We can figure out how long the Fed reserves will last

We can use out Poisson assumption and get a good idea. First we construct out two period model.

Deposits^2-Loans^2 = Liquidity

Now liquidity is going to be low, by law the Fed is not allowed to be a central banker.  But let's set liquidity to 1.0, as if the Fed is perfectly adapted to the Shannon condition.  That chat on the left is loans/deposits, tanh.  We will find the probability distribution of liquidity on the right side of the equation. It will be a distribution named Skellam, and wiki has it here. Skellam is constructed from the two parameters, Cosh^2 and sinh^2, so lets find out what Cosh and Sinh might be when tanh is near one. But one catch, we have not included the reverse repurchase deposits.  But I have looked and I can say that adding them in makes tanh near .98. That makes Cosh^2 about 25, and sinh ^2 about 25.

The Skellam distribution says the mean to variance is going to be 1/(25+24) os about 1/49. What that means is that the Fed has to go through 49 variations of deposit combinations otherwise called Fed press conferences. That would be 2^49, or some 10000 trillion months assuming the member banks alter their portfolio once per month. Mathematicians will give a better answer from the moment generating function which tells us the time, or number of transactions to expect.

Why don't I use log(50,2) and get the number of bits? Because the bankers have to build the encode and decode tree, they have to count all the combinations first.  Mathematicians will correct me, but I think I am close. In this case we have 30 member banks.

But wait, you say, wasn't the tanh  above 1, up to 1.15 during 2012? You bet, and when the Fed does that is it fermion statistics, we use coth, 1/tanh.  During those periods money is sucked from tax payers and handed over to wealthy people.

Can the economy wait 900 trillion years? No, the boneheads in DC will fly the helicopter, as in Nixon Shock.  The super wealthy have their baskets ready, they will know where the money lands.  Hence the urgency of getting banker bot into the pocket of every middle class person in North America.