When making denominations for coins and markers (VP, mana, whatever) in board games, 1 5 20 100 500 is good. I don’t want too small factors between a stepped pair (such as 1:2 or 5:10 or 10:20), or if there is, then I’d want significantly fewer of the lower denom.
For example, in a game where 2-coins exist, that’s fine if there is only one 1-coin per player. Whenever they gain an odd amount of coin, they’d either lose or gain their 1-coin. You provide a bunch of 2-coins that can flow, and then everyone has their 1-coin within reach.
“Neat change” is defined as when you have as few coins as possible in as high denoms as possible. For example, 1 2 5 is a neat way to have 8 in a system that has 1-coins, 2-coins and 5-coins, while, say, 1 1 2 2 2 is an un-neat representation of the same amount.
It’s completely dorky and gauche to ask someone at the table to change to a neat representation just because you have your hangups about neatness. Don’t do that.
However, when there is consistently neat representation, it’s possible to grok the sums quicker and with less effort. It’s easy to underestimate this effect until you’ve experienced it for yourself. When representations are reliably always neat it’s a completely different level of immediacy compared to having to count it out and add it up in a new way every time.
We want to design systems that inherently afford neatness without having to be gauche dorks at the table.
As I mentioned in the intro, scarcity affords making change. At every level where the step factor is small, make sure there is a completely ridiculous lack of coins. If there are 5-coins, 10-coins and 20-coins available, you really only need one 5-coin per player and one 10-coin, and then a huge number of 20-coins. The scarcity itself will enforce people making proper change.
Obviously, having too many denominations (like a 1 2 4 8 16 approach) is cumbersome in its own special way since it’s the additions aren’t homomorphic. Uh, that’s a word I just made up but what I mean is that if you have a bunch of ones and fives, you are gonna get used to making change between ones and fives (like, you gain three? You learn quickly to take 5 and give back 1 and 1) and you are very quickly gonna get used to thinking in multiples of five plus some remaining ones.
With the more binary nature of smaller gap factors, making change is possible to learn but grokking the total at a glance is harder.
Whereas scarcity encourages constantly changing, big gaps afford relative (if not perfect) neatness by you simply not having to (or be able to) change often. If the nominations go 1 20 500, for example, you’re not gonna have to change to 20 until you’ve managed to scrape together twenty 1-coins.
Of course, that is completely ridiculous. Adding up twenty 1-coins is not easy. We don’t want the denom gaps to fall out of subitizing range (a.k.a. “at a glance”-range).
A Goldilocks denom set is 1 5 20 100 500, with numbers being both traditional and familiar, while also being multiples of four or five which is subitizable.
Sometimes you can also leverage the scarcity principle when designing your game’s component set, or when setting up your playspace. If people each have access to four 1-coins, three 5-coins, four 20-coins, and four 100-coins, you basically have ensured constant neatness.
This is a design consideration that pretty much only shows up in gaming, because that’s the only situation where people have one pool each and an always-available exchange bank. Games like Monopoly or Netrunner or the victory points in Caylus 1303 or the life, poison, or energy points in Magic.
Any situation where your money needs to be split into separate pots, like in Jump Drive where each turn of income is its own pile or even poker where your holdings are separate from your current contribution to the pot, gets awkward. You cannot apply the scarcity principle there. You can still benefit from the subitizing benefits of the Goldilocks denom set.
Situations like your real-life wallet, this doesn’t apply. That’s where otherwise completely cockamamie denom steps like 1 3 5 10 or 1 2 5 10 can make sense, since there is no easy way to make change anyway and thus no hope for neatness ever.
Situations where scoring is hidden (essentially “write-only”) are similarly inapplicable. You gain points, put them in your vault, and move on, and never make change. Issues with hidden, but trackable information are what they are, although this also applies to hidden and non-trackable sources of points, like the random point chips in Jaipur.