Forty presses to the pound, and the quantity standing on the other side of that division

1

What a quantity divided by a payment actually reports

Two numbers appear on the banner and a third appears the moment anybody divides them. Two hundred presses over a payment of £5.00 gives forty to the pound. Nobody prints the forty, and everybody computes it, because dividing is what a reader does when handed a quantity beside a price.

The division feels like a rate and behaves like one. A larger result looks like more for the money, a smaller result looks like less, and two advertisements can apparently be ranked against each other in a second without opening anything. That is exactly the service the figure appears to provide, and it is the service this page is about to take apart.

Here is the trouble in one line. Forty presses to the pound is a quantity of events for each pound paid, and events are not money until somebody supplies the unit. Multiply forty by 10p and £4.00 of stake has been bought with every £1.00 paid. Multiply the same forty by 5p and it is £2.00. The ratio did not move. What a reader gets halved.

That unit is nowhere in writing. No published rule obliges anybody to state what one press commits, and this site works at 10p throughout as an assumption rather than a reading. So a division carried out on two published numbers yields a figure whose meaning depends entirely on a third that neither banner carries.

Worked at 10p the arrangement in the title sends £20.00 across the reels. At the 96 per cent return carried here, expected winnings come to £19.20, which is nearly four payments over. A sibling page on solving for the unit itself works out what such a ratio implies about the figure nobody printed, and this page takes that result as read rather than repeating it.

What follows here is the comparison between arrangements rather than the solve inside one. The question is narrow and practical: can a reader holding two banners pick the better of them from the division alone. The answer is no, and the parts below set out three separate reasons, each of which would be sufficient on its own.

2

The ladder of quantity against payment, rung by rung

Start by laying the family out. Every rung below pairs a published quantity with a published payment, divides to get presses for each pound, and then carries that through to money at the unit value this page assumes. The right-hand column is the figure a reader would actually collect in expectation once the usual clause has run.

The third column is the same on every rung, and it is printed anyway. That is the point of including it: the whole ladder is computed at one supposed unit value, and if that supposition moves then every figure to the right of it moves with it, in exact proportion. A column of identical entries is doing more work here than any of the varying ones.

Read the division column downwards and it spans ten to one, from fifty presses for each pound to five. Read the rightmost column downwards and it spans ten to one as well, but in the unhelpful direction: the rung that looks ten times as generous closes ten times as badly. The two columns are the same quantity with the sign turned over.

One rung in the middle carries a rounding worth naming. A hundred and twenty presses at 10p give expected winnings of £11.52, and six tenths of that is £6.912, so the close is printed at minus £6.91 with a tenth of a penny dropped. Every other rung lands exactly on the penny, and the odd one out is odd because 120 is not a round hundred.

3

Weighing two banners means weighing two unprinted units

Take a reader holding two advertisements. One says forty presses for each pound paid, the other says thirty. The second looks worse by a quarter and the comparison seems settled. It is not settled, because the comparison has quietly assumed that a press is the same object in both places, and nothing on either banner says so.

Units differ between arrangements for ordinary commercial reasons, not devious ones. A business may run its promotional presses at the lowest stake its builds accept, or at the stake its usual customer chooses, or at a figure picked to make a round quantity fit a round budget. None of those choices is published, and none of them is required to be.

So the honest statement of the comparison is this: forty presses at an unknown unit against thirty presses at a different unknown unit. Two unknowns, one on each side, and the division has been performed on the known halves only. A quotient built that way is not a comparison. It is a comparison of the halves that happened to be printed.

Two rows are settled where the claim is made and the other four are somewhere else. The division a reader performs uses the first two and ignores the rest, which is not carelessness: the first two are the only ones available at the moment the comparison is being made. A ratio is popular because it is computable from what is to hand, and that is a different property from being informative.

4

Where a smaller division overtakes a larger one

Put the two unknowns to work and the comparison can be reversed on purpose. Forty presses for each pound at 5p buys £2.00 of stake per pound paid. Thirty presses for each pound at 10p buys £3.00. The banner showing the smaller division is handing over half as much again.

Find the crossing exactly. Forty presses at a unit of x matches thirty presses at a unit of y when forty x equals thirty y, so x is three quarters of y. Against a rival running at 10p, a forty-to-the-pound arrangement draws level at 7.5p a press and loses below it. Half a penny of difference in a figure neither banner prints settles which advertisement is the better one.

7.5p a press, the unit at which forty to the pound exactly matches thirty to the pound at 10p

Seven and a half pence is not an exotic figure. It sits between two stakes that builds commonly accept, and a reader has no way to tell which side of it a given arrangement falls on, because the question is answered in no document they can open. The crossing is therefore not a rare edge case. It is a region the whole family sits inside.

