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I am trying to get a foothold into a new area for me. In games of chance (e.g., the lottery or roulette) I would like to understand how to setup the payout matrix. For example, in roulette, there are a variety of bets you can make for which the house take is the same and you can go from as little as doubling your money to as much as 36 times your money. With a lottery ticket you can win from as small as getting your money back to hundreds of millions.

What (sub)fields does the design of the pay off structure fall under and what are some of the keywords that will let me find good introductory literature.

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