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DanielLC comments on Cold fusion: real after all? - Less Wrong
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You get true knowledge either way, but you might only get useful knowledge one way. If you're running the experiment because you want useful knowledge, then it's a gamble.
Also, you're not necessarily getting the same amount of knowledge either way. For example, if you're 99% sure before the experiment, you only get 0.014 bits of knowledge if you were right, but you get 6.6 bits if you were wrong. There's a factor of 458 difference.
Ah! I think I see what you mean. This is a matter of how much one wins, not whether one wins.
As for usefulness. What do you mean?
It's a bit more complicated than that. You have to pay to run the experiment. If you make your decision based on the expected winnings, and pay more than the minimum winnings, then if you get the worst outcome, it's a net loss.
Knowledge tends to be instrumentally valuable. Regardless of your goals, knowledge will be helpful to accomplish them. However, not all knowledge is equally helpful. For example, knowing how to make a cold fusion generator will be useful for making paperclips or running experiments or whatever it is you find intrinsically valuable. Knowing that you can't make a cold fusion generator will only be useful for preventing you from wasting time and money trying to make a cold fusion generator.