In a gambling game a single icosahedron (a polyhedron with 20 faces, or a die with 20 sides or faces) is rolled by a player. Each face of the die has a monetary amount associated with it. The monetary amounts range from one dollar to twenty dollars in increments of one dollar, that is, $1, $2, $3, . . . , $19, $20. A player wins $1,000,000,000 if the first roll is $20, or if the first roll results in an odd number of dollars and the sum of the amounts on the first roll and the optional second roll total $20. Assuming a rational player and equally-likely outcomes, what is the probability that a player wins $1,000,000,000 (as well as many new "friends") playing this game. Write any assumptions that you might have used.

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