Almost every rewards program bends its math so big wallets can't take everything. At Zeru we score wallets with zScore and build incentive tools through Zaps, so we get to see how these formulas behave on real wallet data. The bend pays someone, and it isn't the small user.
The wall every program hits

Every points program and token distribution runs into the same problem. A handful of wallets do most of the trading. If you hand out rewards in proportion to volume, those few wallets take nearly everything and everyone else gets a rounding error.

That looks bad, so the standard fix is to bend the math. Every dollar from a small wallet gets more weight than every dollar from a big one. Square root is the usual choice. Big wallets still win, just not by as much.

It reads as fairness. What it does is pay you to split up.

If the rule gives small wallets more per dollar, then spreading the same money across a hundred wallets earns you more than keeping it in one. You did nothing extra. The formula pays small wallets better, and now you have a hundred small wallets instead of one.

Here is one clean example. Three days of trading on Base: 2,539 wallets, each making a single swap of roughly $201, with wallet numbers running in sequence. Between them they moved $510,414, about a quarter of one percent of everything traded that week.

Under plain proportional math they would earn a quarter of one percent of the pool, exactly their share.

• 0.27% is what they would earn under straight math.

• 9.32% is what they would earn under the "fair" curve.

The biggest genuine trader in the same window would earn 7.7%. Under the rule designed to stop big wallets dominating, the small ones out-earn the real top trader while doing a fraction of the trading.

We are not saying one person runs those 2,539 wallets. We don't know who owns them, and it doesn't matter. The formula pays extra for money that arrives in small pieces. Whether it's one operator or 2,539 separate people, the payout is identical.

It works like a shop that offers a bigger discount on small baskets. You don't need to catch anyone. People just start splitting their trolley.

There is a second argument for it. Under straight math most people earn amounts too small to care about, a few cents. Bending the curve is supposed to lift them.

It doesn't. On a small pool, even the most aggressive bend leaves two-thirds of traders under a dollar. The formula isn't the problem. Trading is just that lopsided to begin with. In our window the middle trade was $186, the average was 117 times that, and nearly two-thirds of all traders made exactly one swap in three days.

A curve can't fix that shape. It can only change who profits from arguing with it.

A minimum spend would clear out the dust in one line, and it would work. We didn't use it. Any hard line creates a spot just above it to stand on, and people find that spot fast. It's the same reason we don't cap the top. Small earnings roll forward instead of being rounded away.

You can spend every campaign hunting for wallets that shouldn't be there, and do it again the next time. Or you can use math where extra wallets help nobody, and stop.

Straight proportional rewards have one useful property. Split your money a thousand ways and you earn what you would have earned with one wallet. Nobody has to prove who owns what, and the question stops mattering.

If you run a campaign and want to see how your reward formula behaves on real wallets, Zeru builds the scoring and incentive layer for it.