Beat the odds

Team D

Description• This game involves the rolling of two die. This is individual

game that gives the participant the opportunity to win money. First, the participant rolls two die at the same time. Then, based on what they roll, they either win or lose money. If the participant rolls a sum of 5, then they win ten dollars. If they roll a sum of 8, then they win eight dollars. If the sum is an odd total, they win two dollars, with the exception of a total of 5. Finally, if they roll doubles, then they lose two dollars with the exception of an 8(4,4). The amount it costs to play this game is only five dollars up front before starting to play this game.

Theoretical mean and standard deviation

• Mean(x)= (10)(4/36)+(8)(4/36)-(2)(5/36)+(2)(14/36)=2.5

• S.D(x)= (10-2.5)^2(4/36)+(8-2.5)^2(4/36)+(-2-2.5)^2(5/36)+(2-2.5)^2(14/36)+(0-2.5)^2(1/4)=3.75

Mean and standard deviation through simulation

• Mean(x)= 2.2(calculator, we added up total winnings then divided by 50)

• S.D(x)= 9.8(calculator using variance formula, then square rooting the answer)

Results

• The means of both theoretical and simulated data were extremely close(2.5,2.2 respectively). As for the standard deviation, the theoretical was much smaller than the simulated data(3.75,9.8 respectively). Their seems to be a greater chance of variability in real life when playing the game. We could have improved by making the house earn more money by lowering some of the amounts that someone can win. Also, if we lowered the winnings enough, we could lower the price to make the game more appealing to people.

•