Double or nothing

Level 2

Suppose a robot is playing a game of double or nothing. In the game, you start with a prize of $1. Every round, you can either choose to take your current prize or attempt to double it. If you attempt to double the prize, there's a 50% chance that your current prize gets doubled, and a 50% chance that you lose the entire prize. If the robot randomly chooses to take the prize or double it, what is the average prize it will win?

\infty

\frac { 3\pi }{ 10 }

$2 $

\frac { \pi }{ 3 }

$1 $3 $

\frac { e\pi }{ 10 }

\frac { \sqrt { 3 } }{ 2 }

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Double or nothing

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