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Comment by thethirdone | Hacker News Reader

> For example, it might be okay to risk a $1 bet to win $1,000,000 if the probability is one in 500, but it is quite another thing for the average person to risk $50,000 to win $1,000,000 if the probability is one in 400. Even with better odds in the second case,

The author either made a typo (intended billion rather than million) or doesn't understand probability. The second case is on average going to lose you money. The expected return from getting $1,000,000 1 in 400 times is only $2,500. So betting $50,000 will on average lose you a lot of money.

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An interesting real world example of a group of rationalists failing to convert belief into action:

https://www.lesswrong.com/posts/MajyZJrsf8fAywWgY/a-lesswron...

A large number of people in this community regretted failing to invest in cryptocurrency, despite being the perfect group of people to recognize the spectacular potential payoff of the decision.

Some folks who try to be rational pulled out of bitcoin/similar when their stakes were lost in one or more of the exchange hacks / inside jobs. I know I bailed when my ~.25 bitcoin disappeared in an exchange "hack" 5-6 years ago (back when that amount was worth something like $100).

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.

> The odds of 1:500 are worse than 1:400.

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.

The author was using the "pay 50k to win 1M at 1:400 odds" example to illustrate how the calculating the expected value (in a mathematical sense [1]) does not always result in the "most reasonable" decision. If I understood correctly, his point was that _even if_ the expected value (reward*probability - cost) is positive, it still might not make sense for the average person, because of the non-linear relationship between the money they have and the utility they will derive from it (i.e. the first dollar is more valuable to them than the millionth dollar).

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.

[1] https://en.wikipedia.org/wiki/Expected_value

I think it's reading too much into it. It was to illustrate that better odds are not necessarily an overall improvement.

Yeah, expected return only makes sense in e.g. a diversified portfolio.

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.

penis

Please don't.

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