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Need help with Math question
During a chat over coffee with a colleague, we had a math argument which has not been resolved. I need your help.
Here's the problem. We were sharing experiences at a casino. I told him(JH) I like to play roulette, especially the outer table. I usually bet on just the Black or Red. Me: "If I see a series of black  black black black black black, I usually bet on Red." JH: "Well. History shouldn't matter. The odds of it being black on the next round is still 50% (if you ignore the green for now)." Me: "Yes, but isn't there a natures way of reverting to the mean? It 'feels' like the odds of a Red are higher than Black!" JH: "The odds would be close to mean if you take into consideration ALL the roulette tables over a prolonged period. On any given turn the odds are not any higher than the previous turn." Me: "But what if I arrange for a private bet with the casino. I will bet on 3 consecutive Reds. What are the odds of that happening?" JH: "Well, that would be 0.5 x 0.5 x 0.5 = 0.125" Me: "Yes, so my payoff is 8 times (1/0.125). But I would get this payoff regardless of making the exact prediction." JH: "What do you mean?" Me: "Imagine 2 people at the roulette table, each betting $1 million. Person A is betting 'on each turn'. Person B has signed up with the casino that it will be RedRedRed on the next 3 turns. If it is NOT RedRedRed, he loses his $1 million. If he wins, he wins $8 million. Person A bets on RedRedRed, but DOES NOT make that initial commitment. He has the flexibility to switch to black after each turn. However, if Person A chooses Red on each turn, he also wins $8 million. That's not fair!" JH: "Why is it not fair?" Me: "Because at the start of the first round, Person A has a probably of 0.5, while Person B has a probability of 0.125. So how come Person B does not get a higher payout that Person A?" JH was confused. I'm also confused. I know there is some logic error somewhere, but not sure where. I'm looking for feedback.
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Re: Need help with Math question
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