The odds of 1:500 are worse than 1:400.
Anyway, can you even talk about "expected return" on independent events like these? There is no expectation of you winning, ever, in either scenarios.
Anyway, can you even talk about "expected return" on independent events like these? There is no expectation of you winning, ever, in either scenarios.
The example doesn't support that point very well because the expected value of making that bet is negative, so the bet would not make sense even in the naive case, where all dollars have equal utility.
Indeed odds of winning are technically "better". But if I gave you the opportunity of getting $1,000,000 99/100 times for the cost of $1,000,000 I don't think anyone would say those odds are better than 1:400.
> Anyway, can you even talk about "expected return" on independent events like these?
Technically, I used the wrong term. I meant "expected value" which is `probability of winning * value of winning`. However, you definitely can use "expected return" to talk about singular events if there are known probabilities involved.
> There is no expectation of you winning, ever, in either scenarios.
Surely you expect to win occasionally (namely 1 out of 500 times or 1 out of 400 times). If you had no expectation of winning, there would be no point; it would just be lost money.
Just that "expected" sounds like there's a certainty about it. If I lose 100 times in a lottery with 1:500 odds, it does not mean my odds have now improved to 1:400. Playing the lottery 500 times does not give you expected return of 1, the odds are the same 1:500 in every round.
It does seem give a sense of certainty, but is not how "expect" is used in probability. The expected value is just the average value per attempt as converges as attempts approaches infinity. So its a useful measure of a distribution (which can be used to make informed gambling decisions), but shouldn't be used to make a prediction on any single attempt.
edit: You can downvote all you want, but it still doesn't make sense to consider the expected return on one item in isolation. If you disagree, provide a reason.