little math/programming problems April 2023

[David Hayden]

Simulating the experiment 100,000 times, I get an average of 5.49893 rolls with 5 dice. Here are the results with different numbers of starting dice:

Code:


Initial # dice    Average rolls
1                 2.2266
2                 3.25986
3                 4.10384
4                 4.84957
5                 5.49893
6                 6.08402

Someone smarter than me will have to figure out the exact values.

Dave