Roll Die Puzzle

Reply #4

cottoneyedjoe — Mon, 31 Oct 2022 01:57:03 GMT

That is very interesting, DB. Luckily the sequence you found has an entry in the OEIS: https://oeis.org/A073593

Looks like you're right about it being sub-exponential, the entry says it's asymptotic to n^(log(n) + c

Reply #3

db101 — Sun, 30 Oct 2022 18:00:16 GMT

It is interesting to chart the relationship between the number of sides of the dice and the minimum number of rolls for there to be at least a 50% chance of getting every number.

number of sides min number of rolls for 50% chance

1 1

2 2

3 5

4 7

5 10

6 13

7 17

8 20

9 23

10 27

11 31

12 35

I used cotton's script to simulate random rolls. Considering the second column to be a function of the first, it grows faster than a p... [ More ]

Reply #2

Orange71 — Sun, 23 Oct 2022 17:41:51 GMT

cottoneyedjoe, the exact solution is 2124571 / 3779136, which works out to be 56.22%. If you're interested in the steps to the exact probability solution, I can post.

Reply #1

cottoneyedjoe — Sun, 23 Oct 2022 17:24:00 GMT

The probability at least one number doesn't show up is a bit over 56%. I did this by random simulations of die rolling rather than working out an exact probability because it was too tedious.

For fun, I wrote a script that handles variations of this problem. You can change the number of times you roll the die and the number of sides of the die to estimate the likelihood at least one number doesn't show up.

https://sagecell.sagemath.org/?z=eJx1UNFOhDAQfCfhHyYYY3uHHtyDDyb8g-_GXAoUrSkt6e7F3... [ More ]

Roll Die Puzzle

Orange71 — Fri, 14 Oct 2022 18:15:54 GMT

A fair six-sided die (faces 1 through 6) is randomly rolled 12 times. What is the probability that at least one number (face) will not occur in the 12 rolls