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Thought Experiment 6: Wheel of Fortune

4/6/2015

2 Comments

 
Picture
This week's thought experiment is a straightforward math problem. Can you solve it?

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    Marge was no mathematician, but she knew she had just discovered a foolproof system to get rich playing roulette.
     She had been observing the spin of the wheel at the casino for several days. During this time she had noticed that it was surprisingly normal for there to be a sequence of spins when the ball fell into only black or only red slots. But five in a row of the same color was very unusual and six in a row happened only a couple of times a day.
     This was going to be her system. The chances of the ball falling into a slot of the same color six times in a row were tiny. So, she would watch, and once it fell into, say, red, five times in a row, she would bet that the next one would be black. She was bound to win more often than she lost because six in a row was so rare. She was so confident that she had already started to think about how she would spend the money.

Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 16.
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What do you think? Will Marge strike it rich with this plan? I'll be back on Friday with a quick response to this one.

2 Comments
Andrej
4/7/2015 09:29:58 am

Please send Marge to my house for poker games. If you want a mathematical discussion, I could do that, but if the wheel is fair then any sequence of black/red/green is random. (Disregarding the greens) Having five reds come up in a long run of spins is not that unusual, 1/32. The next roll is 1/2 red and 1/2 black.

If however you are measuring Marge's happiness gained from gambling and she has had fun coming up with the system and can afford to lose what she gambles, then she probably gains positive utility from doing what she is doing. This is why coin slots have metal pans (ching, ching, ching, look at me I am a winner) and why the lights and bells at other games. Table games have well dressed dealers and croupiers and an air of fun surrounding them, all part of the game.

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@EdGibney link
4/8/2015 01:04:16 am

I'll send her your way if you give me 20% of the profits on the night. She might even enjoy the experience. But if she does, due to a poor understanding of probability and logic, is that happiness actually damaging over the long term because it lures her into dumber and dumber behaviour?

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