The answer to the 6 questions is that they're all guaranteed to be +EV jams. If you ever openfold K3o at 10bb or Q5o at 7.5bb, you're losing money in that hand compared against openshoving, period, no matter how loose or tight or downright weird his calling range is. And that's useful information. Sometimes we know our opponent is calling looser than NASH, but NASH doesn't tell us if we can still jam our hand and be +EV despite that. Chubokov is a quick place to check to confirm that yes, in fact, just because your opponent is a weirdo and you can just feel yourself about to be snapped off by Q6o 7.5bb deep, you should still go all-in. The power of your queen high makes it so even if your hand was flipped up, it's still a jam.There are two reasons why it makes more sense with these type of hands and not the others.1) The hands that are deciding whether to call or fold are basically flipping against us anyway, and it doesn't make a big difference whether they call. In the case of K3o 10bb deep, chubokov allows our opponent to call with 54s - crazy! - but him getting it in with 47% equity or folding preflop doesn't really matter that much to us. It makes Chubokov's number off, practically speaking, but not drastically. That's much different than when we jam 65s and our opponent calmly snaps us off with 76o and has 63% equity instead of folding preflop.2) There aren't so many of those hands that can make cheeky superuser calls when we have K3o when compared against 54s. 54s has all weak 6x, 7x, 8x, 9x, Tx, and Jx that are inexplicably calling off a jam. That's a ton of hands. K3o just has some random suited connectors which is a ton less combos. Fewer ridiculous calls from the model means it's more practical to apply it.(still more to come...)

Based on this, when deciding whether to go all-in from the button, we should only really care about what Chubokov has to say when...1) It's not completely obvious. Nobody needs to tell you that you can shove jacks.2) All-in isn't clearly dominated by minraise/call.3) Our hand doesn't make Chubokov ridiculous, as per above.Given that, here's probably the 25 most important hands to have a general sense of from the table: Basically, this is just a "sanity check" for when you're playing against a loose opponent and even though NASH says it's a jam, you're not sure if it's a jam against his calling range. Chubokov says, "don't be a nit. It probably is". Kx can be jammed 10bb deep for sure and jamming K4s is better than folding up to 15bb for sure. That's useful information when you're deciding on those light shoves 10-15bb deep.

One last thing. There's something pesky I've been adding to everything: "Better than folding". Since we're not folding with a ton of these hands ever, it's a ridiculous comparision. Still, we should be pretty familiar with this by now: NASH has the same restraint, telling you how deep to shove before folding is better. That's why chubokov is best used to comfort people who are thinking about folding weak Kx hands and Qx instead of jamming versus weird opponents - it's a fair comparison and extremely strong proof.An additional summary that I pretty much agree with everything except for some minor points is here:http://forumserver.twoplustwo.com/185/heads-up-sng/finishing-opponent-he...Questions?

"better than folding" is a pretty weak criteria. Lifetime over about 1500 hands of A2o-A5o on the button 15-20bb deep, I have an expectation of about a quarter of a big blind in the positive - That's over 0.75bb better than folding, a massive difference. True, this is against the whole range of opponent tendencies, but go ahead and run the numbers for an openjam of A2o 18bb deep against what calling range you think is appropriate. I would be surprised if the expectation wasn't <0bb from the start of the hand.

:) Good stuff.

I wonder if a "0EV Chubokov" table would be useful - the deepest stack you can jam and have positive expectation in the hand, not just better than folding. This seems to be to be a very good comparison to limping and minraising, which is realistically the fair alternative for most of these hands. The only thing is that generally Chubokov is useful as a sanity check [I don't have to say it's not a strategy again, do I?] jamming mediocre hands against opponents who are too loose, and against people who are too loose, limping and minraising often aren't options because they'll be very aggressive against them. I think it might be useful against loose passive opponents, though. A lot of the time I'm worried that my opponent is calling shoves really light but is also really passive versus limps and minraises so even though it's +EV shove, I don't know if jamming or limping might be better.0EV Nash might be similarly useful - how deep can I jam a hand and still have positive expectation against the NASH calling range at that stack depth? That seems even more applicable especially against passive players where limping and minraising are very much options.Any interest?

HHMiner: I'm in love. Thanks for doing all this work. I have another project I'd like to work with you on - 0EV shoves versus practical calling ranges that we devise. I think that's going to be the most valuable in terms of actually using it to make gameplay decisions.

A,KK-22,KQ-K7,QJ,Kx6x,QxTx-Qx9x,JxTxI think that's a much more reasonable calling range 11-12bb deep than NASH's, which includes JTo, QTo, K4s, K5s, Q8s, J9s. When we use that calling range, the strongest suited connectors really start to shine.

Yes.I still would advise you to forget Chubokov completely because it's doing you more harm than good. But not to beat a dead horse :)

Cog is wrong.(I'm wrong about stuff too. It's OK to be wrong).