What I'm trying to say is what would be the point of asking for such an exercise if you're just allowed to bet once then nothing? It would be pointless talking about EV if you're just allowed to bet once.
This is just a simplified, easy-to-understand example of a potential real-life scenario, such as e.g. a sports bet with miscalculated odds (as mentioned in the discussion somewhere above), where you don't have any guarantee that a similar opportunity would happen ever again.
EV in gambling is the amount of money won a certain bet makes on average. 'On average' is a key phrase here as it means it isn't just making one bet. It's about taking these +EV spots as much as possible and coming out ahead in the long run. And it shouldn't be from a small sample size either, it should be from a large sample size to even things out and minimize variance from the equation.
It should be a repetitive bet over a large sample to achieve this...
EV = (83% x -BTC1) + (17% x BTC11) = +BTC1.04
The EV formula presented is widely used in many areas, not only in gambling (i.e. as a business decision-making tool), and does not only work when you have an unlimited number of attempts and does not represent a guaranteed outcome.
But yeah, if you want to see +
BTC1.04 average profit on each bet, you'd need to be able to place an unlimited number of bets. But that's not what this thread is about.
But then why call the whole exercise a sort of argument for EV when it's just one bet then nothing. Sure people should take the bet and sure it's +EV, but does one bet prove the theory in practice? No, it should be a series of +EV bets done with a large sample. In your example, if it's just one bet then there's more chances hero would lose in practice making arguing for EV useless.
I guess what I'm trying to say is if it's a +EV bet but allowed only to take once then what's the point of EV? One bet means nothing EVwise unless proven over a large sample.