The problem: Say two people each roll 3 20-sided dice (a total of 6 dice). Person 1, only keeps the lowest die from the throw. Person 2, only keeps the highest die from the throw. What is the chance that person 1 rolls higher (not equal) than person 2?
Furthermore: I am going to check what happens to the percentage if they roll 4,5,6 dice instead of 3.
Solution: Obviously I am interested in all the help I can get. I would like a solution/approach that can be used with different amounts of rolls, and give an answer, preferable something like change x for amount of dice in each roll. I don't study math in university.
My attempts: I have tried to calculate it in Excel, but my math/excel skills were not great enough for me to get beyond a scenario where person 1 rolls 2 dice, and keeps the lowest and checks if it is higher than person 2, without removing the highest. I check before posting if I could find the answer in this site.