Alright, what'd you got?
>> I'm going to say it's one, one.
>> Alright, how would you figure that out?
>> Well first, I would ask you if that's correct. [LAUGH]
>> [LAUGH] We'll see when you try to.
>> [LAUGH]
>> Figure it out.
>> Okay, so, the idea here is I'm trying to
figure out what Curly would get, if Smoove was out to
get, make certain that Curly got the worst possible value.
So, Curly gets to ch Curly gets to choose among rows.
And Smoove gets to choose among columns. So, If
I chose the B column, then Curly could get
a one. You're given choice Curly would go for
the first row instead of the second row, because
Curly would get a one. If I took the
S column, as Smoove, Smoove took the S column,
then Curly would choose the second row, and would
get two. And one is lower than two. So,
Smoove would choose the first column and Curly would have to get
the first row and would end up with a one. That make sense?
>> Yes, but here's what you haven't figured out.
>> Yes?
>> What happens if Smoove, no because, because
Smoove says, I'm always going to choose the Backstreet Boys.
>> Mm-hm.
>> Then you're right, Curly should also choose that and at least coordinate.
>> Mm-hm.
>> But what if Smoove is random say
half and half random between the two options.
>> And I
don't know what's going to happen before then?
>> And you don't know what's going to happen, sorry?
>> I know that, I know it's half Curly knows it's half
and half but doesn't know which one he's choosing any given time?
>> Exactly.
>> I see. Then, I would end up with, one half and one.
>> Then for choosing B.
>> Uh-huh.
>> Expect the score would be a half, and for choosing
S, they'd expect the wor, expect the score would be one.
>> Yep.
>> Oh, I see. And, and then Curly would choose S and
get the one.
>> Right.
>> And that's still consistent with, with that?
>> Mm-hm.
>> Can we work out what the what the worst case is?
>> What do you mean?
>> Well I feel like, we should solve it
like a [INAUDIBLE] game, like we did in your lesson.
>> Oh.
>> Say that Smoove is actually choosing a
pro, probability either X or 1 minus X.
>> So I thought you were asking for like
a pure decision, I wasn't even thinking about mixed decisions.
>> Uh-huh,
yes, it could be a malicious and randomized adversary.
>> [SOUND] So we are.
>> [LAUGH] You said yuck [LAUGH].
>> We, we are really talking about my ex-girlfriends.
Okay so you just do the math. Do the math.
>> Alright, so if we, if Smoove chooses Backstreet Boys
with probability X and Sting with probability of one minus X.
>> Mm-hm.
>> Then, Curly for choosing Backstreet Boys will get X on average and
for choosing Sting, we'll get two times one minus six on average. And the
useful point is going to be to discover when these are equal to each other.
>> Yep.
>> So in fact, Smoove, by being malicious and
stochastic, can actually force things down to 2 3rds.
>> Hm. And things being symmetric as they are, Curly can do the same.
>> Okay.
>> So, basically, Curly can behave in such a way, that even against a
malicious adversary, it could, he could guarantee himself to a score of 2 3rds.
>> Yeah, a malicious possibly mixed adversary.
>> That's right.
>> Okay. But one, one would be right if we
were sticking with pure strategies, but why would we do that?
>> That's right, but for the purpose, if that's right, and you can do a
version of the folk theorem. In fact, there's
lots of different flavors of the folk theorem.
The one that we're going to focus on
is going to allow for these mixed strategies.
>> Mm-hm.
>> But. In fact in general you could say you know,
no I kind of like the mixed strategies, let's just stick with that.
>> No, I like the mixed strategies too, I just wasn't thinking about them.
>> So, I want to point out that in fact the solution that you gave, I
think that actually does correspond to what is
usually called Minmax, which is the pure strategy.
>> Yeah!
>> So the, [LAUGH] the minmax is, is in fact one, one.
The other concept is really important too though. And I think
it's sometimes called the security level profile. So instead of the min
max level profile the security level profile. And that allows for
the possibility of, of mixed strategies. So that gets you down to
the 2 3rds, 2 3rds. I think you know, it turns
out that there's folk theorems that can be defined with with either
of those concepts. I prefer this one. But I do like this
name better [LAUGH]. So I, I apologize if that made things confusing.
>> I'm not
confused now. I think in the end Michael,
the important thing is we were both right.
>> Well, the example that I'm going to next, these two concepts line
up. So let's let's do that, and then we don't have to care. [LAUGH]
>> I, I'm all for that. Let's do that.