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I'm dealing with a problem as follows:

  • I have a finite set of money $m$ to spend over $r$ different raffles, and I need to spend approximately to my budget, with the goal of maximizing my probability of my total winnings across all raffles being a constant $w$. Each raffle has a different prize amount $p$, and there is a certain amount of time $t$ between now and when the raffle winner is drawn, and at each interval a random number of people $pe$ enter each raffle(which I have perfect information of), and a random number of people refund their raffle ticket $pr$. So, the probability I win each raffle can go up or down each temporal period. I start the scenario with a differing number of raffle tickets in each game, and I have a defined value function for each raffle so I know the increase I get in probability of winning the raffle based on the amount of money I spend buying raffle tickets for it.

I've looked into multi-armed bandit problems and knapsack problems but I don't feel the problem perfectly fits into either bucket. Are there multiple problems at hand here, and that's why it doesn't appear to fit into any of those categories?

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