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This example comes from Sklansky: Suppose you are in a very loose wild limit game, where seven players (other than yourself) call for the maximum four bets on every hand. Sklansky then asserts that you are a statistical favorite if you call with only AA, KK, QQ, and AK suited, and recommends playing those hands. Basically his level 1 hands. I accept this as given.

Sklansky also concedes that you might do well by playing a few more hands, perhaps JJ, AQ suited, and AK offsuit but recommends against it. His reason is that the "average" value of these three (level 2) hands is much lower than the average value of the four hands he recommends. Here, I agree with his premise. But as will be seen, I disagree with his conclusion.

The reason is, you need AA and KK just to cover the blinds (in the above example). Your NET wins come from your "marginal" 10 hand combinations, the four AK suited, and the six QQ.

The three other hands I mentioned aren't much worse than AK suited and QQ. They represent 22 hand combinations, and let's say that in the aggregate, they are 10% worse, so they are equivalent in net wins to 20, not 22, combinations of the AK suited-QQ variety. If my example is correct, I've TRIPLED my potential NET wins.

Was Sklanksy right to base his recommendation on "average" hand values? Or am I right to recommend playing the three more "marginal" hands?

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IMHO, only QQ and AK suited are truly level 1 hands on the "Sklansky" continuum. I'd call AA and KK "Super 1's," they're basically "off the charts" compared to other hands. – Tom Au Apr 22 '13 at 23:32
It would be interesting to have the exact source of this example. Would you mind adding the book and the page number to your question? Thanks! – azimut Apr 23 '13 at 9:12
@Azinut: I believe it was Sklansky and Malmuth (Hold 'em for Advanced Players). I have since lost the book, but believe that the example was toward the end (last one-third or one fourth). – Tom Au Apr 23 '13 at 12:20
up vote 1 down vote accepted

I'm assuming you are playing against 7 players who never fold and always raise if possible, on all the streets. Then any hand with an equity > 1/8 = 12.5% is worth playing. The blinds have practically no influence, since they are tiny compared to the huge pots.

I've played a bit with PokerStove: The best hands are AA (38.8%), KK (32.9%), QQ (28.3%), AKs (24.9%), JJ (24.6%), AQs (23.3%), KQs (22.6%), AJs (22.1%), TT (21.7%), AKo (21.6%), KJs (21.4%), ATs (21.0%), QJs (20.8%), KTs (20.4%). So all these hands are clearly worth playing. Also, it's interesting to see the high value of suitedness in these multiway pots.

The results are surprising me a bit. I didn't expect the >12.5% range to be that big. It goes down to 22 (13.2%), Q2s (13.2%), 53s (12.6%), T9o (14.1%), for example. However, since the range consists of suited hands mostly, it looks a bit larger than it really is (the ratio "suited hands to offsuit hands" is 1:3, generally).

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