Game cc

GAME DESIGNPROJECT:

HIGHS and LOWS

Team CC

HOW TO PLAY

This is a very simple game. The player pays $100 to play, and they then roll two dice. The sum of the rolled dice is calculated, and the player is given the amount of money that corresponds to the number that they have rolled.(See table)The game looks attractive to a potential player because they can win more than they paid for six of the possible outcomes, but the game actually has a house advantage.

2 3 4 5 6 7 8 9 10 11 12

$200 $100 $50 $0 $0 $0 $0 $0 $50 $100 $200

THEORETICAL EXPECTED

VALUES AND STANDARD DEVIATIONS

X 2 3 4 5 6 7 8 9 10 11 12P(X) 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36

$$$ $200 $100 $50 $0 $0 $0 $0 $0 $50 $100 $200

μx=200(.0556)+100(.111)+50(.1667)+0(.666) =11.12+11.1+8.335+0 =30.56 Since the average win that I can expect is about $30.56, I will set the price of the game at $40. The players will still want to play because they will see that the prizes

are higher than what they paid to play, and people usually don’t remember to think about things.

δ2x=.0556(200-30.56)2+.111(100- 30.56)2+.1667(50-

30.56)2+.666(0-30.56)2

δ2x=1596.2712+535.232+62.998+621.99

δ2x=2816.4912

δx=53.07

EXPERIMENTAL RESULTS

Sum Rolled 2 3 4 5 6 7 8 9 10 11 12Money won $200 $100 $50 $0 $0 $0 $0 $0 $50 $100 $200

Frequency 0/50 3/50 5/50 6/50 8/50 8/50 9/50 7/50 2/50 2/50 0/50

Total Amount Won $850

Mean of Experimental $17.00

Standard Deviation $32.57

μx= (200)(0)+(100)(5/50)+(50)(7/50)+(0)(38/50) =0+10+7+0 =17

δ2x=0(200-17)2+5/50(100-17)2+7/50(50-17)2+38/50(0-17)2

=688.9+152.46+219.64 =1061

δx=32.57

CONCLUSION

With the results that I have gathered from running a simulation of this game, I can see that the person who played lost a lot more money than expected. The player lost an average of $23 per game, because the player won an average of $17 per game and the game cost $40 to play.

I have concluded that the game is difficult to play because of the low odds of winning, but the results achieved fell within a reasonable range of the expected values.