The useful thing about that drawing is the vertical reading rather than the slope. Pick any height on the right-hand column and find which rows reach it from the left-hand one, and the overlap is immediate: rows that look ordered on a banner are interleaved once the unknown unit is allowed to vary across the range the family plausibly uses.

5

The rung at which a generous ratio becomes a heavy one

The second reason the division fails is bigger than the first, and it does not depend on the unit being unknown. It depends on the multiple written over the winnings, and it turns the ratio inside out rather than merely blurring it.

Expected winnings at a 96 per cent return are 0.96 of whatever crosses the reels. A multiple of W on those winnings asks for W lots of them to be turned over, and a margin of 4p on the pound takes 0.04 W of the winnings away. The balance left is one less 0.04 W, so the sign turns over at W of twenty-five, which is the rung where twenty-five lots of 4p add up to a whole pound.

Below twenty-five a reader keeps a positive share of whatever the presses returned, so a larger quantity is a larger keep and the division points the right way. At twenty-five the share is nothing, and the division points nowhere: every rung on the ladder closes at nought, whatever its quantity. Above twenty-five the share is negative, and every extra press on the banner adds to what the clause expects to collect.

Forty times, which is the figure this page applies throughout as an assumption, sits well above that turning point. At forty the balance left is one less 1.6, so six tenths of the winnings travel the wrong way and the close is negative by that fraction. Two hundred presses at 10p return an expected £19.20, and six tenths of £19.20 is £11.52.

Read the bars from the largest quantity down and the ordering never changes, which is the finding. The rung a reader would pick by division is the rung with the longest bar in both directions at once: most stake handed over, most expected cost collected back. The division is a faithful measure of size and a reversed measure of value.

6

Loss for each pound paid, which tracks the division exactly

Put the two previous parts together and a clean relationship falls out. The expected close is minus 0.576 of whatever the presses sent across the reels, since 0.96 of the stake comes back and six tenths of that is lost to the clause. Divide by the payment and the expected close for each pound paid is 0.0576 multiplied by the division on the banner.

That relationship deserves slow reading, since it compresses this whole page into a line. At 10p a press and forty times, the expected loss for each pound paid is the advertised division multiplied by 5.76 pence. Forty to the pound costs an expected £2.30 for each pound paid. Ten to the pound costs £0.58. The ratio a reader uses to rank advertisements is proportional to the expected loss they are ranking.

Expected off 200 presses, read on its own £19.20 What survives once the second document applies minus £11.52 What a £5.00 payment actually buys £30.72

Thirty pounds and seventy-two pence arrives from either end without a shared step. Forty lots of £19.20 is £768.00 of staking, and a margin of 4p on the pound takes £30.72 of it. Or subtract the foot of the block from its head: £19.20 less minus £11.52 is £30.72. The two agree exactly, as they must, the clause having one effect only.

Six times the payment is the right way to hold that figure. A reader sends £5.00 and the distance between the two available readings of the arrangement comes to £30.72, which is more than six payments. Nothing in the advertisement is false at either end. One reading is simply computed from the banner and the other from a clause in a second writing, which the banner never links to.

The per-pound figures carry a rounding, named here rather than hidden. Forty to the pound gives 230.4 pence and prints as £2.30; ten to the pound gives 57.6 pence and prints as £0.58. The proportionality is exact in pence and the pounds column rounds, which is worth saying on a page whose argument is that a printed figure can be a tidied one.

7

Why the arithmetic supplies no highest rung at all

A reader meeting a ladder of this shape reasonably expects it to stop somewhere. Rates usually do: a thing can only be sold so cheaply before the seller stops. Here the expectation fails, and the reason is the turning point in part five rather than anything about costs.

Above twenty-five times, the margin collected on the staking a clause demands exceeds the winnings handed over to start it. A quantity of presses therefore funds itself, and so does a larger quantity, and so does a larger one still. Nothing in the arithmetic puts a ceiling on the tally, because the tally pays for itself at every size.

What is left to set the ceiling is how a number reads. Round hundreds are what appear, and the payments cluster on £5.00 and £10.00, so the divisions available in the family are a short list of round results: five, ten, twelve, twenty, thirty, forty, fifty, a hundred. A quantity that only ever takes tidy values is a quantity chosen for the eye rather than computed from anything.

That is an observation about advertising and not an accusation. A business picking between 287 presses and 300 presses has no arithmetic reason to prefer either, and one of them reads better, so the choice is made on reading. The honest conclusion is that the top of this ladder measures confidence in the clause rather than generosity about the presses.

Two consequences follow for a reader. A large tally is not evidence of a better arrangement, because a large tally costs the party offering it nothing in expectation. And a small tally is not evidence of a worse one, because a small tally may sit beside a gentler multiple that no banner mentions. Neither direction of inference survives.

