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People always like to evaluate the variance, but is there any way for variance to be interesting to the gambling game makers?

In another word, what is a pratical gambling game that involving some distributions that is relating to variance other than the normal distribution?

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  • $\begingroup$ Anyone would like to answer the second interpretation? $\endgroup$ – Victor Sep 30 '13 at 19:41
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    $\begingroup$ As far as I know, there are no casino games whose distribution is normal, because they all rely on discrete events (cards, dice, roulette wheels, etc.). Over time the central limit theorem kicks in, but that's for all distributions. $\endgroup$ – vadim123 Sep 30 '13 at 19:41
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Definitely yes. The variance relates closely to the "risk of ruin" for any given bankroll of the gambler (including the house).

Here is an example that shows variance and not just odds can matter in the design of a gambling game: suppose you had two gamblers who were flipping coins against one another with fair odds for \$1 a flip. One of the gamblers has \$10 and the other has $100. If someone goes broke the game is over.

Based on odds and "expected value" it appears to be a fair game. Should either gambler be interested or disinterested in playing this game?

Of course, there are myriad other reasons as well for game makers to consider variance, including "soft" issues such as gambling psychology. In the limit, imagine a slot machine which returns 98 cents every time you put in a dollar. This game will probably not be very profitable for the game maker.

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It's what makes gambling work (for casino's and the like, that is). With no or very small variance, no one in his right mind would play a game with negative expected value. With a large variance, people will play a game with negative expected value and will therefore, on average, lose.

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    $\begingroup$ But with too high of a variance, the casino will risk going broke. I believe that most casinos limit how much "high rollers" can wager in a single bet precisely to protect themselves from variance. Of course, math is used to determine what the bet limit should be. $\endgroup$ – Michael Joyce Sep 30 '13 at 19:45

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