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.
> However, you definitely can use "expected return" to talk about singular events if there are known probabilities involved.
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.
> Just that "expected" sounds like there's a certainty about it
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.
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.