there is no consensual expected value.
The efficient market hypothesis would tell us that the best predictor of future price is the current price. The price is the consensual discounted value.
If N is less than 3, say, "value" can only mean the market price at that time. One cannot predict the BTC price even 5 minutes ahead of time, much less N years from now.
You can predict the BTC price 5 minutes from now. The price now is a good approximation. On that scale any deviation is pretty well characterized as stochastic volatility.
You seem to aver heavily to volatility. But there is a robust and long established financial theory of volatility. It has well-understood characteristics, and rational financial decisions are made in the presence of varying degrees of instrument volatility every day. Bitcoin is not even all that volatile. Any pre-IPO venture might easily trade shares at integer multiples of the volatility of Bitcoin. That does not make them bad investments. The characteristics of the enterprise and the utility metric of the valuer determine whether it is a good investment or a bad one.
It can be easier to make a useful longer-term prediction than a useful short-term one. (Your implicit argument seems to assume the opposite.) In the long-run stochastic volatility just doesn't matter much because fundamental factors dominate, because they persist, while stochastic volatility tends to (1) cancel, and (2) be damped.
If "N years from now" is taken to mean "after cryptos are in general use", then one needs to assign probabilities to "cryptocoins will eventually be in general use", "cryptocoins will be used in more than 1% of e-commerce transactions", "the same cryptocoin cannot be used more than N times per day", "X% of those cryptocoins will be bitcoins" and so on.
Very true. Estimating the parameters of the valuation model is critical to accurate valuation. A well-informed actor can make a better estimate than an ill-informed one. I consider myself reasonably well-educated and well-informed on the subject -- I am paid well to be so -- and have estimated the distributions of these parameters. I consider Bitcoin to be an excellent investment, in the sense that it's risk/reward characteristics are suited to my utility function. I suspect that our utility functions differ, but perhaps less than immediate appearances would indicate.
On the other hand, indeed Bitcoin is a bit better than a lottery ticket, in that it is not demonstrably a bad investment. The expected value of a lottery ticket is invariably less than its price, so it everybody will agree that it is a bad investment. Since the expected value of a bitcoin is not defined, one cannot prove mathematically that it is less than its current market price. But by the same token, one cannot prove that it is a good investment, either.
A fair and accurate assessment, I think. But one can form a Bayesian model which indicates whether or not it is a good investment, under a given utility function. Again the utility function. A theme is forming.
So, how can one honestly recommend investing into bitcoin as a hedge against a possible dollar collapse, as a way of becoming a millionaire, or whatever the "salesmen" are saying these days? It is like buying a ticket for a crazy lottery that does not tell its clients what are the odds and prizes, and may or may not be seeking to lose money.
I think it is reasonable to believe on the basis of structural characteristics that Bitcoin will be uncorrelated with USD both in the tails in any run and in the center in the long run. The facile summary for the latter is: Because inflation. Uncorrelated instruments are the foundation of modern (and post-modern) portfolio theory.
Your use of "millionaire" is a rhetorical device. Leaving the rhetoric aside, observing the correlation of bitcoin fiat value with bitcoin network growth and the persistence of bitcoin network growth is sufficient to demonstrate to any reasonable follower of markets that buying bitcoin is likely to outperform buying the market, for the forseeable future, in a very simple, direct, and obvious statistical sense. That is very unlike your "crazy lottery".
Your reasoning always seems to start with facts and sound principles and then suddenly take a hard turn into la-la land. I am becoming hardened in my inference that you have a utility function which is not serving you well. Utility functions are slippery things, often left unconsidered, unreflected, but with profound impact on outcomes. I recommend this literature to you. Read about the utility function in relation to Kelly criterion, exponential discounting, and modern behavioural economics. Maybe some Taleb, some Ariely, and some Kahneman/Tversky would do you good. Certainly Kuznetsov's "Complete Guide to Capital Markets for the Quantitative Professional" would be a helpful read.