Bellatrix is moving forward with the topic of Facing the Nemisis of Game Theory. Homework for the week is posted here.
Bellatrix takes you on a journey through The Mathematics of Poker by Bill Chen and Jerrod Ankenman, breaking down each chapter one at at time. Warning - if you haven't figured it out by now, there will be math!
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enjoying the whole series so far, unfortunately not a lot of action on this series
Time Link to 00:25:05
nice series so far!
i just want to add a tiny bit:
if we play the 50% strat without adaption .. nemesis can do whatever she wants .. she does not have to match the 50%-strat to get max ev=0 .. she will get max-ev even if she chooses 1 every single time.. since we are not adjusting..
same for the stone paper scissors of course
and that might be important in poker as well :
if the opponent bluffs gto-frequency we should not worry too much about calling exactly the right gto-frequency .. until he might deviate in some way
nice series so far!
i just want to add a tiny bit:
if we play the 50% strat without adaption .. nemesis can do whatever she wants .. she does not have to match the 50%-strat to get max ev=0 .. she will get max-ev even if she chooses 1 every single time.. since we are not adjusting..
same for the stone paper scissors of course
and that might be important in poker as well :
if the opponent bluffs gto-frequency we should not worry too much about calling exactly the right gto-frequency .. until he might deviate in some way
Not sure I agree with the follow-up for poker. As a counterexample I would say using a dominated strategy like folding the nuts will always minimize your EV even if the other guy is playing optimally. So the most the other guy can achieve via optimal play assumes that you are playing optimally, too. You could achieve more playing optimally in theory if opponent chooses really bad strategies that approach exploitative strategies for you without you consciously doing anything about it.
I don't know if I made myself clear, but yeah, in a dichotomous case like a coin toss, sure it doesn't matter what you do, once your opponent plays optimally the EV is set, but the corollary does not hold true.
well folding the nutz is obv a dominated strategy
i was just talking about bluffcatchers .. since a hand that can beat valuebets is always a snapcall against the optimal-strat and most other strategies
but all the hands that can only beat bluffs are ev=0 and so it doesnt matter what our strategy with those is.. as long as our oponnent is playing gto we dont have to call a certain amount ..
so i dont want to promote random play or something .. but as long as we dont know if villain bluffs more or less than gto we can not exploit him .. and if he can not adapt to our play with an exploitive strategy then all the ev=0 decisions are not important ..
of course this is not true in many games, because oponnents are adapting .. but more often than not 1 hand does not make our strategy readable .. so dont worry too much about the single neutral-ev decision.. i guess ..
pulo, think about it this way when bluff catching:
If opponent bluffs in a game theory optimal way, then -by definition- he's made you indifferent to call with your bluffcatchers, so yes, it doesn't matter whether you call or not. Let's even assume that the villain plays GTO when bluffing and is never adapting, so your best solution is to always fold so you get to the next hand as soon as possible (assuming you're +EV against him in other spots).
But your opponent most likely doesn't play a GTO bluff strategy, he isn't the nemesis, he's flesh and blood. He's running good/bad, tilted, playing way too low or way too high for his bankroll. He's making mistakes, either bluffing too much or too little. But you only have 10 hands on him, so you can't tell which. Even if you have 10000 hands with him, you likely don't have enough to know his bluff betting frequency to the decimal.
So now the real life, imperfect villain bets on the river and you have a bluff catcher and you don't know how to exploit him and you don't want to get exploited. What's the best strategy you can take?
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