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Challenging a Fundamental Principle of Game Theory

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Challenging a Fundamental Principle of Game Theory

In honor of Easter Sunday, I thought why not make the theory gods roll over in their empty graves!


Here's are two excerpts from posts made by a member who was trying to devise closer-to-optimal 3-bet ranges:

MOP defines a GTO strategy pair as two strategies who are maximally exploiting each other.

One of the main tenets of game theory is that you always take the line which is highest EV against your opponent.  You never really take a lower EV line for the sake of balance. 


Rules are usually made to be broken, but this is one i've always just assumed was made of steel.  I think we're all probably in agreement here more or less, but i'm challenging us to prove it using two recent examples that have me a bit thrown.  By sheer coincidence, i came across both of them while cruising Tyler Forrester's videos.  (you're off the hook tyler!)


Ex 1: Tyler 4bets and calls off AKo CO vs BB for about 115bb effective.  In video he says the EV of calling the 5bet is about neutral.  When a member asks why he 4bet if it's 0EV to call 5bets, his main reason was for range expansion -- adding AK to the call 5-bet range incentivizes BB to 5-bet more aggressively, which in turn raises the EV of CO's KK-AA as 4-bets.  I'm assuming tyler took this line b/c he also thinks its the most +EV play for AK (anticipating villain will play a call 4-bet range), but it got me thinking: if we increased stack depth to the point where raising 3-bets with AK became slightly -EV relative to calling, could it be possible that the existance of AK in the 4-bet range still raised the EV of AA-KK enough to justify taking the lower EV line?


Ex 2: Tyler does a CREV analysis MP v BTN coldcall, 872 flop.  He concludes that it's sound for MP to check his entire range OTF.  Sauce comes into the thread and agrees, saying that he thinks MP should devise his range on this texture in a way that allows him to realize as much equity with overcards as possible.  This seems like a very solid argument.  At the same time, with ranges being relatively symmetrical on this flop, I think i could make strong arguments that if MP starts by checking his whole range, BTN would be correct to respond passively enough that we would see MP regaining incentive to c-bet some premium hands, since they don't appreciate BTN taking a street out of the game at a high frequency.  I suppose that's another thread in itself, and i could be wrong,  but i've played with the ranges enough that i think i can give the counter-argument at least a good run for its money.  


Cliffs:

If we assume that a particular hand is -EV in line 1 relative to line 2, does that automatically mean that line 1 is a sub-optimal strategy?

Is it possible that hands can perform ritual sacrifice to serve the EV of the range on the whole?  Sorry for being dramatic but i think it's fun to treat hands as people.  


happy egg hunting guys!


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