The Closed Loop / The numbers
All the arithmetic
Every figure on this desk, and the sample it comes from
Nothing here is quoted from an operator. Six samples carry the arithmetic; everything on the other fifteen pages is derived from them, and this page collects the derivations so they can be checked in one pass.
Rail stub
- Samples
- six, all invented
- S1 cap
- 200.00 + 240.00 = 440.00
- The released tail
- 60.00, or 12.0%
- The split
- 1.40 payments a request
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 answerSix invented samples - a two-rail account, a partial withdrawal, a test deposit, a dead rail, a third-party payer and a book of 12,000 requests - produce every number here. The caps, the split, the released tail, the re-route fee and the frozen share are all one or two arithmetic steps from them.
440.00The total cap on S1: 200.00 by card plus 240.00 by bank, which is all the money that can travel the rails
60.00The released tail on S1: a 500.00 request above a 440.00 cap, or 12.0% of it
18.00What moves between two rails on S2 when the rule changes from a waterfall to a proportional split
7.5%The 15.00 re-route fee on S4 as a share of the 200.00 that cannot travel on its own
34.1%The share of a 440.00 account frozen by a 150.00 third-party deposit on S5
1.40Payments per request across the sample book: 16,800 payments for 12,000 requests
The samples, and what each one is for
S1 - the two-rail account
200.00 card + 240.00 bank = 440.00 of cap; balance 500.00; 500.00 requested. It carries the cap formula and the released tail.
S2 - the partial withdrawal
30.00 card + 70.00 wallet = 100.00; 40.00 requested. It carries the waterfall-against-proportional arithmetic.
S3 - the verification deposit
A 10.00 test deposit and a 400.00 request. It carries the difference between opening a rail and enlarging one.
S4 - the dead rail
200.00 behind a card that expired 14 months ago. It carries the re-route fee and the indemnity exposure.
S5 - the third-party payer
150.00 deposited from a card in another name. It carries the frozen share and the document count.
S6 - the desk’s book
12,000 requests across mixed rails. It carries the split rates and the averages.
The derivations, in one pass
S1 - the cap and the released tailcap, card 200.00 - 0.00 = 200.00
cap, bank 240.00 - 0.00 = 240.00
total cap 200.00 + 240.00 = 440.00
requested = 500.00
looped min(500.00, 440.00) = 440.00 88.0% of the request
released 500.00 - 440.00 = 60.00 12.0% of the request
payments 200.00 card + 300.00 bank = 2 payments
S2 - the split, under each rulewaterfall, oldest first 30.00 card + 10.00 wallet = 40.00
proportional 12.00 card + 28.00 wallet = 40.00
difference 30.00 - 12.00 = 18.00 between the rails
caps left, waterfall card 0.00, wallet 60.00
caps left, proportional card 18.00, wallet 42.00
S3 - the test depositcap created 10.00 - 0.00 = 10.00
request 400.00
reach 10.00 / 400.00 = 2.5% of the request
still needed 400.00 - 10.00 = 390.00 from other rails
S4 - the dead rail, and the three routescap behind the expired card 200.00
route 1, hold nothing moves; a replacement rail starts at 0.00
route 2, re-route fee 15.00 = 7.5% of 200.00; wait 11 working days
exposure 200.00 + 20.00 = 220.00 = 110.0%
route 3, a fresh rail 10.00 test -> 10.00 cap; 190.00 still stuck
S5 - the third-party depositfrozen 150.00
inside 440.00 150.00 / 440.00 = 34.1% frozen
free to travel 440.00 - 150.00 = 290.00
documents asked 3 over 9 working days
S6 - the sample bookrequests 8,160 x 1 + 2,880 x 2 + 960 x 3 = 16,800 payments
average 16,800 / 12,000 = 1.40 payments a request
split rate 2,880 + 960 = 3,840 = 32.0% of requests
rails gone 744 / 12,000 = 6.2%
name mismatch 408 / 12,000 = 3.4%
withdrawn 12,000 x 268.40 = 3,220,800.00
per payment 3,220,800.00 / 16,800 = 191.71
What is deliberately absent
The desk publishes no operator’s cap, fee, timeline or policy, because none of these samples is a company. It also publishes no figure for how often a loop is applied at all: that number lives with supervisors and operators, and inventing it here would be the one thing that would make the rest of this page untrustworthy.
Every figure is illustrative. A reader can replace a sample with their own payment history and re-run the arithmetic - which is what the page on reading your own payments is for. The samples exist to show the shape of the calculation, not to describe any account in particular.