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# Problem of Points 2

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Brit:How are we ever going
to figure that out exactly? Let's just split the pot and call it even. Sal:Let's think about it this way, the next flip I have a 50% chance. Brit:I'm going to need to draw this out. Sal:Draw it out, draw it with trees. Brit:Okay so the next
flip we'll go trees, so. Sal:It's either be heads or tails. Brit:Let's say it's heads or tails. Sal:Right, if it's heads Sal wins. Brit:If it's heads, Sal wins. Sal:And I get eight. Brit:And you get the whole
pot, but if it's tails... Sal:If it's tails, then we keep playing. Brit:Oh so I need to do- Sal:Do another branch.
Brit: Another branch. Brit:Oh I like this. Sal:So see they're going
to be heads or tails. Now, at this point if it's heads I win. Brit:Sal wins. Sal:Sal wins, and if it's tails you win. Brit:Tails Brit wins. Sal:Yes. Brit:See, there's a
chance I'm going to win, that's why I want half the pot. Sal:There is a chance, but
your chance is not half. Your chance is substantially
less than half. There's a one half
chance of this happening. So this one has a half,
and this one has a half. Brit:Okay. Sal:actually you could
write, that's our first flip. And then if we have to
go to a second flip, then each of these outcomes are one half, one over two, one over two. So you have, to get two tails in a row, there's a one half time
one half probability or there's only one fourth
chance of this happening. And there's a one fourth chance of us getting a tails and another heads. So I have a one half plus
one fourth chance of winning. One half plus one fourth, that's two fourths plus one fourth, I have a three fourths chance of winning. So I say, give me three fourths. I have a half chance of
winning the next one. Brit:But there's eight chips here. Sal:Yeah, so this is
how we think about it. I have a half chance of
winning the next one, four chips for that. And then if I don't win
the next one, I still have a half chance of winning that one. So I should get six chips,
which is three fourths of eight. Brit:And I just get two. Sal:Unfortunately for you,
that would be the case. Brit:You know I wanted half,
but I can't argue with this. Sal:You can't argue with flawless logic.