How do you calculate that for bitcoin? You dont. So its not like a lottery ticket. A lottery ticket is throwing money away. Bitcoin is betting on the success of a technology.
If the expected return of bitcoin is positive according to your probabilities, go ahead and invest on it. I am not trying to talk anyone out of it.
But you cannot honestly tell others that it is a good investment, because you cannot claim that your probabilities are more reliable than mine or than those of that guy over there.
It seems that those investors whose expected value is 1,000 USD or more are very few, and they have run out of money; otherwise they would keep buying BTCs until the price gets over their expectation.
Therefore, most of the "loaded" traders have expected values less than 700 USD right now. To get that value they must assign very small probability to "bitcoin will be eventually worth more than 700,000 dollars". Specifically, they think that the chances of that happening are less than 1 in 1000. (Even if they do not externalize that probability, it is implicit in their reluctance to pay more than 700$ for one bitcoin.).
But why P = 0.001 and not P = 0.002 or P = 0.00001? There is no logic or experience that will help one choose between those probabilities. Yet they lead to very different expected values. And indeed, in the last two days we saw that the price is pretty random: it can rally by more than 100 USD on a rumor, and remain there after the rumor is proven to be false.
instead of a lottery ticket, a better analogy could be an old piece of paper that someone claims to have found among their great-great-great-great-grandfather, with what appears to be the map of an island with a "X" and a note "three tons of gold buried here". How much would you pay for such a map? Is paying 700$ for that map a good investment?