Really this is not very difficult to understand but it can be confusing at the same time.

The "Nash push-fold" charts are really a set of charts giving optimal shoving and calling ranges under the assumption that all players are playing optimally if the only options available to each player is push (shove) or fold. Typically they only apply if nobody in front of you has shoved (so you are deciding whether to shove or fold) or only one person in front of you has shoved (so you are deciding whether to call or fold).

And the Nash assumption is that no player can improve their individual EV by altering their strategy (in the push-fold scenario a player's strategy is the player's shoving or calling range).

That is, they are a multi-set of equilibrium strategies. In the SB vs. BB scenario, it is a pair of strategies, a shoving strategy for SB and a calling strategy (if SB shoves) for BB. The BB's calling range is the optimal calling range GIVEN that SB is shoving with his stated optimal shoving range. And, the SB's shoving range is the optimal shoving range GIVEN that BB is calling with his stated optimal calling range. The twin strategies are the optimal "best response" strategies when facing the opponent's strategy. So the twin strategies form an equilibrium pair of strategies. If one person announced their Nash strategy, the other person could do no better than employ their own Nash strategy.

Obviously, if you know or suspect that a player is calling or shoving significantly different from their specified Nash range, then it is typically not optimal any more for you to call or shove with your specified Nash range.

The basic charts are for HUSNGs where both players utilize a pure shove or fold strategy, but you can use software like ICMizer to compute the "Nash" ranges for multiplayer push-fold.

e.g. ICMizer (or Snapshove) can tell you the best jamming range for UTG, and ICMizer/HRC can calculate which range each player acting after him can call with, based on the range that UTG jams in the first place. The moment he deviates from that range, all the calculations are messed up. e.g. If someone only shoves AA at 10bb deep (a weird strategy, but bear with me), then there is no hand that will make money as a call apart from the other combo of AA.
The "Nash" calling ranges for the BB that are calculated with software are based on whatever they think the original shover should be jamming.

EDIT: As an example of ICMizer, here's a hand from a satty that I just played. UTG with about 13bb, I can profitably jam 17% of hands. Most of their EV comes from fold equity. Because of the fairly strong ICM pressure, everyone has to call very tight (most players can only call with about 5.5% of hands) and even with his better pot odds the BB can only call with 7.5% of hands. If everyone was much more stationy, I'd never risk jamming this hand, because my stack is too valuable. (Frequently in the games I play, an idiot will call a jam with something like A3o or 22, when he should actually be calling much tighter).



I study spots like that every day, so I can get a better idea of what optimal pushing and folding ranges look like at different stack depths. As I said before, I make mistakes all the time. Most of the field makes much bigger mistakes though. (e.g. Not shoving often enough, or calling too much).

nash is not gto and its not even close. for example gto vpips about 95% in hu ip 10bb deep (btn is sb), but nash only shoves smth like 50%. in 6max+ w antes settings u can prolly say that gto=nash 10bb deep bc in non hu spots u can prolly never limp. for those situations i suggest icmizer, which also takes payouts and stack symmetrics into account.

Is there a reason why the pushfoldcharts differ from snapshove? I am only using the trial version of snapshove and in one of the examples it ask if its shove or fold


You have about 6bb UTG and have A2s. Well according to pushfoldcharts if you have 6bb, you need a3s+. According to snapshove, a2s is a fold. However... they mention a8s+, a5s


So which chart is the correct chart then? I thought pushfoldcharts was the correct chart but a3s+ vs a8s+, a5s is a bit of a difference. I mean shouldn't all these charts be the same thing exactly?


The thing about pushfoldcharts is it only shows up to 10bb and its 6bb, 8bb, 10bb etc. But snapshove apparently goes up to 25bb. Can someone here confirm snapshove is the best program for this? If so, i will get it but im not sure which chart is the accurate chart.


I also use the floattheturn push fold as well and its definitely a bit different from both pushfoldcharts and snapshove.


So which of these 3 are the best then?


I assume snapshove since not only it tells you what to shove... but i believe it would tell you what hands to call a reshove and isolate based on position? Or does it not do that?


Im curious about this before just buying the app.

Also want to use another example.


With 10bb... you can push a9o + in the lojack position according to pushfoldcharts.


With floattheturn, apparently it seems that a7+ and a5 is a shove. So which is the correct one here?


Also according to floattheturn, you could shove 15bb with a9o in the lojack position. Is that even accurate? That seems just a little bit loose to me? I would think its A10o with 15bb?


I know there is the pushfoldcharts, floattheturn, snapshove and i also believe there is a push fold spreadsheet as well from a while back. But which one is the correct one? Im surprised that its not the exact hands when comparing pushfold charts for 8bb and 10bb when comparing it to floattheturn on the app.

