Multiple line slot machine math

How can one calculate the probability and payout for a After reading this answer on gamedev.stackexchange, and this answer here on math.stackexchange, I totally understand how to calculate the payout for a slot machine. To summarize: In order to pay-out 95% of every dollar spent on a three wheel slot machine, (each wheel has 10 unique symbols) a jackpot match of 10-10-10 would pay out $950.

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Slot Machine Paylines. The number of pay lines available in a game is among the most important features of any slot machine. A payline, in simple terms, is the line on which a payout will be awarded based on winning combinations. There are X amount of paylines in any given slot, whether that number be 1 or 100.

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