Richard said
Thanks, I used to play a lot 8 or so years ago (ofc then I no real GTO knowledge beyond short stacks) but I had to quit for a while due to stress etc, recently I’ve began taking my game pretty seriously, I opened a few eyes as chipleader of the partypoker NPC day1 chipleader and played a few TV tables and my intention is to work on my game and play semiproffesionally while studying and dancing this spring (50%), hopefully I can plug a bunch of leaks and open some more eyes at live events.

 

When it comes to preflop GTO my understanding of it is pretty much that if a whole table is shoving AND calling GTO pre no one is gaining or losing chips over a large sample, that much is obvious, but I think I may have made a mental mistake making this post.

 

Lets say for argument that villain is folding out the bottom 15% of his nash calling range, the question becomes if we’re better off still shoving GTO since we’re obviously now gaining chips from his mistakes or if we want to shove say another Ax another Kx another Qx and another suited 10x at the bottom of our shoving range to gain more chips. I think intuitively this makes sense, if we shove slightly tighter than GTO and villain calls some %age tighter than GTO we again have chip equilibrium I think, if we shove looser than GTO and villain calls GTO he’s gaining chips and if he starts calling some %age looser than GTO we again have equilibrium

but if we shove slightly looser and he calls slightly tighter I intuitively thing we should have a larger edge than if we shove GTO and he calls slightly too tight. If that’s true I guess the only argument for not shoving wider would be that it’s unexploitable, I’m gonna go think about how to set this up mathematically before I start rambling even worse than I am =P  

Most of the second half of this post is correct (except for your usage of ‘equilibrium’ – if neither player is playing GTO, we’re not at equilibrium, since each player has the opportunity to change their strategy and gain more EV), but the bolded is not entirely accurate, at least not in the way you’ve phrased it.

If an entire table is playing GTO over the course of an infinite variety of hands, then yes, they’ll all break even, provided they don’t end their session before playing their last complete orbit of the table. But if we’re talking about infinite iterations of one specific hand, then players do not break even – profit is distributed by position in that hand. The big blind loses a lot, the small blind loses a little, the button wins a lot, and UTG wins a little.

In order to distribute EV equally, you have to run enough iterations of each individual hand in order to achieve equilibrium on that hand, and then run at least an entire orbit’s worth of hands in order to account for positional variations. Even then, you’re not going to be able to account for changes in stack sizes as hands progress, so it’s not going to be super accurate.

Future Game Simulation calculations on SnapShove, HRC or ICMIZER do exactly this, but they’re hard to do unless you’re short-handed or have a massively powerful computer, and they produce very different results depending on whether you simulate two hands, half an orbit, or a full orbit.

Recognizing that GTO does not equal break even is an important step forward in understanding poker. Recognizing that nobody plays GTO – in fact, nobody even comes close on an overall level, and only a few people barely scrape the surface when it comes to short-stacked situations – is also an important step. You have to study GTO in order to know how far away from GTO you can play in each specific spot. Exploitative play makes much, much more money than GTO, but you simply can’t do it very well unless you have a foundation in the principles of the game.

The Riceman said

My theory on how Nash ranges are arrived at in poker is that they simply represent a range of hands for each position at the table (complicated by ICM and BB level), behind which it is improbable that the range will be beaten mathematically in game, and indeed impossible that it can be beaten long term, in an infinite game. The best we can achieve in response is to play a Nash range, whereby we are now in equilibrium, and indeed the game is now solved, and we can all go find another way to make money and entertain ourselves.

John Nash is considered a genius of mathematics. It is no surprise that this stuff is super complicated.  

Actually there’s a more specific definition of a Nash calculation, and therefore of a Nash range. A Nash equilibrium situation is a situation where every participant in the game is playing in a way that prevents their opponents from adapting to gain an advantage, and a Nash calculation is one that runs enough iterations of a specific situation (with every player exploiting the others) such that the equilibrium is reached.

In poker terms, this means that a Nash equilibrium situation is one where neither player can increase their EV by changing strategy, because any change in strategy would allow the opponent to adapt and gain more profit. A Nash range is a range that would be utilized by the player in question if the situation were at equilibrium.

You don’t need to have your own theory as to how Nash ranges are arrived at in poker – there’s really only one way. You start out with a subset of potential hands (either the entire deck if you’re doing preflop, or a specific preflop range if you’re doing postflop), input the terms of the calculation (bet sizings, stacks, flop cards, etc) and the calculation will do its thing.

That ‘thing’ is to run multiple iterations of the situation (in HRC it’s usually 300 by default, not sure about postflop calculators) starting out with both players playing the maximum possible ranges, and allowing each player to adapt optimally from there until equilibrium is reached – until neither player can do any better by changing strategy.

You can actually do this yourself using HRC if you want to test it. Just run a heads-up push-fold hand with one player locked at shoving 100% of hands, then see what the other player is supposed to call (a wide range). Then lock that wide calling range, unlock the shoving range, and see what the first player is supposed to shove to exploit that calling range. Then lock the shoving range and unlock the calling range, and repeat the process as many times as you like. What you’re seeing when you do this is the equilibrium being developed – you’re doing it one iteration at a time.

When you use a Nash range in-game, you’re guaranteeing yourself a certain level of EV, no matter what range your opponent is shoving (or calling). However, you’re not necessarily maximizing your EV against your opponent’s specific strategy choice – if their strategy is exploitable, then exploiting it by adapting away from Nash will always be more profitable. If you get your adaptation wrong by enough of a distance, you may end up making less than a Nash range would, but if you’re adapting in somewhat of the right direction (i.e. towards tightness or looseness), you’ll usually make more than you would by playing a Nash strategy.

The main takeaway from this is that Nash ranges are defined by a specific process, and by changing the variables involved in that process, you get different results. This is why push-fold charts are literally always inaccurate – if you change a few stack sizes at the table a little bit so that not everyone has the exact same stacks, it throws the multi-way equilibrium off a little bit. Generally every shove chart out there – along with any other method that doesn’t allow you to input specific calculations with exact hand parameters – will be inaccurate by at least 1-2%.