elliotvilhelm / Midnight

Midnight Score Probabilities using a Monte Carlo Simulation

Midnight Dice Game Probabilities

Using a Monte Carlo approach we generate the probability distribution of points in a game of Midnight. This project started with the desire to answer the question, "What are my odds of rolling a perfect game?". Using a Monte Carlo simulation we were able to answer that question and many more.

• The odds of rolling a perfect game with 6 dice is ~5.2%.

• The odds of not qualifying with 6 dice is ~8.3%.

• The odds of rolling a perfect game with 5 dice is ~8.0%.

• The odds of not qualifying with 5 dice is ~19.8%.

Distributions

6 Dice

---

No Strategy

std          4.407029
min          0.000000
25%         11.000000
50%         14.000000
75%         16.000000
max         24.000000

With Strategy

count  1000000.000000
mean        17.791511
std          5.943059
min          0.000000
25%         17.000000
50%         19.000000
75%         21.000000
max         24.000000

5 Dice

---

No Strategy

count  1000000.000000
mean         9.269614
std          4.486434
min          0.000000
25%          7.000000
50%         10.000000
75%         12.000000
max         18.000000

With Strategy

count  1000000.000000
mean        11.372786
std          6.075701
min          0.000000
25%         10.000000
50%         13.000000
75%         16.000000
max         18.000000

Authors

• https://github.com/amansourian
• https://github.com/benjaminykim
• https://github.com/ElliotVilhelm

References

• https://en.wikipedia.org/wiki/Midnight_(game)
• https://en.wikipedia.org/wiki/Monte_Carlo_method