You're arguing like a gambler who puts his house on the poker table but tells everyone it's just for show, as it's practically impossible that he could lose this round.
-- $E(X_t|F_s) = X_s,\quad t > s$
Which means people will keep buying the IOUs. For now.
Ask youself who is stupider: investors and creditors who accept worthless pretend IOUs to cover known bad IOUs, or taxpayers who believe that the IOUs their government has issued in their name are fake and will never be paid out when asked.
You can't have it both ways, either you "solve" the problem with real IOUs, or you issue fake IOUs and "solve" nothing, since everyone knows they aren't worth anything.
The point of real IOUs is that there is real risk attached to them. It doesn't do to hope that things will work out without anybody requiring payment. -- $E(X_t|F_s) = X_s,\quad t > s$
It is, on average, a losing strategy, but if you're going to gamble... The brainless should not be in banking. — Willem Buitler
So the question, as expected, is whether you win before you run out of liquidity... In the long run, we're all dead. John Maynard Keynes
However, the expected number of bets to achieve the outcome is infinite, since the strategy is nonintegrable, and while one game might(!) let you win 1 with certainty, in repeated games you will run out of money, or if you have infinite funds, you will fail to achieve any strictly positive rate of winnings in the long run (and depending on how you compute the rate of winnings, you could fail to achieve any finite negative rate of winnings either, ie the losses can't be usefully limited). -- $E(X_t|F_s) = X_s,\quad t > s$
