X = btc/usd on Jan 1 2023 (16605)
Y = btc/usd on Jan 1 2100
Resolves PROB to 5*((Y/X)^(1/77)-1)

If the prob would be less than zero, it resolves NO.

If USD ceases to exist we use the successor currency at the last available exchange rate from USD to the successor currency.
If BTC ceases to exist we use the successor currency at the last available exchange rate from btc to the successor currency.

If USD ceases to exist without an obvious successor this resolves YES
If BTC ceases to exist without an obvious successor this resolves NO

If AI kills everyone and both cease to exist simultaneously, this uses the last available exchange rate.

How I think about this problem:
my expectation for the long term change in BTC/USD is: (fed inflation target) + (average fed overshoot) + (average world real gdp growth) + (increased adoption factor)
fed inflation target = 2%
average fed overshoot = 1% (Range: 0-3%)
average world real gdp growth = 3% (maybe higher with AI or lower with demographic collapse and dysgenics. Range: 0%-6%)
increased adoption factor = 4% (this one is the most uncertain. I'm basing it on 25x adoption over 77 years because bitcoin is currently 1/25 the market cap of gold and my median case is parity with gold as a % of global financial assets. Bull case is parity with fiat and bear case is parity with dogecoin, Range: -5% to 7%. )
Could add another 1.65^(1/77)=0.66% for the 65% increase in btc/usd that already occurred between Jan 1 and market creation time but it's too small to matter.
Combined range: 0% to 18%
Combined median case: 10%

my model for the long term change in GLD/USD starts with the same first three numbers but instead of a positive adoption factor there's a negative factor for inflation in the gold supply of 2-10% per year with a 3% median. The high end is if asteroid mining pans out. This gives a combined median of 3% and a combined range of -8% to 9%.

Regardless of your thoughts on bitcoin in particular, it should be clear that any fixed-supply global currency people agreed to use would outperform fiat by 6% in expectation over the long run. Constant supply + constant velocity implies deflation equal to real gdp growth (3%), instead of 3% inflation via QE. Also making a big assumption here that downward nominal wage rigidity is no big deal and the choice of currency won't affect long-run gdp growth.

arbitrage-free interest rate parity requires the depreciating currencies have higher risk-free-rates than appreciating ones, so this analysis doesn't necessarily reflect the total returns realized by the investor.

related arb-able markets: