You know how if you have 25% chance to win 20$, this is equivalent to a 100% chance of winning 5$ (it uses the assumption that 20$ are four times as important as 5$, which isn't 100% true and it probably would be much less true if we use 1 in millions chance to win millions of dollars vs. 100% chance to win 1$). I'm having some trouble with proving why is this approach the best approach to probabilities. I just know that it is and I have evidence that is really hard to explain.

I'm trying to explain to my father why he shouldn't play the lottery, but I don't know how to explain it to them. He is highly intelligent, but he isn't good with counter-intuitive things (a.k.a. dysrationalia, if you're into cognitive psychology).

The above text is my own hypothesis, trying to prove the expected outcome approach - if it's vague (it probably is), just ignore it, it's not vital for my question.

One of the explanations I thought of is that if there is 50% chance to win something, that would mean there are two alternative "universes" (the only difference between them is that in one of them, I won that thing) and they are equally probable, so I might as well count that they both semi-happened (can I? this is the part of my hypothesis that might contain a fallacy), because that would be like they both happened, but then I divide it by two - and by "semi-happened", I mean that everything counts to a half-degree (so most things would remain the same if it was a 50% chance to win 1$). There is a single result (which is the average of the two possible results - they don't have to be two), which is what I need - when I consider a decision which has probabilities (say, playing the lottery), I'll compare two results - in one of them, I take the result I got from combining the probabilities, and in the other one, I take the result I'll get when I decide to not make the decision. The second result is often me winning/losing 0$, so it all depends on whether I have a profit or loss at the first result. That is how I deal with situations with probabilities, I just need a way to explain this approach understandably, because I sometimes have issues with that. Any alternative explanation would be very useful, this is probably what am I looking for, because my explanation doesn't seem convincing enough and is very counter-intuitive and hard to understand (even if I find a way to explain it more clearly). It doesn't have to be clear, though - I'm also looking for a way to explain it to myself, because I'm not certain it's true at all - there should probably be a widely accepted explanation, which is what I'm hoping to get.

Also,any criticisms of my ideas are welcome!I don't expect you to agree with me, and if you prove me wrong, that would help me.