0

In a pool of polyhedral dice (made up of $4$ to $6$ $2$-sided, $4$-sided, $6$-sided, $8$-sided, $10$-sided, and $12$-sided dice) how do you determine the chances of matching the last digit rolled on a $20$-sided die?

I am interested in determining the chances of one or more of the pool results matching a simultaneously-thrown d$20$'s final digit. (i.e. a "$1$" on a die matching the "$1$" or "$11$" on the d$20$, or a "$10$" on a d$12$ matching the "$10$" or "$20$" on the d$20$)

Specific points of interest for me include:

  1. What are the chances of $0, 1, 2, \dots$ matches?
  2. Does an increase in the number of sides of the dice in the pool translate into greater chances of matches?
  3. Is there a difference between a d$10$ and a d$12$ in terms of how likely one or the other is to generate a match to the d$20$?
Air Mike
  • 3,806
Mathew Reuther
  • 1
  • For 1. the python source (and the result of exhaustive search and summation) is here. For 3. d12 is more likely to produce $1$ and $2$ than d10. The chances of match are the same -- $\frac{1}{10}$. – Alexey Burdin Aug 17 '20 at 06:25
  • The final digit is the one that must match. A 10 matches a 10 or a 20, as the final digit is 0. A 1 matches a 1 or an 11, as the final digit is 1. I am unsure how to make that clearer, given that I explicitly state this... – Mathew Reuther Aug 17 '20 at 12:19

0 Answers0