I think this statement is wrong because In a Nash equilibrium the caller would play perfectly too therefore if the shove range changes (as you have done above)then the caller would change his calling range too which will probably result, then, in a lower EV for the shover.

This is what makes it so difficult to evaluate. Any changes from one player result into one from the other player as they are playing perfectly in a equilibrium. You can not change one range and keep the other one still.

no

edit: n/o tho

I like it. Can I call it SSS Equilibrium?

Independant thinking is a prerequisite for greatness, but here you are simply wrong and basically just making a different point.

The Nash-chart is an equilibrium chart, it is not per se THE BEST way to play a HU endgame. What you are referring to and advocating is playing exploitably. The Nash chart just hands you an unexploitable strategy.

If you change your strategy in the way you propose (or any other way for that matter), you may do better than with the equilibrium chart, but you are no longer playing unexploitably. Whether your opponent will (be able to) take advantage of that fact is a whole different matter.

I know this is kinda a lawls question, but if you were raising AA would you raise T7o?

Thanks for starting the OP here spamz, I did read this some time back but never said thank you.

sorry yaqh but why no?

(what's n/o?)

I found those interesting points on the pokerhound website NRT FAQ I thought they might be of interest

"This point is extremely important, please make sure you understand the following concept:
The calculated push ranges are hard to exploit, in the sense that your opponent can not improve his own EV significantly by deviating from the calculated call range. However[....] this does not imply that you will gain EV if your opponent incorrectly deviates from his optimal calling range."

also

"If a hand is in a calculated pushing range, this does not mean pushing the hand is an unexploitable push on its own. The weaker part of the push range will rely on the protection of the top part of the range."

Yeah, you're missing that yaqh is apparently really good at this stuff, so I'm just not going to try to argue with him anymore, cause I always lose.

One important thing to note about differences between nash and chubukov.

Nash is an unexploitable strategy. You can clearly do better against many opponents by adopting a strategy that is exploitable but that they're extremely unlikely to exploit.

But if chubukov tells you to shove a hand, and you ever fold it, you're making a pretty large mistake.

Yes SKlansky Chubakov is obviously profitable but you are missing some value since the basic assumption is that your opponent can see your hand. In reality he doent have that luxury so this must mean that we are sacrificing some value.

the question is why is there such a huge difference between nash and SAGE??? SAGE is supposed to be based on nash..... and what justifies treating 54s so differently from its ofssuit counterpart???

The fact that villain can't see our hand means we gain value since villain can't call perfectly.

SAGE is an approximation made to be easy to remember.

54s is different from 54o because the potential FD makes a big difference when many hands are ahead of it or dominating it.

Bluemage is correct on both points. Sklansky/Chubukov shoves are neutral EV *if villain calls perfectly*. It only goes up from there, because every hand he folds that he shouldn't gives you +FoldEV, and every hand he calls that he shouldn't gives you +EquityEV, because your hand is a favorite.

Now, shoving might not be the *best* play with a hand that chubukov numbers tell you are shovable, but folding is clearly worse than shoving, so you should never ever fold.

And sage is an approximation that approximates hands like 45s very poorly.

you seem to be confusing 'equilibrium strategy' with 'maximally exploitative strategy'. maximally exploitative strategy is what it sounds like it is. it turns out that if you're playing nash, your opponent's maximally exploitative strategy is to also play nash. this is what we mean when we say that if you're playing nash, villain can't increase his eV by deviating from it.

but anyway, an equilibrium strategy is an unexploitable strategy which (neglecting the fact that some games have multiple equilibria) is something of a static thing. it's a property of the game. if you change your opening range away from nash, then villain's maximally exploitative strategy changes, but the equilibrium doesn't.

no offense

i doubt that's the reason. equity difference is small. the reason probably has to do with combos (4 versus 12)

No, that is the reason. When you're talking about small edges, 2% means a lot.

you do realize that 54s is a shove at 20+bbs and 54o at only 2.1bbs right?

look at it another way. K5o has more equity than 54s pf. yet K5o is only a shove at 14.2bbs.

what to shove isn't always about equity.

Sorry for my poor explanation. I meant we can push hand X with S-C rank Y for more since our opponent cant see it. So if the S-C value is 18 we could probably still shove it with 19 and be +EV instead of folding it. If we fold it with 19 we sacrifice value.
In the original book I remember reading through this exact point.

K5o has more equity against what range exactly?

Yes, it is about equity. If K5o had better equity than 45s against the calling ranges, then it would be higher on the table than 45s. Period.

This is true. S-C numbers are basically just sanity checks. You should never ever fold a hand that is a shove on the SC table. But you can obviously shove hands profitably deeper than SC numbers against just about any opponent.

i'm just guessing, but i think you're not accounting for the calling range.

it's likely that 54s does better against the calling range than k5o.

edit: oops, thread is active, tnixon beats me

READ page 1 for differences between suited and offsuit. Spamz exlpained it so well that even a non maths guy like me totally understood. It has nothing to do with making flushes.

i think the thing about shoving suited hands because there are less combos has some truth to it since if we shoved more 5x4x hands, then villain's range could include more 56,57, etc type hands, and then none of the 54s would be profitable.

but at the end of the day, it's definitely about the equity. shoving 54s for 20bb is +eV against the nash calling range (relative to folding), while shoving 54o isn't.

let me put it yet another way in response to your question about ranges.

if villain is calling with top 20% up to 100%, then K5o is better than 54s equity-wise when called.

if villain is calling only with top 15% or better (i stoved ranges of 15%, 10%, and 5%), then 54s is better than K5o equity-wise when called.

but here's the thing: 54o and K5o have roughly the same equity against a very tight calling range (top 15% or better), yet K5o is a shove at 14bbs whereas 54o only at 2bbs. So this isn't just about equity when called.

Yes, 54s forms less combos and has a few % more equity, obviously its a completely different hand. However is it that much different that it deserves to be shoved that much deeper?

(maybe your opponent will assume u do this with 54o as well thus far more often in terms of combos and will incorrectly readjust his range so you gain more on your stronger hands making this strategy inexploitable... just an assumption)

who cares about top 15% or top 20%? we're talking about the BB nash calling range at 20BB which is:

33+,A2s+,K9s+,QTs+,A5o+,KTo+

and you can see very clearly that 54s is significantly better than K5o vs that range:

5,362,936,128 games 0.005 secs 1,072,587,225,600 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 67.774% 66.84% 00.94% 3584436912 50213514.00 { 33+, A2s+, K9s+, QTs+, A5o+, KTo+ }
Hand 1: 32.226% 31.29% 00.94% 1678072188 50213514.00 { K5o }



1,897,232,832 games 0.043 secs 44,121,693,767 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 63.865% 63.43% 00.44% 1203369304 8294644.00 { 33+, A2s+, K9s+, QTs+, A5o+, KTo+ }
Hand 1: 36.135% 35.70% 00.44% 677274240 8294644.00 { 54s }


---