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**preview**shows half of the first page. to view the full**1 pages of the document.**Sean Xiao and Shangara Flora 12/12/2011

Case Study #2

(Theoretical Probability)

The appeal of Dice games is rooted in the fact that when two or more Dice are thrown

simultaneously, a beautiful interaction occurs. Before the initial throw the Dice are in fact separate

entities. However, once multiple Dice are thrown, the totals they create (arrived at by adding all the

values together) unbalance the games in which they are being used into various channels of chance

and strategy. Based on the number of Dice thrown, certain totals become increasingly more likely

than others. As more and more Dice are thrown together at once, the expected outcomes begin to

fluctuate and alter the strategy that a player may use accordingly.

This game was inspired by the famous ‘Roulette.’ The players are supposed to guess which side of

the die shows up. The players will first place their bets on 1, 2, and 3,4,5,6 and then the "dealer"

will roll 3 dice simultaneously. Payouts are 1:1 if the chosen numbers shows up once (on any of

the 3 dice), 5:1 if the chosen no shows up twice, and 30:1 if the chosen number appears on all 3

dice.

So, the expected return is 30*(1/216) +5*(1/12) +1*(75/216)-1*(75/216) = 0.947%. This

percentage is slightly in favour of the casino. Theoretically, this game is declared to be fair.

Values (1,2,3,4,5,6) PROBABILITY (%) DEFINITION /PAYOFF

1 Matching 3x25/216 = 75/216 = 34.72 1:1

2 Matching 1/36* C(3,2)= 1/12 = 8.33 5:1

3 Matching 1/216 = 0.463 30:1

0 Matching 100-34.72+8.33+0.463=

56.487

Lose investment

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