Two part question


1. If I play an exploitable range (e.g. overbluffing/underbluffing or overcalling/undercalling) vs a GTO range that isn't unadjusting to my exploitable tendencies, am I losing EV compared to if I play GTO myself.

I think I ran a sim a while back and it showed that if a player is betting polarised on the river and keeping the bluffcatchers indifferent (so at equilibrium), but villain is either overcalling/or overfolding, the non GTO player is playing a losing strategy. Where does the EV lost come from.

Otherwise where is the edge from GTO player if it's not adjusting to an exploitable strategy. This isn't scissors, paper and rock where GTO is breakeven against every strategy, in poker GTO is supposed to be winning against non GTO strategy right?

Even if you use a static GTO range and don't adjust to your opponent, your overall strategy should still be winning...



2. At GTO, most bluffs are 0EV, but blockers could be +EV due to card removal. If a bluff is +EV, it would be 100% in the bet range right? The only hands that are range mixed (e.g. bet 70% check 30%) are hands that are indifferent at 0EV. Is this statement correct?

1. Yes you are losing EV if you play anything remotely exploitative when compared with (instead) playing GTO.

In theory, any edge gained by playing completely GTO is indirect, as the edge is gained when villain makes mistakes. In essence, GTO is a method of perfection, and only thrives vs imperfection.

2. Sometimes a +EV bluff can be bluffed at a 100% frequency, however it is situational, as there are times where a +EV bluff becomes -EV due to you (thereby) overbluffing.

P.s. nice 2p2 location!

I used a toy game and I can't see EV being gained in this simplificated poker spot

So this is a polarised v bluffcatcher spot

Let say 100 in the pot on 22223 and players have 100 behind, vilains range is 2 combo of AA and 2 combos of QQ and we have KK only, at pot sized GTO he value bets 2 AA combo and bluff 1 QQ combo and we call 50% of the time, let say he starts betting 2 AA combo and 2 QQ combo (now overbluffing) but we still remain at 50% calling frequency (no adjustment v pot size or change in bluffing frequency).

The EV of our bluffcatchers is supposed to increase because we win more often when called, but we also see a showdown less and possibly lose some pots that would otherwise have gone check check.

Can someone who knows the maths help me to show how and where does caller gain EV in this whole line if the bettor where too overbluff by betting all four combos, instead of three with a pot size bet (and caller defending GTO at 50%)?

If the bettor bets all 4 combos the equilibrium falls apart and KK should see an increase in EV from 0 made from a perfectly balanced betting range.

EV of caller when bettor bets all combos:

1/2*200 - 1/2*100 = 50

EV of caller when better bluffs appropriately:

1/3*200 - 2/3*100 = 0

EV of bettor when they bet all combos:

1/2*100 + 1/2*(1/2*200 - 1/2*100) = 125

You can interpret that as half the time the caller folds and the bettor wins the pot with all of his hands. The other half when the second player calls, the bettor wins 200 (the pot plus the caller's call) and the other half of the time loses his bet.

EV of bettor when they bluff appropriately:

1/2*100+1/2*(2/3*200-1/3*100) = 100

Same scenario only the calling EV equation changed to reflect the bettor's change in betting frequency.

No you might say why doesn't the bettor just bet all his combos because he makes more money? Well it's because the caller can move to a 100% call strategy and then bettor's EV equation becomes:

1/2*200 - 1/2*100 = 50

So the equilibrium breaks down and the bettor moves more towards the perfect ratio again. The definition of equilibrium is that no player can unilaterally change their strategy to increase their EV. When both strategies are at equilibrium then that's the most they can make without encouraging the other player to change their strategy for exploitation.

In the scenario where the bettor always bets but the caller only bets at the appropriate ratio, the caller's extra money comes from the increased frequency of winning the dead money in the pot plus the bettor's bet.

The increase in EV for the bettor comes from the fact his bluffs are't losing money as frequently as they should be because the caller isn't calling at the correct frequency.

