmetrical, i believe, so if you're up against a short stack you could play as if you were the short stack. I'm trying to come up with an example, but i don't find it very convincing:

Say you're sitting at a table with 100BB. To your left is a short stack with 20BB. You are in the small blind, holding A8o. It is folded to you. Then S-C tells you not to fold, but i guess you knew that already. You could profitably push. But i think most here would do a 4BB raise instead. If he plays tight short stack strategy this will make him fold often, and when he pushes, you can fold. If he pushes often, well then you could raise him all-in instead. But if he pushes very often, he might deviate from the statistically perfect poker the S-C assume him to play. Specifically, if he pushes too often, you'd like him to be in a situation where he can make that mistake as often as possible, so you'd rather not be pushing yourself.

So i think, whenever the stack sizes are small enough for S-C to matter, you'd probably consider a couple alternative strategies, all better than pushing.

[wallenborn]

...and there is of course this thread right next door. MP1 has 50BB and limps, MP2 raises with 20BB behind, Hero has them covered and TT. The S-C number for TT is 257 (86 in terms of M), so folding would be incorrect for effective stacks lower than ~$130. Seems Hero can profitably push here.

But does S-C tell us something we didn't know before?

[fishfinder2000]

The system has its merits. But I think you'd have to be prepared to deal with the significant variance it could lead to when playing with and against full stacks. I wouldn't feel comfortable using the system playing against unknowns.

[wallenborn]

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I wouldn't feel comfortable using the system playing against unknowns.

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I disagree here. You see, Villain's ranges don't appear anywhere in the calculations. You don't need any reads on him to calculate your hand's S-C. So, i think, if i push based on S-C considerations, it's going to be precisely against an unknown. As soon as i have reads on someone, there probably are better options.

[curtains]

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...and there is of course this thread right next door. MP1 has 50BB and limps, MP2 raises with 20BB behind, Hero has them covered and TT. The S-C number for TT is 257 (86 in terms of M), so folding would be incorrect for effective stacks lower than ~$130. Seems Hero can profitably push here.

But does S-C tell us something we didn't know before?

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This is a totally incorrect application of the S-C numbers.

They are much more relevant if you are shortstacking or playing tourneys to be honest.

[wallenborn]

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This is a totally incorrect application of the S-C numbers.

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I should have allocated a few more brain cells to it.

[img]/images/graemlins/spade.gif[/img] In that hand, MP2 reraised. That means his hands are not evenly distributed anymore. Especially, hands that beat TT make up a significantly larger percentage of his range than S-C assumes.
[img]/images/graemlins/spade.gif[/img] Likewise, hands that fold to Hero's push make up a significantly smaller percentage of his range.
[img]/images/graemlins/spade.gif[/img] Same goes for MP1. Also, if he decides to stay in the pot it's three-handed, and the pot odds change completely.

So let's just pretend i'd never had come up with this, ok?

[LearningCurve]

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This is a totally incorrect application of the S-C numbers.

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I should have allocated a few more brain cells to it.

[img]/images/graemlins/spade.gif[/img] In that hand, MP2 reraised. That means his hands are not evenly distributed anymore. Especially, hands that beat TT make up a significantly larger percentage of his range than S-C assumes.
[img]/images/graemlins/spade.gif[/img] Likewise, hands that fold to Hero's push make up a significantly smaller percentage of his range.
[img]/images/graemlins/spade.gif[/img] Same goes for MP1. Also, if he decides to stay in the pot it's three-handed, and the pot odds change completely.

So let's just pretend i'd never had come up with this, ok?

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Forgotten. Leading this stuff every day is a great deal of work. You're doing a fantastic job! [img]/images/graemlins/grin.gif[/img]