A coin machine accepts coins of 32 different colors. Every time you insert a coin of a certain color, it gives you two fixed choices to choose from. Every choice consists of receiving a monetary amount between $0 and $10 and maybe another coin of the 32 colors. You and Daniel both have a white coin to start with. You see Daniel win $500 from the machine. Can you win $1000 from the machine?

**Details and Assumptions**:

For example, the coin machine might have that inserting a blue coin outputs either a white coin and $5 or a yellow coin and $1. This output is constant; the machine won't output something different next time you insert a blue coin.