8

The one thing a division of this sort reports reliably

Having taken the ratio apart it is only fair to say what it still does, and it does one thing honestly. The division reports how many separate events a payment buys, which is a statement about duration rather than about money, and duration is a real thing some readers want.

Somebody who intends to use the presses and stop, with no attempt on the clause and no expectation of collecting anything, is buying time at a reel. For that person the tally is the product and the unit value is irrelevant, because they never intend to convert anything into cash. Two hundred events is two hundred events whatever each one stakes.

For that reader the entire apparatus on this page is beside the point, and every figure in the ladder is as well. The expected close matters to nobody who does not attempt a withdrawal, and the clause in the second document is never triggered by somebody who leaves the balance where it lies. This is the one branch where the division is exactly the right number to read.

It is worth saying how narrow that branch is. It requires a reader to send £5.00, receive the presses, use them, and then treat whatever lands in the balance as nothing. Any intention to collect moves them straight back into the arithmetic above, and the arithmetic above says the division is proportional to the expected loss.

9

Rules written about proportion, and what their absence permits

Britain has written rules about exactly this ratio, which is unusual: most of what a page on this site measures has no rule behind it at all. Three published provisions bear on the relationship between what a reader pays and what an arrangement hands back, and together they describe a ladder that would look different from the one in part two.

The first is a rule about slope. Advertising guidance for casino promotions online wants what a player receives to bear some proportion to the money and the hours they have put in, and it stops a promotion steepening as that spending grows. Worked against the ladder, it is a test on the rightmost column. At one fixed unit value the stake committed rises in exact step with the payment, so the slope is a straight line and every rung passes. What the test cannot reach is the unit value itself, where all the variation on this page is hiding.

The second is a figure, and it is the nearest thing to one on this subject anywhere. The same guidance treats a solitary reward following fifty pounds of staking as capable of passing, under a condition that must travel with it: a reward on that scale has to be ordinary for the sort of gambling in question. Fifty pounds of staking is five hundred presses at the unit value supposed here, so the example describes a tally above every rung in part two and a payment ten times the one in this page’s title.

The third governs what one incentive may be built out of. The date is 19 January 2026, from which a licensee has been forbidden to pack two product types into one incentive, with betting, casino, bingo and the lottery named as the types it separates. Three softenings sit underneath that bar, each one bearing on a division. Where both halves fall under one heading they may still be put together, the illustration given being a scratchcard beside a raffle. Promotions for different products may arrive in one message where the recipient has agreed to hear about both. A credit spendable wherever its holder likes is untouched, nothing having been tied to anything.

Why a packing rule bears on a ratio at all. A division ranks two advertisements only where what sits on each side is the same sort of object, and a rule holding one product type inside one incentive is a rule holding the objects alike. Lift it and a tally of presses can share a headline with a tally of something counted differently, at which point a reader’s division runs across two units at once instead of one.

A concession keeps this straight. One regulator beyond Britain keeps a rulebook, and it was opened for this build. That rulebook wants the conditions on a bonus set out plainly and it stops promotion pitched at heavy play. It sets down no ceiling on a multiple, no test of proportion and no limit on packing product types together, and that gap is what the note above measures.

10

Weighing two banners when neither prints the unit

The method is short and it replaces the division rather than refining it. Write both advertisements down as a pair of published numbers each. Then refuse to divide them, and instead carry each one separately to a figure in pounds under a stated assumption, and print the assumption beside the answer.

Step one, convert each tally to stake at a named unit value, and name it in the same sentence. Step two, apply the return to get expected winnings. Step three, find the multiple in the second document for each arrangement, because that is the figure that decides the sign and it is the one most worth a click. Step four, apply it and print the close.

Step five is the part a division skips. Repeat the whole thing at a second unit value, chosen to be as unfavourable as the family plausibly runs, and look at whether the ordering between the two advertisements survives. Where it does not survive, the comparison has failed and the honest answer is that the banners cannot be ranked from what they print.

Worked on this page’s own pair that produces a short result. Two hundred presses for £5.00 at 10p gives £19.20 expected and minus £11.52 after the clause. Three hundred for £10.00 at the same unit gives £28.80 and minus £17.28. Drop the first arrangement to 7.5p and it falls level with the second on stake bought for each pound paid, so the ordering a reader started with has already gone.

Two habits make this reliable. Name the unit value as an assumption every single time it is spent, because a figure carried silently from one line into the next stops being an assumption and starts looking like a reading. And rank nothing on a quantity that cannot be converted into money, since a number computed from the halves that happen to be printed is a number about printing.

The conclusion is narrow and it is the one worth carrying away. Forty presses to the pound tells a reader how much time a payment buys and tells them nothing whatever about what the payment buys in cash, and under any multiple above twenty-five the same figure is proportional to the expected cost rather than to the expected benefit.