Hiya

I’ll briefly mention that GTO based strats can potentially be losing strats against some types of players in a multiway scenario. What I want to know is: is this one of them? And if it is / isn’t, is there a way to figure this out concretely by yourself via some rule of thumb?
Okay here’s the spot:

UTG opens with a slightly nittier range than GTO dictates. He plays GTO for the adjusted ranges for all further actions.

BB plays GTO vs the UTG raise, as if UTG was playing true GTO. BB then plays GTO for the adjusted ranges for all further actions

True or false:
1. UTG’s nittier range (compared to the UTG GTO range) causes BB to lose money when he 3bets.
2. UTG’s nittier range (compared to the UTG GTO range) causes BB to win more money overall.

1. False, BB 3-bets will still be +EV versus call or fold. I think you mean “will win less money” and that is also false. The only player losing EV here is UTG since he is open raising less often.

2. True.


I think maybe you might better describe UTG as a nit who 2bets only for high value hands and hardly ever folds to a 3bet from the blinds. Such a player will have a range tilted towards value, and loses EV preflop by playing tight and loses EV post flop by not having enough combos for bluffing at a majority of flops (that miss his range).

Just my 2c. Did I mischaracterize what you meant for UTG?

Now, ON THE RIVER, if UTG hardly ever bluffs and hates to fold, GTO could lose some money, absolutely true.

This is because of all the extra value combos in UTG range, and GTO should not try to defend in balance against an imbalanced player, on the river.

Imagine UTG only opens aces. Does BB make money by 3-betting into the nuts?

Hey Arty!

Yes, you are correct. If UTG only ever places bets on any street with the nuts, then any player who ever raises will lose money. I suppose it depends on how we characterize what level of nit we are dealing with.

If UTG is just tighter, but does have some hands that can bet-fold, then BB will have at least some profitable 3-bets, and will give up some EV preflop versus UTG nit, but will recoup this EV on later streets since UTG will not have nutty hands or draws often enough to make it to the river.

At least, I think so.

What do you think, Arty?

I think it depends.
It depends what villain's range is, and how each hand in our range does against that range. e.g. When we have aces, we print money against a nitty villain that doesn't have much air (because our value bets will get called more often if he isn't folding). When we're at the bottom of our 3-bet range, we're bloating a pot we're unlikely to win. Exactly how it all pans out is too complex for me to calculate, since different starting ranges result in different post-flop "solutions".

I admit I didn’t consider the effects of less board coverage on EV. I’d think though that with solid but nitty ranges, BB makes less money with his 3bet vs this nit, than he would make vs a GTO player.

What I’m slightly confused on is whether he makes more money or not in general. See below:

All five other players pick up some EV from UTG when the UTG player folds a hand he should’ve opened. Since now a hand that must 3bet or fold vs an UTG raise, can now be opened since UTG open folded. let’s say the EV lost by UTG is 1.

This figure is divided by 5 players (unevenly, since BTN has position and blinds have better pot odds). So maybe BB gains 0.21.


But when UTG 3bets and loses money, he alone suffers the cost. So maybe EV of 3betting nit + EV gained when nit open folds pre = net loss for BB?

Don’t think this makes sense though, because every other position suffers this dilemma. And in a scenario of GTO play vs non GTO play, the imperfect player must lose.

So EV of 3betting nit + EV gained when nit open folds pre = net gain for all players regardless of position?

It's somewhat trivial to prove in a HU game that a nit loses to a GTO player because the nit folds hands that are +EV, thus donating all the dead money, but it's obviously much more complicated in a 6-player game.

I'd imagine (but I'm not entirely sure) that in 6-max, the BB still gains more than enough from getting walks to make up for any losses he sustains when he 3-bets light into a tight range.

e.g. Suppose the nit doesn't open AJ, KQ or JTs. Every time he folds those UTG (and no one else plays), the BB picks up all the dead money without having to battle for a share of it. Since the BB gets so many walks, it doesn't matter that he occasionally loses a bunch when he 3-bets into KK+, because the monsters are rarely dealt to the nit in the first place (he's literally folding much more often than raising/4-betting), and they also block a chunk of BB's 3-bet range.

When UTG overfolds, though, the problem is that it doesn't translate into BB getting a walk--much more likely is that the players between UTG and BB now have profitable plays with the (weaker) parts of their range that they would have folded to an UTG open but can now play. The frequency of the times this happens clearly depends on how many other people are in the game, but the point is that UTG overfolding might just be making the other positions more profitable without helping the BB at all.

^^^^ this is exactly my point.

The counter to that though, is that the table as a whole must gain from UTG’s deviation. Imagine if we were looking at MP instead of the BB. Does he lose money overall because of UTGs nittier range? If the answer is yes, then we can extend this question to all positions other than BB’s and at some point someone must gain from UTG’s deviation or else the theory is wrong.

Thinking about it more, I think BB actually gains the most +EV from a nitty UTG open as he can get a walk, but all other positions must put money in to maintain their equity share.

So MP probably gains the least from a nitty UTG open. Or the small blind. But is this a net positive for these positions?

Or should the GTO middle position range always be +EV vs UTG’s solid but nitty deviations? Not sure we can ever really answer this, but to get everyone’s opinions would be interesting.

Can we approximate this with raise only strats where everyone is 20bb deep maybe? Then everyone can raise or fold to 3bb and 20bb

Possibly we could look in the database and compare EV when UTG opens vs EV when UTG folds, and check this for all positions. But this needs a huge sample size to be accurate. And of course we don’t have a record of the EV drop when we 3bet a nit.

I hate to post this again but it’s super relevant and the inspiration for this post:
http://blog.gtorangebuilder.com/2014...at-it.html?m=1

If you see the example used in that link, and work out why SB loses EV from BTN’s deviation, I think we could get close to answering original question.


Looking at the link some more ...would it be possible that every position loses EV vs a nitty UTG open except for the BB, who gains massively?

The BB 3bets a very narrow and super strong range to begin with so it doesn't really care how nitty UTG is, the effect is likely marginal. CO and BU will be hurt more because their 3bet ranges are wider.

From looking at the push-fold example in the link, I think that you are correct. If the BB gets to close the action with a call, then mistakes earlier in the hand can only help the BB. Really stinks to be stuck in the SB, however.

The bolded is actually not true--everyone's EV staying the same is a theoretical possibility. In addition, UTG's EV staying the same while shifting EV around between the other players is a theoretical possibility as well. Any shifting of EV that doesn't result in strictly more EV for UTG, the deviating player, is theoretically possible.

So for example, the following is theoretically possible: UTG loses EV by passing up profitable opens, but gains it back when he faces 3bets while having a stronger range than GTO; meanwhile, people who 3bet UTG with a GTO range are losing money on every 3bet of UTG, but gaining it back by having more profitable plays (either opening, or 3betting someone else) when UTG folds a hand that should have been an open. It is actually theoretically possible that all these gains and losses could cancel out for every player.

(At the same time, UTG deviating means that now the OTHER players can theoretically deviate from GTO in a profitable way.)

While it’s true multiple different strats can exist that GTO cannot beat, I don’t think UTG reducing his RFI is one of those spots ...but I guess I have nothing to back this up. Nice COTMs btw.

The best way to answer the question of “who loses most” in the nitty UTG scenario is probably with a toy game.

Based on the scenario in the link I posted and the comments of others here it sounds like BB will definitely gain the most, and everyone else who VPIP the most vs an UTG raise will suffer. So MP may actually fare ok.