I know they're all about balance and ranges but do they ever play hands that are mathematically -ev in a vacuum in order to achieve that balance . Or do they literally profit in every situation ?

All hands that get opened are 0+ EV; no -EV hands get opened preflop.

At the Nash Equilibrium the highest EV action is always taken. If multiple actions have the same EV they can be mixed for balance purposes, but since folding is considered 0 EV a -EV action will never be taken at any frequency. This all assumes the opponent is also playing a Nash Equilibrium strategy.

The Nash Equilibrium doesn’t take into consideration opponent tendencies, game flow, etc. It will still 3-bet A5s vs a nit who’s chips have a layer of dust on them. In that sense it will take -EV actions, but from a strategy vs strategy perspective it’s unbeatable.

Solvers attempt to approximate the Nash Equilibrium based on the parameters you give to them, like allowed bet sizes and ranges for each player. Since they are only approximations they can take some -EV plays, but that’s not by design.

what about bb hands and sb hands where you're -ev for less than you already have in the pot?

Folding in solvers is 0ev. If you defend a hand from the bb that means it has ev>0 (ev play > ev fold).

ok a slightly related question at the micros is it ok to sacrifice balance and forgo playing a hand that charts say i should play but is losing money so far? For example poker snowie the free version says to RFI QJo utg 24% of the time. That exact situation appears in my DB around 70 times and im lossing -17.74 BB/100. So should i give up on the hand or is the sample size still to small ?

70 hands is a completely worthless sample. You will never realistically get a sample size big enough to determine if specific near-breakeven hands are profitable from specific positions. Even a lifetime of play might not be enough.

I thought the rest of the thread covered that you don't play -EV hands for the sake of balance though. If you think QJo is a -EV LJ open for you then just fold it. Always take the highest EV action for your specific hand.

I figured as much but how many samples of that exact situation would I need ? The main reason I learned preflop charts and study pokersnowie and now zenith is because someone else has put on the leg work some might call that lazy or cheating but I could play for the rest of my life and not get a large enough sample of say 3betting AQ In the BB versus a CO 2 bet and a button call

Someone with better stats knowledge than me might point out where I'm wrong or have a better method, but I would get an estimate of the standard deviation out of pokertracker and calculate the size of the sample required to reach a desired confidence interval.

Since your sample is small and we only want an estimate you could group similar hands to get the SD stat for that group when you open. If it's 500BB/100, for example (no idea if this is close to what it would actually be), and you observe a win-rate of 10BB/100 with the hand that you want to know about, the 1 standard deviation confidence interval takes 250,000 hands to get to +/- 10BB/100.

1*500/sqrt(n) = +/-10
n = 250,000

If the you are looking at something like a suited connector UTG that's 4 combos out of 1326 and 1 position out of six, so your total sample would need to be 250,000*6*1326/4 = 497,250,000 hands to be about 85% confident that your open is profitable if you observe a win-rate of .1BB on average when you open that hand.

You could grind 24 tables full time every day for your entire life and still not confidently know whether 98s is a profitable open from the LJ. And over the course of that amount of time the games will likely be totally different and the sample you modeled after won't really be relevant anymore. There are probably methods to analyze this spot better, like looking at similar hands and extrapolating, but you need a lot of hands.

There might be a better way, but the point is that a hand on the cusp you will just never know, and a hand not on the cusp is clear enough that you don't need statistics to know it's a profitable open. I would just use charts as a baseline and adjust based on game conditions rather than try to use database analysis on specific combinations of hands and spots. Database analysis needs to be more general.

I'm not going to comment on the actual hand - but solvers are saying you should open hands that are going to be more profitable than folding. However, they are only as good as what you input - so there will be some deviations from solver solutions for players because either you play worse than the solver postflop thus won't actually be able to show a profit, or because the rest of the pool plays so far off solver solutions that it no longer becomes profitable.

For example, in most games rake starts postflop, so there is lots of advantage in raising preflop and winning the hand pre - and in solverland this happens far more often than in microstakes. In microstakes, when players are calling far more than they should, there will be some hands we don't really want to raise and go 4way multiway when most of the profitability comes from being able to open and win preflop.

There will also be hands that are very marginally +ev, and if you don't play well enough postflop you just won't be able to show that profit.

So basically a GTO chart/understanding of preflop is useful, but then you need to also have the poker awareness of when to adapt (for example, the solver will tell you to raise X% on the button vs two solver blinds but if they are two 70yr old nits, you'll be able to show a profit raising 100%).