Assume that there is a raffle that randomly selects a number from 0 to 9.
You can choose a single number to place a $1 and gain $5 if you win.
You can choose as many numbers as you want.
Which is the best strategy to maximize the possibility of making money?
I feel that the best shot that you have is to pick 4 different numbers, which will land you a 4/10 probability of wining $1. But I can't help it feel that it seems a bit simplistic. Truth is, I know little about probability.
Though I might as well come in and ask, because it really peeked my interest. Is there maybe another possibility with better odds? maybe pick one number N times, another one M times, and yet another X times?, or any other approach maybe?
Seemed interesting to me, and since my probability knowledge is basic at best, I am also thinking of variants as "what would happen if the payout differ for a specific number?", or what would happen if "there was a second raffle with only the remaining 9 numbers?", "how did they calculated that a 1 to 5 pay out would help the house odds?", "is there another payment that works?", "what would be a bad pay out for the house?" and a whole lot of similar general questions, however not sure what to read to learn about it, will love any suggestion.