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What were tally sticks, and how was it that they they worked for the economy? I understand that they were a form of currency and were of fixed value based on the notches, but how did they work as a currency? Were they used like banknotes and coins are used today - exchanged for one another from the highest to the lowest levels of economy? I can't imagine them being too useful on a small scale due to their size.

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Tally sticks were credit-based money used by the King of England from roughly the XIII to the XIX century.

The idea was quite simple: in a credit based system, you have to find a way to represent the credit which is uncounterfeitable and cheap to produce. It also had to have no value as an object, otherwise you can have a market for the object rather than for the money it represents. To do that, you take a stick, make notches on it and split it into two parts (split lengthwise). The way notches are done is important: intervals between them for instance is quite important. An amount of money is encoded with the notches.

When you want to pay something to the Crown (=taxes), you just give your part of a tally stick for the amount. Your part is then matched against the other half which is kept at a central location. If the match is okay, then your payment is validated.

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