Thank you so much for the video -- it was very helpful in breaking down some concepts for me. I am, however, getting stuck on a very basic concept & was hoping you could clarify, even though the video is old:
In an example you give early on (the 20% nuts/70% BC/10% air one), you initially calculate the defense frequency needed to make EV(bluff) for V = 0. You then note that V can instead check back, and EV(check) = 0.1 (assuming V beats your air). You then say that we should modify the defense frequency such that EV(bluff) also = 0.1.
I understand that this is a key concept for game theoretic approaches, but I don't understand why it's true; I suspect the problem is in how I'm coming at the issue. I approach it as:
* If we select a defense frequency such that EV(bluff) = 0 and EV(check) = 0.1, V will sometimes bluff and sometimes check, and the average EV of his actions will be between 0 and 0.1. If V plays perfectly, he will always check back given these options, in which case his equity across all actions will be 0.1. If V plays less than perfectly, however, he will occasionally bluff, and his equity across all actions will be slightly less.
* If we select a defense frequency such that EV(bluff) = EV(check) = 0.1, no matter what V does, his EV is 0.1.
From the way I'm approaching this, this makes it seem like choosing a defense frequency such that V is indifferent between checking and bluffing basically gives him an EV freeroll, and is a strictly worse strategy than choosing a defense frequency such that EV(bluff)=0 (i.e. can yield the same or better, but never worse, results).
Hi Steve --
Thank you so much for the video -- it was very helpful in breaking down some concepts for me. I am, however, getting stuck on a very basic concept & was hoping you could clarify, even though the video is old:
In an example you give early on (the 20% nuts/70% BC/10% air one), you initially calculate the defense frequency needed to make EV(bluff) for V = 0. You then note that V can instead check back, and EV(check) = 0.1 (assuming V beats your air). You then say that we should modify the defense frequency such that EV(bluff) also = 0.1.
I understand that this is a key concept for game theoretic approaches, but I don't understand why it's true; I suspect the problem is in how I'm coming at the issue. I approach it as:
* If we select a defense frequency such that EV(bluff) = 0 and EV(check) = 0.1, V will sometimes bluff and sometimes check, and the average EV of his actions will be between 0 and 0.1. If V plays perfectly, he will always check back given these options, in which case his equity across all actions will be 0.1. If V plays less than perfectly, however, he will occasionally bluff, and his equity across all actions will be slightly less.
* If we select a defense frequency such that EV(bluff) = EV(check) = 0.1, no matter what V does, his EV is 0.1.
From the way I'm approaching this, this makes it seem like choosing a defense frequency such that V is indifferent between checking and bluffing basically gives him an EV freeroll, and is a strictly worse strategy than choosing a defense frequency such that EV(bluff)=0 (i.e. can yield the same or better, but never worse, results).
Can you set me straight?
Oct. 29, 2015 | 8:03 p.m.