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Most probably, but not necessarily. A calculated nemesis to a GTO strategy won't be a mixed strategy. There also might be spots where a player deviates from GTO in spots that never come up against a GTO opponent (for example if a player folded 100% against a 100bb open shove). In general practice though (as in human play), if you aren't playing GTO you're almost certainly making -EV mistake (overbluffing or underbluffing for example) when playing against a GTO opponent.

It just depends on whether villain is overcalling or overfolding. Obviously if villain is overcalling it comes from the value hands and if overfolding it comes from the bluffs.

Even in an imbalanced RPS game where say rock gets say a 25% chance to reverse and rip through paper, you still have a GTO solution and situation where a pure counterstrategy can be calculated.

Again, usually but not necessarily.

I would say most bluffs are semibluffs or are using blockers, so must bluffs are +EV. The opponent's calls are also +EV. This is the case when there is money already in the pot.

Against another GTO range yes, otherwise you wouldn't be at equilibrium.

No. This one is a bit harder to explain but generally ranges involve mixing with better hands in order to be uncapped in certain spots. The difference in EV between checking and betting might be zero, but presumably both spots would have a positive EV.

I'm confused by the double negative in the first question.

Out of position on the river, this is true, but in all other situations, only the worst of the worst bluffs will be 0ev.

Not necessarily. At the Nash equilibrium, neither player can gain EV by deviating. Sometimes a player can still break even when deviating.

This is actually a great example of the above point. In the described scenario, the non GTO player is not playing a losing strategy. There is no EV loss. By the definition of indifference, it doesn't matter what strategy the caller chooses. The bettor's range is constructed in such a way that the caller's EV is the same no matter what strategy he chooses.

A bluff may not be 100% in the bet range, because the hand may still have value as a check equal to or greater than bluffing. Sometimes you can check back air, make a pair and win, or you beat your opponent's worse air, or you can have a +EV bluff on a later street. A hand's strategy can be mixed when the EV of multiple actions is the same.

Would this example apply for a cappred non-GTO bluffcatcher with no card removal effects in his range against a GTO river shove range?

The problem here is we all play a sub gto level game. Therefore, we all have a weakness.If I over call just a little bit, Value bets gain more value against my style. Now, if I fold a little too much, bluffing some can become far more profitable. Remember the types of bad players? Loose passive, calling stations, and maniacs. GTO doesn't really apply here. My idea of gto loses vs maniacs. It doesn't really max out vs passive players who are really loose due to my tight range. We need to beat sub gto players. Not worry about being gto all the time

this is just my take on it or how i try to see it. In poker you have strong Hands (will win at Showdown) and weak hands (will loose at Showdown). you have most value by having strong Hands. but every Player has the same amount of strong Hands. so in order to increase the value of* your strong Hand range you add bluffs. the assumptions is that bluffs increase the value because you either make more Money because villian is over folding and you win more pots or villain is over calling and you make Money because of your strong Hands. so your Job is to find out how much bluffs to add to your strong Hands to get the most value of your range. aka being balanced. by being unbalanced your range does not hold max value so. if a max value strategy Plays vs a non max value strategy it has always an edge not matter where it Comes from.
if villain calls 100% on the river and your range is 80%value and 20% bluff, it will Show a Profit. it will Show less Profit than a less gto strategy that is 100% value based but it does Show Profit. in this case the Profit decreases the more you Play gto. if you Play balanced on the river and he calls 100% on the river, your ev is always the pot. there is no extra ev gained on the river. but my assumption in this case would be he is over calling the river because he is probably over folding some Prior streets. so in this case you would have made your ev in this hand preflop, flop or turn, where he is over folding. for example if your gto a strategy wins one pot on the turn by bluffing which you would usually loose because checking back and loosing it doesnt matter that the river strategy does not bring additional EV because your GTO strategy already turned a Profit.
this answer was quite Long and i hope i was able to express my thoughts (english is not my language )
fwiw i think all that is more theoretical because the Point of GTO is being able to see the leaks in your opponents strat and exploiting it. you can not exploit a leak if you dont know it is there. so the closer you get to gto so more you will be able to spot villains leaks.

This is horribly wrong. GTO is never the perfect strategy. The only time you might say that it is perfect is when the opponent is using GTO, and if this is the case, it will be a losing strategy for both players.