the house rolls 5x 100 sided dice
the sucker rolls 1x 100 sided dice
the sucker must roll a higher sum than the house to win

what % chance to win does the house have in this situation?


~thanks

Are you saying the House gets to sum 5 rolls and the Player has to beat that sum with 1 roll?

If so, I ran a simulation since this question is very easy to program.

Over 100,000,000 trials, the Player only won 118,595 times.

If I am doing this correct, the House won 99.881405%.

Are the sides numbered uniquely 1 to 100? This can be solved mathematically. I'd start with the EV of 50 and use a normal distribution for the sum of N rolls.

(1) I would not suggest applying a normal approximation for the sum of only 5 iid variates. That is way too few for the PDF to approach normality.

(2) The PDF of a sum of 5 iid discrete uniform variates can be derived, but the general formulation is "messy" (IIRC involving sums and partitions).

(3) The mean (of course) and standard deviation of the sum of 5 iid discrete uniform variates is easily derived. Maybe applying standard theorems of CDF's based upon mean and standard deviations (e.g. Chebyshev) is a way to go.

(4) Since modern computers are so fast and this is very easy to program, I preferred a simulation over 100 million trials. Standard sampling theory suggests that the above simulation result should be near the true percentage plus/minus .001%.

Edit to add: I just ran another simulation of 100 million trials and this time the House won 99.881196% of the time.