Talking about the Nash's push fold ranges with respect to payouts, stack sizes and blinds.

Picture the typical PokerStars scenario in a 6max S&G with top 2 places paid.

Hero(BTN): 1800 Q4
Villain1(SB): 3600
Villain2(BB): 3600

The blinds are 100/200.

Nash equilibrium's shoving range is only 16.7% or {22+ A7s+ A5s-A3s ATo+ K9s+ KJo+ Q9s+ JTs}.

A very tight range IMO as the other two stacks will rarely ever confront and you'll be out of the game in 6 orbits (18 hands) if you don't make a stand. IMO any fold-equity at this point should be considered making an all in move.

Am I wrong to think that I would shove here a range much much wider than Q4s? None of the other two stacks will want to call unless they have a real hand and even then you still have live cards most of the time.

On the flip side (same blind levels):

Villain1(BTN): 1800
Hero (SB): 6300 84
Villain2(BB): 900

Nash equilibrium says to shove any two from the SB. Your fold equity is almost none here as the Villain2 knows he will be blinded out of the money if he doesn't make a stand. However, even if you fold your SB to the SS, you can still successfully shove almost everytime from the BTN when the SS is SB and the medium stack is BB. The former hoping the BB will have a hand to confront so he can walk ITM with a short-stack, while the latter knows the SB is about to get blinded out.

Nash is an unexploitable range, not an optimal one. Optimal ranges are dependent on your opponent's ranges.

I am having a hard time understanding "unexploitable" and explaining it.

I tell someone that shoving KTs from the BTN when in X-MZone, you are unexploitable. "But what if he has just one ace and calls you?" - "what if he calls and sucks out".

Nash tells you to shove 89s is some positions where it also tells you to shove A2o. Both hands will be behind when called but A2 will be WAY behind and 89s will be live most of the time.

unexploitable means that if your opponent calls wider or tighter than the range NASH suggests vs. the range you shove he will lose money. he can't exploit your range.

if everyone would play NASH everyone would break even over the long run. (assuming no rake)

depends on the definition of exploiting
yes, caller wont make money vs nash, but u might neither. Assuming that i have better rakeback than you and/or bigger bankroll and/or better mindset, wouldnt that be exploiting your play by making loose calls costing both of us money?

for me unexploitable push is when there isnt a calling range that makes my push -ev

As I understand it, the point of shoving a Nash equilibrium range is that it gives us a good default rule when we haven't played enough with a given villian to know exactly what his/her calling range is. In that scenario, we can usually shove a Nash range and figure that we aren't making too big of a mistake.

If, however, we know that our opponent is calling off either much wider or much tighter than Nash, we need to adjust our shoving range to exploit their deviation. I.e. if they call too tight, we shove a wider range... If they call too often, we tighten up.

add to that the fact that icm/nash is extremely lacking for short stacked situations. Nash can defintely be "wrong"

thats not what unexploitable means dyboss, at least not from a game theory standpoint. Some who calls you too wide and makes you lose money isnt exploiting you. Hes making your shove unprofitable at the cost of making an unprofitable call.

The only way to do that is to push only AA. That's a very -ev plan.

^no

the better question is when the f it is right

Yup. Nash is an unexploitable system within the evaluation criteria is measuring. If I tell you that shoving equals tomato and folding equals orange, and you want to maximize vitamins, it will only tell how to best maximize results within the scoring it gives. Donks don't care about equilibrium pushfold, so equilibrium is different versus these players because they don't evaluate decisions based on ICM.

Also, since pushfold ICM ranges are a flawed concept, it is guaranteed to give you incorrect ranges even if we assume both players are using ICM equilibrium. Whether or not ICM pushfold is better than other methods for evaluating tEq is another question. For now, ICM is the best answer for many spots, unless we have good reason to believe it is wrong.

+++ these ones

Damn, I write all of that crap and you beat me to it with this much better 1 sentence response...

Nash is only really useful 2 way without ICM factor. If you shove according to Nash HU, and your opponent deviates from Nash calling strategy he will be losing. But then again you can limp minraise and do various stuff which will show much bigger profit than such a limited strategy as "Nash push/fold" HU.

3 way with ICM in play someone can change his range in such a way that we both will be losing money if we shove according to nash suggestion (if he calls too light for example), and third player will be taking advantage of our collision. Notice how this is different from HU scenario, where we were increasing our EV if opponent deviates from Nash suggestion. It usually means that Nash push/fold strategy is pretty useless in any real tournament games outside 2 way HU spots against strong players.

As for original OP question: nobody is calling according to nash, so using nash shove ranges is always wrong, compared to using optimal range which is calculated using real ranges of opponents.

This is called unspiteable.

Unexploiteable = villain cant make you loose money, without loosing money himself.

Unspiteable = villain cant make you loose money, no matter what he does.

For me whenever I used the Nash range to shove with 4 to 6 people remaining in an S&G, 90% of the time it gets folded. Even when I shove a hand too strong to shove like 99 from the BTN. I mean why try to extract value and let hands like KJ or QT catch up?

Also, when Nash tells you to shove 98s, does it take into account that T4o will automatically fold? Or when it tells you to shove ATo (but not A7) and also JTs... does that mean Q6 will fold to your JTs shove?

I noticed that whenever I deviate even a bit from Nash, I get burned. I get insta-called and either cracked or lose the flip.

Also, when someone is min-raising from the CO/BTN 80% of the time and folding to 3bets most of the time, I still use the Nash shoving range as if I was the first one in the pot. More money to steal imo.