Three hundred presses bought with ten pounds, and the figure that has to join them

1

Two published quantities, and the one that has to join them

An advertisement of this build publishes exactly two numbers. One is a payment of £10.00, settled on the banner and requiring no further document. The other is a quantity of 300, settled in the same place and just as firmly. Everything else about the arrangement is somewhere else, and the arithmetic cannot begin until a third number arrives from outside.

That third number is the cash a single press commits. Without it the quantity of 300 is a tally of events rather than a sum of money, and no comparison can be made between this arrangement and any other. The number is nowhere in writing: no rule obliges anybody to state it, and this site assumes 10p throughout rather than reading it anywhere.

Put the assumption in and a first result lands at once. £30.00 of stake crosses the counter, treble the £10.00 the reader sent. Ninety-six pence of each staked pound comes back, a rate this page assumes rather than reads anywhere, so expected winnings reach £28.80, and the 4p missing from every pound is the margin funding everything else here.

Three times the payment is an odd thing for a business to hand over, and the oddity is the whole subject here. A firm giving away £30.00 of stake in return for £10.00 of somebody else’s money has priced that £10.00 against something, and whatever it was priced against is not on the banner. The ratio therefore carries information about a figure nobody printed, whether or not anyone meant it to.

So the question this leaf asks runs backwards from the usual one. Instead of asking what the arrangement is worth to a reader, it asks what one press would have to be worth for the arrangement to make sense to the party offering it. That turns an advertisement into an equation with one unknown, and an equation with one unknown can be solved.

Three constraints bound the solve, and a part apiece is given to them underneath. The payment produces a margin once it is staked. The presses produce an expected payout when they are used. A play-through clause produces a further margin when it is worked off. Set those against each other and the press value either falls out of the sum or turns out not to matter, and which of the two happens is itself the finding.

2

Solving for a press value the advertisement withholds

Begin with the barest version, in which the payment is staked once over and the presses carry no condition whatever. The reels retain 4p from each pound pushed through them at the rate supposed here, so £10.00 going round a single time yields £0.40. That is the whole income this reading generates.

Against it stands the expected payout on the presses. Three hundred presses at a press value of v stake 300v and are expected to give back 288v, since 96 hundredths of the stake comes back. The firm is handing over 288v and collecting £0.40, so the two are equal when 288v equals two fifths of a pound.

Solve that and v comes to 0.14 pence, which is about one seventh of a penny. At any press value above that, the simplest version of the arrangement loses money for whoever offered it, and at 10p it loses a great deal: £28.80 handed over against £0.40 collected, which is seventy-two pounds given away for every pound earned.

0.14 pence a press, the value at which a single pass of £10.00 would cover 300 of them

A seventh of a penny is not a press value anybody runs. It is below the smallest coin in circulation and far below anything a reel would accept as a stake, so the simplest reading can be discarded on arithmetic alone. Something other than one pass of the payment is funding this, and the rest of the leaf is a search for what.

Notice what has already happened to the banner. A ratio of 300 presses to £10.00, read with nothing but a return figure and a note of what a press might cost, has produced a statement about an unpublished quantity: either the press value is a fraction of a penny, or the payment is not the thing paying. The advertisement did not set out to say that. It says it anyway.

3

The multiple at which the unknown drops out of the sum

Now put the play-through clause back. Winnings from presses of this kind ordinarily have to be turned over before they can be taken out, and the clause sits in the bonus terms rather than beside the quantity it governs. Forty times is the figure applied throughout this page, picked because terms drafted beyond the British licence tend to land in that region, and it is an assumption here rather than a reading of any document.

Expected winnings of 288v turned over forty times put 11,520v through the reels, and 4p a pound of it is retained. Margin recovered comes to 460.8v against an outlay of 288v. Divide one by the other and v disappears: recovery is 1.6 times outlay at every press value there is.

That cancellation is the result this leaf exists to print. Work out which multiple makes recovery equal outlay and the answer is 25, because twenty-five lots of 4p make up a whole pound. Twenty-five turns up here on the firm’s side of the ledger, having turned up elsewhere on this site from the reader’s, where it marks the rung at which winnings are expected to have been handed back whole. Two separate calculations, one number, and no step shared between them.

Above twenty-five the arrangement funds itself out of the clause, whatever one press is worth. Below twenty-five it does not, and the press value starts to matter again. The multiple is therefore a switch rather than a dial, and it decides whether the quantity on the banner is constrained by anything at all.

Follow that through and the banner’s quantity stops being evidence of generosity. Where the clause stands above the break-even multiple, 300 costs the firm nothing in expectation, and neither would 500, 1,000 or 3,000. The only ceiling on the quantity is what reads well, which is a fact about advertising and not about value. A sibling leaf on the ratio of quantity to payment takes that ceiling apart across the whole family.

