|Spoiler Inside: Solution to Puzzle||SelectShow>|
To figure this out, compute the expected value.
One-half of the time you win two dollars; this is represented by 1/2 × $2. Continue for the other probabilities. Add them together. You get an expected value of 1/2 × 2 + 1/4 × (-1) + 1/8 × 5 + 1/8 × (-4). This evaluates to $7/8. On average, you win not quite a dollar per bet. However, since it cost you one dollar to play, on average, you lose a little.
Do not take this bet.