Suppose you need to keep track of victory points or some common resource using tokens or chits. Suppose, furthermore, that you would like to have two denominations—a single unit token and some higher value. To minimize the number of chits that have to change hands, what values should you use?

I’ve created two tables. Both show the number of chits that must trade hands as a function of the higher denomination (across) and the number of chits traded (down). The top table assumes that change cannot be made, while the bottom table assumes that it can.

Things to note:

• If players usually won’t be able to make change, and transactions are fairly small, 3 or 4 is likely the best choice. Assuming transactions evenly distributed in size from 2-10, the average transaction is 2.4 chits.
• If players are often able to make change, 4 and 5 are better choices, with an average transaction size of 2.2 chits. Denominations of 2 and 3 do not benefit at all from change-making.
• Large denominations like 10 are probably only a good idea if your transactions tend to be very large, or if players will be accumulating many dozens of points.