Two of the figures on that drawing are the only ones a reader is handed, and neither is the one that decides the money. The payment is published because it is a condition of entry. A floor on what the exit will shift waits at the cashier, supposed at £20.00 for the drawing, a figure invented to show the shape because nothing published sets one.

4

What the written clause puts back, worked in pounds

Drop the assumed press value back in and the algebra turns into money. Expected winnings stand at £28.80. The clause asks for forty of those, so £1,152.00 has to go through the reels, a sum 115.2 times the payment that started it. At 4p a pound the firm recovers £46.08 from a sentence it drafted and the reader never opened.

Set £46.08 of recovery against £28.80 of outlay and the arrangement clears by £17.28 in expectation, on the presses alone, before the payment is staked at all. The reader’s expected close is minus £17.28. The two figures are the same money seen from opposite ends of the table, which is a check on the arithmetic rather than a coincidence.

Expected off 300 presses, nothing else applied £28.80 The same presses under a forty times clause minus £17.28 What the unopened document is worth £46.08

Forty-six pounds and eight pence arrives twice over, with no step shared. Take the staking demanded and apply the retained 4p a pound: £1,152.00 worked that way gives £46.08. Or take the two ends of the block just printed and subtract, £28.80 less minus £17.28 giving £46.08 again. They agree exactly, a clause of this build having no function beyond handing turnover to the margin at a fixed rate.

One figure in that block is read and the other is solved. The £28.80 follows from the banner plus one assumption about press value. The minus £17.28 follows from a sentence in a second document, and a reader who never opens that document will act on the first figure while the second one governs. The gap between them is the price of the document, and on this arrangement it runs to more than four times the payment.

A ceiling on what a bonus balance may pay out is a separate clause and usually sits in the same document. Where one is written, it does nothing to the expected close, which is already under nought, and takes a great deal out of the single branch where the presses ran well. Pricing it would need a figure, and nothing citable here sets a usual ceiling, so this page declines to supply one.

5

A ladder of candidate values, each one implying a different offer

The press value is unpublished rather than unknowable, so the honest way to carry it is as a band. Below is the same banner read at five candidate values, with the staking the clause demands and the expected close beside each. Every row has identical wording on the advertisement and none of the rows can be told from any other before clicking.

Five rows, one advertisement, and a spread of five to one between the top and the bottom. A reader who assumed the middle rung would be out by up to £25.92 in either direction on the expected close, and nothing in the published wording would have told them which rung they were on. The arrangement is accurately described at every value.

Reading the rightmost column from top to bottom shows what is at stake. Every rung is a different commercial proposition wearing identical words, and they grow less plausible as the value climbs, because the outlay climbs with it while the payment stays at £10.00. That is a weak argument for a low press value and it is the only argument the published figures support.

Weak is the right word for it, and the reason is part three. Once the clause stands above twenty-five times, every rung in the table is self-funding, so the implausibility disappears and the ladder stops narrowing anything. The band only tightens where the multiple is low, which is precisely the case the written terms out here do not describe.

6

Making the payment pay for the presses on its own

There is one further way the payment could fund the presses, and it is worth working because it produces a figure the banner implies and never prints. A pass of £10.00 leaves £0.40 behind. The presses cost £28.80 at the house value. Divide and the payment would have to cross the reels seventy-two times.

Seventy-two passes of £10.00 is £720.00 of staking by a reader who was told they were paying ten pounds. That is the quantity the arrangement needs from a payment with no clause attached to it, and it is roughly two thirds of what the forty times clause demands anyway. The two routes to the same funding differ in one respect only: one of them is written down.

Nobody sends £10.00 intending to stake it seventy-two times, which is the point. The deposit route funds the presses only for somebody who intended a great deal of play regardless, and a reader of that description was never the person the quantity on the banner was aimed at. So the deposit route is real but narrow, and it cannot be the general explanation.

Read the middle column and the structure of the arrangement is visible without any further argument. The two routes that would be gentle on a reader are settled in no document whatever, so nobody can be held to them. The route that is written down is the harsh one, and being written down is what makes it the one that actually operates.

A fourth possibility exists and this leaf cannot price it, which is worth saying plainly. The payment may simply be the first of several, with the presses bought as an introduction to a sequence of later payments. Nothing published supports a figure for that, so it is named here and left unpriced rather than filled in with a plausible number.

7

Three answers to the solve, and what each commits an advertiser to

The solve admits three answers, and each is a different statement about a figure nobody published. Setting them side by side is the useful product of this leaf, because a reader cannot tell which applies and can at least know the list is short.

The first answer is a low press value. If one press is worth a fraction of a penny, the quantity of 300 shrinks to a few pence of stake and the ratio on the banner stops being remarkable. This answer is internally consistent and costs the reader almost everything, because a quantity priced that low converts into no meaningful sum at all.

