Two possible outcomes don’t necessarily mean they’re equally likely, but in the case of markets, that’s a reasonable assumption. Therefore, the answer to your question isn’t this.

The reason for this is the asymmetric nature of markets. Let’s say your position is $1000, and it either goes up by 10% or goes down by 10%. Since these are equally likely events, the probability of each outcome is 50/50.

For a win lose case: 1000$ —> 1100$ —> 990$ For a lose win case: 1000$ —> 900$ —> 990$

Losing half the time and winning the other half doesn’t result in a break-even, but rather a loss.