Posted by: dschadewald | November 6, 2008

## Gambling

I was reading an article somewhere about this famous french gambler named de Mere who was famous for making tons and tons of money gambling way back in the 1650s.  He made money by exploiting differences in probability between two events that the average person would think were definitely equal.  He had a few tricks he used on people.  His main one involved dice and went like this.  He would ask a person if they were willing to make this bet:

He would roll a die 4 times and if at least one six appears in the 4 rolls of the dice he would win, say \$10

The other person would roll a die 24 times and if at least two sixes appeared they would win \$10

To the average person (and to me) this seems to be equal, and thus most people would make the bet.  But if you actually compute the probability, you would see that the de Mere would win with a probability of (1-(5/6)^4)=.52 where as the other person would win with the probability of (1-(35/36)^24)=.49.

In the short run a person might do ok, but if they played 50 or 100 times, the probability would be greatly in de Mere’s favor.  This trick worked for him for ages, and apparently he made a killing off of exploiting this simple difference in the probability of the two events.

## Responses

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2. …and of course, the Gambler’s Ruin problem shows us that even with a measly 1% advantage, the House will always rob you blind. Even in fair games, the House will win with probability (very very close to) 100% since its bankroll is vast and you are not Warren Buffett.

Here is a good treatment of the Gambler’s Ruin:

3. hmm, okay, well, the last comment ate my hyperlink, so…

Here is a good treatment of the Gambler’s Ruin:
http://mathworld.wolfram.com/GamblersRuin.html

4. This is a nice story I hadn’t heard before. Beware probability! 🙂

5. Not quite. There are 6^24 = 4,738,381,338,321,616,896 different possible outcomes from rolling one six-sided die twenty-four times. 4,392,674,398,624,351,271 of these include at least two 6s. So the probability of “the other person” winning is roughly 92.7%.