The second answer is the clause. At forty times the recovery is 1.6 times the outlay at any press value, so the firm is indifferent to the press value and the quantity can be set wherever it reads best. This is the answer the published multiples support, and it is the one that makes the banner’s ratio uninformative about generosity.

The third answer is the sequence: the payment is an introduction, and the presses are priced against payments that have not happened yet. This answer makes the arrangement rational without a low press value and without a punitive clause, and nothing on this site can put a figure on it.

The ten times rung on that drawing is the only one with a published ceiling behind it, and it exists in Great Britain alone. Inside a British licence a play-through requirement on bonus funds may not exceed ten times, a ceiling that took effect on 19 January 2026, the regulator having recorded multiples reaching sixty in places before it arrived.

Worked against this leaf’s figures that ceiling does something specific. At ten times the staking falls to £288.00, the margin recovered is £11.52, and the firm is £17.28 short of its £28.80 outlay. The arrangement stops funding itself, the press value stops cancelling, and the quantity on the banner becomes a real cost to whoever offered it. A ceiling on the multiple is therefore a ceiling on the quantity, by arithmetic rather than by drafting.

8

What arithmetic of this sort leans on, and who is bound to supply it

Every figure above rests on one imported quantity, the 96 in the hundred, and on an assumption that the quantity means what it appears to mean. That assumption is not free, and in Great Britain three published duties hold it up. Outside a British licence none of them binds anybody, which is the loss that bites on a leaf whose method is a solve.

The first duty settles where a return figure can be found at all. Requirement 3C of the technical standards puts whatever would let somebody judge the chances within easy reach before anything is committed, and it offers a choice rather than demanding one disclosure: an account of how a game runs and how prizes get allotted, the return percentage, the house edge, or the odds on whichever events pay. A backwards solve wants the third of those and may be handed whichever the operator prefers.

The second duty is about whether the figure holds while the reels turn. Requirement 7A demands outcomes that are acceptably random, and it bars a compensated build, so nobody may nudge the probabilities by hand or by machine, and a drawn number has to be spent in sequence rather than thrown back for a more convenient one. Without it the ninety-six pence a pound describes a population this page cannot see, and every sum printed here is a guess wearing a decimal point.

The third duty is about what the screen is allowed to imply. Requirement 7C bars designs expected to mislead about the likelihood of results, and it names one practice outright, the swapping of a plain loss for a loss dressed as a narrow one. That rule protects nothing in the ledger and everything in the reading of it, since a sequence that feels close to paying changes how long somebody keeps pressing while every figure tabulated above stays exactly where it was.

Two honest concessions belong here. The first is that a rulebook published by one regulator outside Britain was opened for this build, and it does ask for the conditions on a bonus to be stated plainly, so this is not an empty field. The second is that it carries no requirement about randomness, no bar on a compensated build and no rule about what a screen may imply, and that gap is what the three paragraphs above are measuring.

9

Running the solve on any quantity-and-payment pair

The method takes four lines and no special knowledge, and it works on any advertisement pairing a sum with a count. Write down the two published numbers. Take the count, multiply by a candidate press value, and a stake appears. Apply the return to that stake and expected winnings appear. Then ask what the payment would have to earn for those winnings to be affordable.

Step four is where the work is. The payment earns the firm one minus the return for each pound that crosses the reels, so a £10.00 payment staked once earns £0.40 at a 96 per cent return and £1.00 at a 90 per cent one. Dividing the expected winnings by that figure gives the number of passes the payment must make, and a number of passes above about five is a signal that something else is funding the arrangement.

Then apply the clause, which turns the question round. Scale the expected winnings by the multiple for the staking demanded, scale that by the margin per pound for what comes back, and set the result beside the winnings handed over. Above the break-even multiple the recovery exceeds the outlay and the press value drops out of the comparison entirely.

Two habits keep the method honest. Name the press value as an assumption in the same sentence that spends it, every single time, because a figure carried quietly from one line to the next becomes a fact nobody checked. And print the band rather than the middle of it, since the band is the genuine result and the middle is a preference.

Run on this leaf’s own advertisement the method produces six numbers and stops: £30.00 of stake, £28.80 expected, £1,152.00 of staking demanded, £46.08 recovered, minus £17.28 expected to the reader, and a break-even multiple of 25. Of those, two came off the banner and four came from somewhere a reader would have to travel to, which is the measurement this whole site is built to take.

The useful conclusion is narrower than the arithmetic. A ratio of presses to payment tells a reader nothing about value until the press value and the multiple are both known, and once the multiple passes twenty-five it tells them nothing even then. What it does report, reliably and for nothing, is how long the reels will turn, and for somebody who wants exactly that the ratio is the right number to read.