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Course: Math for fun and glory>Unit 5

Lesson 1: Expectation warmup

Problem of Points 2

Created by Brit Cruise.

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• why could they not eat dinner then continue the game?
(358 votes)
• Good point, also I hope everyone realizes that they took longer finding out who should get more of the pot than actually playing the game...
(55 votes)
• It would have taken much less time to actually finish the game than argue or analyse the fair share if the game was interrupted.
(5 votes)
• So, I don't quite understand something. If Brit has a 1/2 chance of winning on the first flip, and then a 1/2 chance of winning on the second flip, why is the probability 1/4, instead of 1/ 2 + 1/2 = 1. I know it wouldn't make sense, but why are you multiplying the odds instead of adding them?
(2 votes)
• Think of it this way, the first flip Brit needs a tails to continue playing, a one in two chance occurrence. If he succeeds in the first flip, he still needs another tails to win. This makes the probability of Brit winning one half of one half, or one in four.
(2 votes)
• Make this for poker too. I don't play head and tails on real money, but sometimes poker games are interupted. Maybe create an application which calculates this.
(6 votes)
• wait did it not take longer to talk than to finish the game?
(3 votes)
• brit you need to think things through before wanting half next time against sal
(3 votes)
• Why can't he just put dinner on hold for gambling?
(2 votes)
• how old are you to not know the "dangers" of gambling?

Personally, I think their mom wouldn't approve.
(2 votes)
• Why don't they just keep playing because there is a chance of getting tails twice.
(2 votes)
• Couldn't they have just finished the game?
(1 vote)
• Technically, yes. While they were talking I bet they could have easily finished up the game. They could have even finished eating and played later. Sal and Brit were just trying to teach us the math for this case scenario.
(3 votes)
• Wouldn't dinner become cold when they actually finished the splitting?
(2 votes)

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)