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Old August 12th, 2014, 12:41 PM
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kalidas kalidas is offline
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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 Red-Red-Red on the next 3 turns. If it is NOT Red-Red-Red, he loses his $1 million. If he wins, he wins $8 million. Person A bets on Red-Red-Red, 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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Old August 13th, 2014, 04:38 AM
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dhurandhar dhurandhar is offline
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Re: Need help with Math question

Quote:
Originally Posted by kalidas View Post
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 Red-Red-Red on the next 3 turns. If it is NOT Red-Red-Red, he loses his $1 million. If he wins, he wins $8 million. Person A bets on Red-Red-Red, 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.
You have used math in argument but it is not mathematical argument. This because mathematical arguments are based on a fixed premise. Your conversation does not seem to have a fixed premise...like probability theory or otherwise (although your colleague seems to try best to remain within confines of probability theory).
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