▣The Closed Loop Open the partner account
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The Closed Loop / The cap
The arithmetic of the cap

Each rail may return what it paid in, less what it has already returned

The cap is the only part of the loop that a reader can compute exactly, and doing so turns the whole arrangement from a mystery into a table. It has one formula, it is per rail, and it has a bottom it cannot go below.

Rail stub
The formula
paid in minus already returned
Per
rail, not account
Floors at
0.00
Above the caps
released money
the railA payment method that has carried a completed deposit - not a method saved on the account
the capWhat a rail paid in, less what it has already returned, and never below zero
released moneyThe part of a balance above every cap: payable, and travelling by the operator’s own route
Direct answerA rail’s cap is what it paid in minus what it has already paid back, and it never falls below zero. The caps add up to a total that can travel back along the rails; anything requested above that total is released money and goes by the route the operator nominates for it.

The formula, and the two things it is not

The cap is a running balance per rail, not a one-off figure fixed when the rail opens. Every completed withdrawal on a rail reduces it, and every deposit raises it again - which means a reader who deposits and withdraws repeatedly on the same card can cycle through the same cap indefinitely, while a reader who deposits once and withdraws once uses it up permanently.

S1, worked: the caps after a first withdrawal and a secondbefore any withdrawal card 200.00 in - 0.00 out = 200.00 of cap bank 240.00 in - 0.00 out = 240.00 of cap total cap = 440.00 withdrawal of 300.00, oldest rail first card 300.00 wants 200.00; card pays 200.00; cap -> 0.00 bank remaining 100.00; bank pays 100.00; cap -> 140.00 released = 0.00 second withdrawal of 200.00, the same day card 0.00 of cap -> cannot pay bank 140.00 of cap -> pays 140.00, cap -> 0.00 released 200.00 - 140.00 = 60.00 on the operator’s default rail total cap now = 0.00 across both rails

Two withdrawals totalling 500.00 from a 440.00 cap leave the account with no rails at all and 60.00 of released money to move. That last line is the one readers are least prepared for: after the caps are spent, every further withdrawal depends on the released-money route, which is a different policy, a different timeline and sometimes a different fee. It is why the state of the caps matters more than the size of the balance.

Why the cap is not the balance, and the balance is not the cap

Money on an account is in one of two conditions, and the desk names them so the arithmetic has somewhere to live.

Loopable - the total cap, 440.00 on S1, which must travel back along the railsReleased - 60.00 on S1, above every cap, which travels by the operator’s route

The proportions are the arithmetic: 440.00 / 500.00 = 88.0% loopable and 60.00 / 500.00 = 12.0% released. As play continues, the balance can move in either direction while the caps do not move at all - a run of losses shrinks the balance without shrinking the cap, and a run of wins grows the balance without growing it. A reader who has lost most of a deposit can still withdraw without trouble, because the cap is a record of what came in rather than of what is left.

The cap floors at zero, and it can be reduced by somebody else. A chargeback on a card the reader did pay with removes the deposit retroactively, so the cap falls with it - and if the rail has already returned more than it now shows as paid in, the operator is out of pocket on that rail and will say so on the next withdrawal. A cap is a record of completed payments, and a completed payment can be undone after the fact.

Reading a cap table off your own history

The table is four columns and can be built from a payment history in a few minutes. What it tells a reader is the number of payments a withdrawal will arrive in, which rail closes first, and whether any part of the balance has no rail at all.

The rail

One row per payment method, named the way the history names it. Two cards from the same issuer are two rails; a card replaced after a fraud alert is a new rail even if the last four digits match.

Paid in, then returned

The two numbers the formula needs. Deposits add, withdrawals subtract. A history that shows a reversal on a card has to be counted, because it reduces what that rail paid in.

The cap, and its state

The subtraction, then a word for the rail: open if the cap is positive and the rail works, spent if it is zero, dead if it is positive and the rail has gone, frozen if the cap is positive and the name rule blocks it.

The released tail

The balance minus the total cap, when that is positive. This is the part that will not travel on any rail and is the only part whose route the operator chooses freely.