[Boredom]

Actually I think in the first example you gave, $25 is the correct answer. Consider you do two trials, first one you win 100, second one lose 50. You have won 50 bucks, or 25 per trial. Over a long sample you would expect your results to be nearest this hypothetical result (half wins and half losses) so the expectation should remain close to 25 bucks per trial.

So what you need to do is do the 100-50=50 and then divide by two to get the expectation per trial.

In the 75% win 100, 25% lose 50 it's easy because of the round number percentages. (100 + 100 + 100 - 50)/4 gives an average expectation of 62.5 per trial.

What I'm unclear on is how to do it when the numbers aren't so neat, for example 76% win 100 24% lose 50 or something.