Providing a predetermined return-to-player for a skill-based wagering machine

A method of one or more computing devices for providing a predetermined return-to-player for a skill-based game of wagering machine, the method comprising:

• defining, with the one or more computing devices, classes of game states, wherein each class of game states includes game states sharing a common set of game state characteristics that lead to a randomly selected game state;
• determining, with the one or more computing devices for each class of game states, an expected minimum payout for the respective class of games states;
• constructing, with the one or more computing devices for each initial game state of a plurality of initial game states, a decision tree that includes a root node, intermediary nodes, leaf nodes, and collective leaf nodes, wherein the root node represents a respective initial game state, each intermediary node represents an intermediary game state achievable from the initial game state, each leaf node represents a game outcome achievable from the respective initial game state, and each collective leaf node represents a class of game states and its expected minimum payout;
• determining, with the one or more computing devices based on the decision tree for each initial game state, an expected minimum payout for the respective initial game state;
• and
• generating, with the one or more computing devices for the wagering machine, a table that weights each initial game state of the plurality of initial games states based on its respective expected minimum payout to achieve a desired minimum return-to-player.

A non-transitory computer readable medium that provides a skill-based game of a wagering machine with a predetermined return-to-player, the non-transitory computer readable medium comprising instructions that, in response to being executed, result in a computing device:

• defining classes of game states, wherein each class of game states includes game states sharing a common set of game state characteristics that lead to a randomly selected game state;
• determining, for each class of game states, an expected minimum payout for the respective class of game states;
• constructing, for each initial game state of a plurality of initial game states, a decision tree that includes a root node, intermediary nodes, leaf nodes, and collective leaf nodes, wherein the root node represents a respective initial game state, each intermediary node represents an intermediary game state achievable from the initial game state, each leaf node represents a game outcome achievable from the respective initial game state, and each collective leaf node represents a class of game states and its expected minimum payout;
• determining, based on the decision tree for each initial game state, an expected minimum payout for the respective initial game state;
• and
• generating, for the wagering machine, a table that weights each initial game state of the plurality of initial game states based on its respective expected minimum payout to achieve a desired minimum return-to-player.