The Lucky 6’s

Team Z

How to playThe player will receive two fair dice each numbered 1 through 6 on each side of the dice. After rolling both of the dice at the same time, if the player rolls two sixes they will win $6, but if they roll one six, they will win $3. If they roll any other numbers, they will not gain any money. The cost of the game is $2. Would you play?

Theoretical Data

Expected Payout Value: -2(.694)+1(.278)+4(.028)=-.998

Standard Deviation: √[.694(-2--.998)²+.278(1--.998)²+.028(4--.998)²]=1.58

Number of 6s (n) 0 1 2

Money earned -$2 $1 $4

Probability of n .694 .278 .028

Experimental Data

Expected Value: -2(.64)+1(.34)+4(.02)=-.86

Standard Deviation: √[.64(-2--.86)²+.34(1--.86)²+.02(4--.86)²]=1.57

Number of 6s (n) 0 1 2

Number of times rolled 32 17 1

Amount earned -$2 $1 $4

Probability of n .64 .34 .02

Simulationhttps://www.youtube.com/watch?v=4bbSSE5W4HM

ResultsAfter we rolled both of the dice 50 times, we found our simulation results to be very similar to our theoretical results. We expected that there would be a house advantage of $0.998 and after our simulation, we observed that our house advantage was similar to this but was off by $0.138. To improve this game, we could add more trials to see if the simulation information gets closer to the theoretical values.