Task

Consider a lottery where the winning amount is determined by the consecutive number of tails flipped with the winning amount doubling after each flip.

First flip: If heads, the lottery pays $1, and the game ends. If tails, the coin is tossed again
Second Flip: If heads, the lottery pays $2, and the game ends. If tails, the coin is tossed again.
Third Flip: If heads, the lottery pays $4, and the game ends. If tails, the coin is tossed again.
Fourth Flip: If heads, the lottery pays $8, and the game ends. If tails, the coin is tossed again.
Fifth Flip: If heads, the lottery pays $16, and the game ends. If tails, the coin is tossed again.

This goes on ad infinitum: On heads, the lottery pays out double of the prior round and the game ends. On tails, the coin is tossed again.