If I am rolling a 20 sided dice, twice and taking the higher number of the set rolled, and rolling 12 sets, how many times will I get a 19 or 20?

Question

This is a question relating to the game of Dungeons and Dragons.  I am trying to work out if 12 attackers are attacking the same target, and if they need to roll a 19 or 20 on the 20 sided dice how many of the 12 attackers will succeed.  Compounding this is that they are each gaining advantage, so each attacker may roll two 20 sided dice and take the highest result.

Answer 1

This problem is like, similar to, and comparable to, rolling a pair of regular dice and solved the same way.

The only difference between them in fact is that this problem has a 20 sided die

and the outcome of interest is the MAX rather than the sum.

 

THere are 20x20 = 400 possible outcomes.

 

There are 37 ways to get a result of 19.

There are 39 ways to get a result of 20.

So the probability of 19 or 20 is 76/400 = 38/200 = 19/100 = 19%

 

So the expected value for 12 sets or trials, is 19% x 12 = 2.28

You can expect 2 or 3 of them.

 

I have uploaded the spreadsheet that models this experiment in the resource files section.

The filename is 20 sided dice.xls