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Problem of Points 2

Created by Brit Cruise.

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Video transcript

- [Brit] How are we ever gonna figure that out exactly? Let's just split the pot and call it even. - [Sal] Let's think about it this way. (chips clicking together) The next flip I have a 50% chance. - [Brit] I'm gonna need to draw this out - [Sal] Draw it out, draw like a tree - [Brit] Okay, so the next flip we'll do tree, so... - [Sal] It's either gonna be heads or tails. - [Brit] So 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] So I need to do - [Sal] Do another - [Brit] another branch. - [Sal] Branch. - [Brit] Oh, I like this, okay. - [Sal] So it's either gonna 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] Yeah. - [Brit] See, there's a chance I'm gonna 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 1/2 chance of this happening, so this one has 1/2 and this one has 1/2. - [Brit] Okay. - [Sal] So 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 1/2. One over two, one over two. So you have, to get two tails in a row, there's a 1/2 times 1/2 probability or there's only a 1/4 chance of this happening. And there's a 1/4 chance of us getting a tails and then another heads. So I have a 1/2 plus 1/4 chance of winning. 1/2 plus 1/4, that's 2/4 plus 1/4. I have a 3/4 chance of winning, so I say give me 3/4. I have a 1/2 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 1/2 chance of winning the next one, four chips for that, and then, if I don't win the next one, I still have a 1/2 chance of winning that one. And so I should get six chips, which is 3/4 of eight. - [Brit] And I just get two? - [Sal] Unfortunately for you, that would be the case. - [Brit] You know what, I wanted half, but I can't argue with this. - [Sal] You can't argue with flawless logic. (Sal laughs)