# What is wrong with this?

**Discrete Mathematics**Level 3

Step 1. This is equivalent to the first player out-rolling the second player, the first player out-rolling the third player, and so on.

Step 2. The probability that the first player rolls a higher number than the second does is \(\frac{1}{2}\), and same for the other players.

Step 3. Thus, the overall probability is \(\left(\frac{1}{2}\right)^9={\frac{1}{512}}\).

Which of these 3 steps is wrong?

Note: When evaluating a step, you should assume that the other steps are valid.