• The "Kebab Palace Casino" in Madsdale has dice with 20 sides.
• The "house" rolls two 20-sided dice and the "player" rolls one 20-sided die.
• If the player rolls a number on his die between the two numbers the house rolled, then the player wins.
• Otherwise, the house wins (including ties).
Determine the player's probability of winning.
Roll all three dice at once and then randomly select the one which belongs to the player.
The three dice must be have three different values for the player to have a chance of winning. The probability that they are different is (19/20)*(18/20) = 171/200
If the three dice are different, the probability that the player's die is the one in the middle (in which case he wins) is 1/3.
So his chance of winning this game is 171/200 * 1/3 = 57/200.
(Thanks to Kenny M for correcting my typo)
Bonus:
If the dice are n-sided, his chance is (1/3)(n-1)(n-2)/n^2. As n approaches infinity, his probability of winning approaches 1/3.
Edited on April 4, 2023, 8:23 pm
Without counting the number of ways (spoiler)
