Quote from: Picaflor on Today at 02:33:59 PM

Quote from: aseev on February 11, 2023, 02:08:19 AM

The video talks about objectively favorable results. With Bitcoin the possible outcomes are unknown. Expected Value has little to do with this.

If you assume the BTCUSD price is going to infinity over the long term, the volatility is akin to the random outcomes of the coin tosses. The expected value is then objectively positive and increases with the passage of time (with the standard deviation decreasing), just like in a series of positive EV coin toss bets it increases with the number of rounds. So if you buy BTC now, it may be worth less tomorrow (a lost coin toss bet) but it's unlikely it will be worth less in 10 years.

Accepting a coin toss bet is a gamble (even a positive EV one, because you may still lose).
Accepting a series of 100 such EV+ bets is a DCA and hodl plan (you may still lose over the chosen timeframe, but less likely).

Both coin tosses and a Bitcoin hodl can be modeled by 1-dimensional random walks with probability skewed towards one side.

Ignoring trading fees, price going to infinity implies the EV of a BTC buy for a unit of time is positive (if it were negative, the price would be going to zero). So under the assumption of price going to infinity, and zero fees, the two stochastic processes can be reduced to each other. For the BTC side you may need to use a log scale if you believe the growth is exponential though, because for the coin tosses it's linear.

There are objectively favorable conditions in the experiment in the video but there are no objectively favorable conditions in flipping a coin. It is 50/50 in the long run. But even if you ASSUME (although why would anyone assume that anything will go to infinity?) that the probability of tossing your coin skewed towards the favorable side, you use only two outcomes in your assumption - increase and decrease in value. You don't factor in other outcomes, such as those that could cause Bitcoin to cease to exist.

Instead of a coin, it may be better to use a die analogy with different sides that include additional outcomes like government intervention, overtaking by other cryptocurrencies, lack of decentralization, security breaches, technical issues, and the rise of quantum computing that will make cryptography obsolete.