Beyond Sklansky-Chubukov

[BluffB]

In his book NLHTAP, David Sklansky asks (and aswers) the question of what is the biggest stack we can profitably go all in with if we accidentally flip our cards over when being on the small blind in heads-up situation.

I played around with this intriguing idea just to come up with another very similiar problem that I believe to be much more realistic.

Instead of flipping over our cards, what if we just told our opponent (before looking at our cards ourselves) the range of hands we are going to go all-in with? What would then be the all-in range that maximized the expected value (for some fixed stack size)?

So, instead of knowing our exact cards, our opponent would only know the range of hands we are moving in with. All other factors would be identical to the problem presented by Sklansky.

This would be more realistic because against observant opponents they may very well have a good idea of the range of hands we are playing with, but unless we actually do flip our cards over they are still not going to know our exact holdings in any particular hand (assuming of course we don't have any obvious betting patterns or other tells that would reveal our cards).

For the sake of simplicity, I suggest the range to be defined in the order of the Sklansky-Chubukov rankings.

Has anyone tried to solve this kind of problem before?

If so, I would like to compare the results I got from my calculations and make sure I didn't make any mistakes. And if not, I'd like to hear what others think of the idea and if it would be worth to study it further and publish some of the results I got.

[Bang584]

Interesting... I'll crunch a few numbers.

[Magic_Man]

I was just searching the archives for S-C stuff yesterday, and came across something like this that was proposed. I'll look for a link.

~MagicMan

[Alfil]

Unless I am not completely understanding your idea, wouldnt this be covered under calling all-in raises in the previous chapter? So if you tell villain what your range is preflop for going all-in and than stick to your word after looking at your card, villian simply has to compare your range to the pot odds for that range to determine if calling is profitable or not.

[BluffB]

You are absolutely right that that is how I assumed the opponent would be playing.

However, the question I was asking was what should our all-in range be if we wanted to maximize our EV (assuming our opponent plays perfectly like you described).

[Al Mirpuri]

Who is Chubokov?

[Daisydog]

I've got a spreadsheet where I can type in the hand range of either the pusher or the caller, stack sizes, and blinds. It will tell me which hands have a +EV for calling (against the pusher's range) or pushing (against the callers range).

[prinsrob]

bump, has this been done already?

[Mark1978]

AKA Karlson on 2+2.

[mvdgaag]

The SC ratings are flawed unless you are playing against a random hand. You should look up the rating of your hand against his calling range, which is what you are trying to do. This will determine your range to go allin with.

This is why a hand like A9o does well in SC rating, even though it is dominated most of the time. 45s is a better allin hand imo while it does no do very well in SC ratings. This while A9o has a rating of 81.7 45s had only 4.85.

Against AA-JJ, AK-AJ, KQs... 45s has a 33.5% equity and A9o 27.5%... See how this does not correlate to the SC numnbers? The part after the explanation tells you when to use the ratings and when not to.

GL