Prove it – Ep3: Terminating Dice Sums
Let’s follow an algorithm:
- Determine heuristic used in example.
- Summarize math solution.
- Define new heuristic, if possible.
- Discuss Claude’s math solution.
- Provide dashboard solution, if possible.
Claude prompt:
You and a friend are taking turns rolling a 6 sided die and keep a joint running total. The first to reach 6 or more gets to keep the sum. Would you go first or 2nd? Prove answer.
Heuristic:
Visualize grid of dice rolls that total 6. Unlikely to roll more than three times.
Mathematical solution:
Stack up expected values and use matrix algebra. Stars and bars method can be used to turn problem into combinatorics. Use Christmas stocking theorem to chose final combination.
Final answer ~2.16
New heuristic
Expected value of 6 sided die is 3.5. Choose 2 dice for best chance of 6. 3 would be the next best guess, but 2 is the clearly better choice.
Claude math
Claude correctly solves this problem and gives the same answer of ~2.16. There was some confusion as to how many total rolls, but this was easily cleared up.
Efehn’s puzzles completely changed how I think—so engaging and rewarding!
Sarah Lee
Puzzle Enthusiast – Not a real person