This document describes a dice game where the objective is to roll a sum of 2 or 12 to earn $12, or roll the same number on both dice excluding 1s and 6s to earn $6. Each round costs $4. Theoretical and experimental probabilities and outcomes are provided from 50 rounds of the game. The results matched theoretical predictions, with the law of large numbers evening out outcomes over many rounds. One suggestion is to make the game more interesting after many repetitive rolls.

1. EXTREMES
Team X

2. DESCRIPTION
Your objective is to roll two six-sided dice whose sum lies as the extreme end
of the sample space, i.e. a sum of 2 or of 12. Doing so earns the player $12. A
prize of $6 is awarded for rolling the same value on each die, not including 6s
or 1s. Each round costs $4.

3. DATA
Theoretical
Experimental
Outcome
Prob (p)
Value (x)
Outcome
Prob (p)
Value (x)
1&1, 6&6
.0555
12 -4 = 8
1&1, 6&6
4/50= .08
12 -4 = 8
2&2, 3&3, 4&4, 5&5
.111
5-4=1
2&2, 3&3, 4&4, 5&5
3/50=.06
5-4=1
None of the above
.833
0 – 4 = -4
None of the above
43/50=.86
0 – 4 = -4

5. RESULTS
The results experimental and theoretical data were surprisingly on point.
Around the Round 40 mark, there were still only two wins so for a while it was
the data would be completely off. The Law of Large Numbers kicked in
though, and everything was reasonable by the fiftieth round.
One improvement could be making the game more interesting. After 50 rolls
it gets awfully repetitive. Perhaps it would be more interesting if I had actually
used money but I still think it should have been a bit more addictive. Games
of chance aren’t fun without that element of obsession. I considered adding
some sort of skill-based element, like in blackjack or poker, but that would
make the probability of outcomes variable and I couldn’t figure out how to
deal with that mathematically.