Sicherman Dice
Mathematical Modeling
These dice, invented by Colonel George Sicherman, have the same probability of rolling a given sum as a pair of standard six-sided dice, but they are numbered differently: one has sides 1, 3, 4, 5, 6, 8; the other has sides 1, 2, 2, 3, 3, 4. https://trick-dice.com/product/sicherman-dice/
Introduction
"Sicherman dice /ˈsɪkərmən/ are a pair of 6-sided dice with non-standard numbers—one with the sides 1, 2, 2, 3, 3, 4 and the other with the sides 1, 3, 4, 5, 6, 8. They are notable as the only pair of 6-sided dice that are not normal dice, bear only positive integers, and have the same probability distribution for the sum as normal dice. They were invented in 1978 by George Sicherman of Buffalo, New York."Wikipedia"
Guiding Questions
- What is the sample space for this scenario?
- How can you calculate the theoretical probabilities?
- What simulation methods could you use to verify your results?
- How does changing parameters affect the expected outcomes?
- What are the limitations of your probability model?
Key Mathematical Concepts
Game Theory
Probability Theory
Randomness
Statistical Analysis