I have N type of slot machines.
Each Machine have a Winning amount range from $1, 1/2, 1/3, 1/4, ... 1/N$.
I have M people, they can only choose to play with one winning type of machine.
and the slot machine winning probability is 50% (fair machine)
If everyone is allowed to play with machine T times.
And I want to know who are the top-K winners.
Can I look at the results by only a handful type of machine only(those have bigger winning amount type)? With a probability guarantee that I got the top-K winner?
A player gets a slot machine with N slot machines assigned to M of them is $\frac{1}{N^M}$. The probability that he wins with that machine is .5. Thus the probability that a player wins with his slot machine is $\frac{1}{2.N^M}$. If he plays T games, each player winning x games follows the binomial distribution and that the expected number of wins is Tp where T is the number of games he plays with the slot machine and p is the probability that he wins. Since the cash is in descending order, the first K winners are likely to be
$\frac{T}{2.N^M.K}$