little math/programming problems April 2023

[Albert Chan]

(05-02-2023 08:03 PM)David Hayden Wrote:  int sides[6] = {0,0,0,0,2,3};

For a rough idea of expected values, we may try a simple "random" generator.
5 dices, with cycled pattern, different initial state:

Code:

000023000023000023000023000023000023 ... Pattern
1111122333
 111112222233444
  11111222223333344555
   1111122222333334444455666
    111112222233333444445555566777
     11111222333334444455666

Note that 6 throws add to sum of only 5, sequence will always terminate.
Expected values = (3 + 4 + 5 + 6 + 7 + 6) / 6 = 31/6 ≈ 5.2

This "random" generator is super lumpy, with maximal 4 0's in a row.
We expected true expected values slightly bigger.