They are all fairly accurate. As I think I mentioned earlier, a more precise solution to push-fold games would be to utilize mixed strategies. So while one chart might say "Jam A7o+", and another might say "A8+ and A5o", a marginal improvement in EV could be gained by jamming A8o 95% of the time, A7o 75% and A5o 45% or something silly like that. Note that the bottom of each shoving range will be breakeven even against rational/optimal opponents, so it's really not worth obsessing about where you draw the line.
All the apps and charts you mentioned are pretty good. In soft games where you have a skill edge you might be better served by playing slightly tighter, both with regard to pushes and calls, in order to reduce variance and to put yourself in more obviously profitable spots.
I've heard good things about Snapshove, but don't use it myself. My own charts are kind of an 'average' of the others, except I go a little bit tighter when I'm far from the button.

Hi there. Well the fact that pushfold mentions you need to shove a9o+ in the lojack position with 10bb... but floattheturn has a7+ and a5... then im not sure which chart to follow.


The thing is i just want to look at one chart and follow that one chart only. So because of that, does anyone know which chart is the most accurate? Because a9+ as oppose to a7+ and a5 is definitely a noticeable difference. The thing though is on floattheturn, you can make no ante which is almost never the case or 12.5 percent or 10 percent. So isn't the ante suppose to be 10 percent almost always? I mean... it would be ridiculous to try to remember these charts when you have to know both 12.5 and 10 percent antes so i would prefer to stick with one only. So that would be 10 percent ante?


So i like to know which ranking of push fold charts is best


pushfold
floattheturn
snapshove
the push fold spreadsheet that i heard about


The thing is pushfoldchart and floattheturn doesn't show you what hands you should be calling with to a shove or reshove. But i believe snapshove does? So does that mean snapshove would say okay if utg +1 shoves 8bb... say you are in lojack... it would tell you what range you need exactly to call or basically reshove the all in? That is what i would like.


But what about that push fold bot chart that i heard about?


Because i want to know exactly the ranges that i should be shoving in the lojack position with say 15bb or 12bb etc.

As I keep saying, it doesn't make much difference. A7o is basically the same hand as A9o or A5o. None of them want to get called, but all have an ace blocker and all have some equity if you get snapped off by QQ.
Pick a chart and see how you get on with it. If villains call "too often", use a slightly tighter range than the chart recommends. e.g. If the chart says the bottom of your in a spot should be A7o, then maybe you'll only jam A8+. It really won't make much difference. The bottom of the range is "breakeven", and the next hand up is only a tiny bit better.

Never knew about the calculate hand range tool. Mind blown!

A9o is really the same as a7o and a5o? I always thought a9o is much stronger than a7 and a5 mainly because if its big ace vs small ace, bigger chance the kicker plays.


Well i just want a standard chart that assumes everything is average.


Also do you believe 10bb vs 15bb is a huge difference when shoving say in the lojack position? Also 86s is a shove with 10bb on the button. But is it with 15bb? That is what i want to know.

A9 only becomes a much stronger hand than A7 if villain holds precisely A8 or 88/77, which isn't very often

They are roughly the same hand vs typical calling ranges. e.g. If villain only calls with 77+, AT+, your kicker is pretty much irrelevant, since you're losing to every hand that calls. If he calls with QQ, then A9o has about 28.1% equity, A7o has more at 28.3% (because it can make some one-card straights that aren't blocked by queens), and A5o has the most at 29.79% (it can make a straight using both cards). If he calls with 88, then you'd rather have A9 (two overcards). If he calls with any ace, then A9 is clearly better than A7. Against the entire calling range (whatever it might be in a particular spot, but especially when it's a tight calling range), the equities of A9, A7 and A5 will all be very close. But you don't want to get called. You're not shoving A7 or 86s for value. You're trying to steal the blinds. Having some equity when called is the backup plan.
Yes, there's a big difference between 15bb and 10bb. I'd estimate it to be about 5bb.
Study the charts. You should be able to see for yourself that there's not a lot of difference between a 9bb jamming range and a 10bb jamming range (both are pretty wide, especially in LP), but ranges are much tighter/stronger if you're making a (much) bigger shove from an earlier position.
I'll repeat, however, that even top players make shoving mistakes all the time, but the mistakes are somewhat marginal in terms of EV, because the profit (or loss) is measured in fractions of big blinds. Learning a 10bb jamming range will give you a decent idea of what a 12bb range will look like, but it's obviously going to be a terrible strategy to shove the same range if you have 30bb or 80bb.