perplexus.info :: Probability : Kebab Palace Casino Conclusion

Kebab Palace Casino Conclusion (Posted on 2023-04-04)

• 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.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The player's probability of winning is 57/200=28.5%.
If the house didn't win on a tie but the player did, this would be giving an average of 7.65 for a probability of a win being 7.65/400 = 38.25 %.
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.
For an explanation:
Refer to the solution submitted by Steve Herman in this location.
Refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Counting the ways another way	Charlie	2023-04-04 12:58:30
Let me count the ways.	Larry	2023-04-04 12:30:18
re: Without counting the number of ways (spoiler)	Kenny M	2023-04-04 10:23:01
Without counting the number of ways (spoiler)	Steve Herman	2023-04-04 07:30:42

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