Lottery Payout Fun

Question

I'm working on a lottery pay out mechanic for a game, and I'm not quite sure how to address multiple winners. The plan is that the players will always split the lottery earnings, but there are actually two brackets for pay out. There is the 50/50 split for matching three numbers, and a 90% Jackpot for matching all four. Assuming there is only one winning ticket for both the 90% Jackpot and the 50/50 split, what is the best way to formulate an equation that ensures that the Jackpot winner gets 90% of the payout? Closest I came with my pseudo-math is 72/27 split (of the total earnings...)

Answer 1

If you want to ensure the Jackpot winner gets $90\%$ of the payout, you pay it to him. That leaves $10\%$ for everybody else, so you can't pay anybody else more than that. I don't understand what you mean by a $50/50$ split for three numbers, but it can't be more than $10\%$.

It sounds like you have not thought clearly about what you want. One choice is to have a fixed prize pool for each drawing and have rules to allocate it. In that case you cannot guarantee a specific prize for picking a certain set of numbers, because you might exceed the prize pool depending on how many people pick the right numbers. The other choice is to guarantee a specific prize for each number of correct choices. In that case you may go over budget on a specific draw, but if you have chosen the prize values correctly you will do fine in the long run. Which do you want?