A plan's total is a sum, not a rate

Quotes are struck once, at a per-exchange size — here 4,000 USDT — and every provider prices that same figure so the comparison between them is fair. From there a plan's total can be worked out two ways.

The first takes the best provider's quote and scales it by the whole amount: multiply by the total, divide by the size it was quoted at. One multiplication, one number, and it reads as the price of the plan.

The second prices each leg at the provider that leg will actually be sent to, and adds them up.

The one-multiplication version gives 9,895.39. The difference is not rounding. It is the assumption that every leg runs at the best price on offer, when two of the three do not.

When a plan sends every leg to one provider, the two calculations are the same calculation. Scaling one rate across the total and summing that rate leg by leg differ by nothing at all, because there is only one rate involved.

The shortcut stops being equivalent the moment legs can be assigned to different providers — which is the entire reason to split a transfer in the first place. The arithmetic did not break. Its premise expired, quietly, while the code around it carried on.

This is the part worth keeping. The shortcut uses the best quote, and the other legs run at prices at or below it. So the single-rate figure is never too low. It is either exactly right, when one provider takes everything, or too high.

An estimate that is wrong in both directions is a nuisance. An estimate that is only ever wrong in the flattering direction is something else: it is a number that makes a plan look better than it is, on the screen where somebody decides whether to run it.

The gap is the spread between the best provider and the ones actually assigned, weighted by how much each carries. On the plan above it was 0.20% of the total — twenty dollars on ten thousand, which is small enough to overlook and large enough to matter.

It widens with the spread between providers, and the spread widens sharply as transfers get smaller: why small swaps cost more puts it at over 20% between best and worst on a 25-dollar transfer. A plan whose legs are small and spread across many providers is exactly where a single-rate estimate is least defensible.

If a number is a total of things priced separately, it has to be a sum. Any shortcut that replaces the sum with a rate is carrying an assumption about uniformity, and that assumption is worth writing down next to it, because it will outlive whoever made it.

There is a second rule underneath. When a figure cannot be computed honestly — a leg with no quote yet, a provider that did not answer — showing a smaller total is not the safe choice. A sum missing a leg still reads as the whole plan. Showing nothing is worse to look at and better to trust.

One plan of 10,000 USDT into Bitcoin, split by the splitting builder into three deliberately unequal legs and assigned to three different providers, priced against live quotes on the date above. Both totals were read from the same screen in the same session; the per-leg figures are each provider's own quote scaled by its leg's share of the per-exchange size the quotes were struck at.