Friday, December 12, 2008

Wheel of Fortune

Marge is an ordinary woman; she is no genius or a mathematician and she would love to earn some easy money. She had been observing how roulette was being played at the casino and she had discovered an apparently foolproof system of getting rich playing it. She noticed that it was quite common for the ball to fall into only black or only red slots during consecutive spins of the wheel. But the ball falling into the same color for 5 times in a sequence was unusual, and rarer it was for the ball to fall into the same color for six times or more in a row. As a matter of fact, she observed this happen only a couple of times in an entire day.

Hence her plan was to observe the ball falling into the same color for 5 times in a row, and then bet the next spin of the wheel on the other color, confident that her chance of winning was very high than losing. Can Marge afford to believe so?

I wracked my brain for a bit, struggling to find a flaw in her reasoning. You see I'm no mathematician myself, and as much as I tried to recall my classes on Logic and Probability, I really couldn't find anything amiss. And when I finally resigned and read what Baggini had to say, I still didn't get it!! Call me hopeless with Math. So I read it again, carefully, very carefully, and then the bulb finally glowed.

Since I've essentially not been successful in cracking or reasoning this puzzle myself, I don't want to merely repeat Baggini's reasoning. I will leave this as a fresh puzzle to anyone who chances by this article. But a little hint : we often miss out on subtle details of a problem due to our inevitable urge and selective processing, to look for what we want to find...


SUMI said...

BTW, I didn't know if black and red were the only two colors on the roulette wheel (haven't played it myself) and how many slots of each coulour are there and so googled it and in the process I ended up googling this puzzle too, so I didn't end up solving it myself, but I gathered that Marge was essentially assuming conditional probability based on the results of the previous spins of the wheel, but the spins are independent events. Interesting one.

Neeraja said...

Thanks for thinking about this puzzle, Sumi :). Yeah, I should have mentioned more about the game.

I tend to do this almost all the time with situations in my life, but hardly realized so.

SUMI said...

oh, no worries, as it turned out, that data was not relevant to the solution, if you had the right approach. :)