Sklansky-Chubukov: How much of an underestimate ?

[wagon30]

The only nash equilibrium I can find where SB is pushing 100% of the time is at the SC number 1.825.

The SAGE system might interest you:

http://www.cardplayer.com/magazine/article/15250

[JocK]

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For the record, I do think equilibrium ranges are important, in some ways probably more important than SC numbers, but I hope I have shown that they don't strictly trump SC numbers as they contain different information.

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Despite all the long posts, I think we basically agree.

May I summarise as follows:

A strategy based on SC-rankings is not exploitable by any opponent of any skill-level even if this opponent is equiped with X-ray vision.

A startegy based on Nash equilibria is not exploitable by any opponent of any skill level (provided he/she is not equiped with supernatural skills such as being able to look through your cards).

One thing that must have caused confusion, is that my calculations contained two errors (one discovered by Alan Brown). After fixing all results makes sense (including a calibration to the SC numbers). (see: http://www.google.com/base/a/1121639...19402030267222 )

Thanks for the discussions and the excahnge of thaughts (it really helped me progressing some ideas that were initially rudimentary).

[JocK]

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The only nash equilibrium I can find where SB is pushing 100% of the time is at the SC number 1.825.

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I agree!

Up to a stacksize of 3.4 times the small blind, SC-numbers and Nash equilibria agree (they have to as SC derives a 100% BB call range).

Above that value (hands 92o and better) NE and SC start to disagree (with NE demonstrating that strategies more agressive than SC are even more profitable yet unexploitable).

Thanks for the link to SAGE. I was aware of this strategy, but can't find (nor reproduce) the game-theoretical calculations that led to this system. (At the moment I am more interested in the 'why?' than in the 'how?'...)