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.