A Polythene citizen visits a bar on the border & buys a drink for 5 cents. He pays with a poly note of his own country, and receives in change a Polydor poly note, worth 95 cents in Polythene.

No he doesn't. Rename the currencies A and B. B1.00 is worth A0.95 in Aland. A1.00 is worth B0.95 in Bland.

So Polycytes from Aland goes into a bar in Bland, asks for a B0.05 drink and pays with A1.00. This is worth B0.95 so he receives B0.90 change, not B1.00. He takes his change and buys a drink in Aland, tenders his B0.90, here worth A0.855 and receives either B0.80 or B0.81 change, depending on how the rounding is done.

And so on. He'd get more drinks at home.

If on the other hand the agreement were that the neighbour's currency were valued at 1.05 times its value at home, the conundrum would work.

In this most generous case, the bars in each land have their stack of x0.05s, and Polycytes has x1.00, depending on the location of the last purchase. All are happy. The following day, waking late with a bad head, he draws all his savings from the bank, a mere A99.00 because of his drinking habit, crosses the border, and exchanges his money with a passing citizen of B, Polycrates, who gives him B103.95 in exchange. He returns to his bank, banks B100.00 and is credited with A105.00, He spends the remaining B3.95 on drinks and doesn't get up the following day.

Polycrates however is a teetotaller, and grasps the opporrtunity. He takes his A10000.00 to the bank and is credited with B10500.00. He withdraws B10000.00, crosses the border and opens an account in a nearby bank, and is credited with A10500.00. He immediately withdraws A10000.00, recrosses the border, and returns to his own bank where he is credited with B10500.00, his balance now being increased by B11000.00. He repeats this as fast as his little fat legs will carry him.

The following day, he tries to repeat the same process, but finds that his own bank is closed. The staff have failed to turn up for work. He goes to the next nearest branch, and withdraws his B10000.00. On crossing the border, he finds the nearest bank closed, as coincidentally the staff therehave also absented themselves. Continuing to the next bank, he finds himself in a queue behind several people whom he recognises with some puzzlement as the staff of his own bank in Bland. Eventually banking his B10000.00 and withdrawing his A10000.00, he returns to Bland, only to find himself in a queue of the staff of both banks nearest the border.

Do I need to describe the mad dash to withdraw his entire savings, and race to Cland where despite a very disadvantageous exchange rate, Polycrates manages to open an account just before the currencies of both Aland and Bland irrevocably collapse?