300% deposit bonus: £45 credited comes to £27.00 and £45 of own money costs £1.80

1

Three parts credit to one part money, and which part gets priced

Treble a payment and the balance divides four ways: one quarter belongs to the reader and three quarters are bonus funds held under a condition. On a £15.00 payment supplied by this publisher that is £15.00 against £45.00, a screen reading £60.00, and a single figure doing duty for two things that behave differently in every respect that matters. What this bill prices is the £45.00. The £15.00 belonged to nobody else first, can be asked back at any point, and no sum computed about an offer has business holding it.

A treble is the point in the family where that separation stops being a quibble. At one hundred per cent a reader who adds the halves overstates the gift by a factor of two. At three hundred they overstate it by a third, which is smaller, but the absolute quantity of their own money sitting inside the headline is the same £15.00 they handed over, and a quarter of £60.00 is still £15.00 of their own. The direction of the error never changes. Combining the two always flatters the arrangement, because the reader’s contribution is always positive.

A treble supplies a second reason for holding them apart, and it is what this bill is about. A condition written as a multiple has to be a multiple of something, and the something is not always the credit. Where it is the credit, £45.00 turned over ten times is £450.00 of play. Where it is the credit and the payment together, £60.00 turned over ten times is £600.00, which is a third more play for exactly the same £45.00 of bonus funds and therefore a worse offer by a quantity this bill can print. A reader who has merged the halves cannot even ask which base applies, because they have stopped being able to see that there are two.

So the order of business is fixed. Part two prices £45.00 against ten turnovers of itself, which is the kindest base and the one a British licence writes about. Part three prices the same £45.00 as the reader’s own stake, which needs no condition at all. Part four does the arithmetic again with the £15.00 swept into the base, part five shows what that does to the point where the whole thing stops paying, and part eight says which term decides it and what happens when the term is not in front of anybody.

2

Forty-five pounds of bonus funds and what ten turnovers leave

A balance with a turnover condition over it is priced by E = B × (1 − W × (1 − RTP) ∕ g). The letters carry a sum each. B is the credited balance, £45.00 on this bill, the payment forming no part of it. W is how many turnovers get demanded, taken here as ten because that is the most a British licence allows to be asked of bonus funds a condition on a licence. The return, written RTP, is 96 per cent, which this publisher takes as an industry-wide value and attributes to no title ours, and flagged as ours. And g is the weighting, which is taken at full because no contribution rate is published and an unpublished term is read here at its most generous.

The sum runs through in three steps. Forty-five pounds turned over ten times makes £450.00 of play. The margin on £450.00, four hundredths of every pound, is £18.00. Forty-five pounds with £18.00 taken off it is £27.00, which is three fifths of the credited sum, and three fifths is what survives ten turnovers whatever the sum happens to be. A reader wanting the shortcut can skip the pounds: at this return, ten turnovers always costs two fifths of the credit.

The figure to carry away is £450.00 rather than £27.00. It is thirty times the £15.00 the reader paid in, and at 30p a round a stake this publisher supplies it is 1,500 rounds of play standing between a reader and any part of £45.00. The £27.00 is what the arithmetic says the credit is worth. The £450.00 is what the offer asks for, and the two numbers sit at opposite ends of a treble match without either ever appearing on the front of one.

Both cautions from the top of the section apply. £27.00 is an average over many attempts, not an outcome, and most single attempts at £450.00 of play off £45.00 of credit finish with nothing left. And ten turnovers is a bound nobody here has accepted, since it binds a British licence holder and these offers are placed without a Great Britain licence, so anything heavier than ten leaves under £27.00 of it standing, which is what part five works out.

3

The same forty-five pounds out of a reader’s own money

Price it again the other way round, which is the half of the question a publication with one column cannot answer. Let the £45.00 belong to the reader and go through the same play a single time. Nothing was advanced and so nothing has to be discharged. No multiple applies, no base question arises, no weighting matters, and no maximum on winnings can be reached, because none of those things attaches to a reader’s own stake.

Forty-five pounds through a play keeping four hundredths of each pound is expected back as £43.20. The cost of the exercise is £1.80, and as a position on the bill it is minus £1.80. Against the £27.00 on the credit side, the distance is £28.80, which at 30p a round is 96 rounds of play. Both forms are worth printing because a reader counts in rounds and settles up in money.

£45.00 of bonus funds worth £27.00 when a cashier credits it and minus £1.80 when a reader stakes it, £28.80 apart, which is 96 rounds of play in hand

The ratio between £1.80 and £18.00 puts this site’s question into two figures. The return is identical on both sides: four hundredths of whatever is staked, charged without favour. What differs is the volume of staking each side has to produce, which is £45.00 once against £450.00 once. A condition does not change the price of play. It changes how much play has to be bought before anybody is allowed to leave, and the bill for that extra play is £16.20 on these numbers.

None of which is an argument against taking a treble match. Accepting it costs the reader nothing in money and is expected to be worth £27.00, and declining it leaves £15.00 of spendable money whose single turnover is expected to cost 60p. What the arithmetic rules out is the belief that £45.00 of bonus funds is £45.00, or that a £60.00 screen is a £60.00 offer. Three quarters of the screen is conditional and three fifths of that three quarters is what comes through.

4

The quantity a multiple is written against, which is not always the credit

Ten turnovers of what, exactly. The question sounds pedantic and is worth £6.00 on this bill. Where the condition is written against the credited sum, the play owed is £450.00. Where it is written against the credited sum plus the payment that drew it, the play owed is ten times £60.00, which is £600.00. The credit being valued is £45.00 in both cases, so the wider base does not make the gift larger. It makes the price of collecting the gift larger, by a third.

The formula handles that without being bent, because a wider base is the same thing as a larger multiple expressed against the credit alone. Six hundred pounds of play is thirteen and a third turnovers of £45.00, since £45.00 goes into £600.00 that often. Put that in as W and E = B × (1 − W × (1 − RTP) ∕ g) gives £45.00 times one less thirteen and a third four-hundredths, which is £45.00 times seven fifteenths, which is £21.00. The arithmetic is the same arithmetic; only the effective multiple has moved.

Six pounds is 22 per cent of the finding, taken off by a phrase a reader would skim. It is also more than the whole cost of the paid side of this bill three times over, since staking £45.00 of a reader’s own money costs £1.80. A term deciding the base is therefore worth more attention than the ratio in the headline, and it is usually one clause long and sits a long way from the figure it modifies.

Whether the wider base is permitted under a British licence has not been settled in anything published. The ten-turnover ceiling names bonus funds and nothing else, and nobody has published an example of a condition reaching a payment too off the rule sheet. This bill therefore states what has been published and goes no further than that: the ceiling exists, its words are about bonus funds, and the question of a wider base is open. A reader meeting the wider base at a cashier outside the British regime has no ceiling of any kind standing between them and the £600.00.

5

Where a swept-in payment moves the break point, and by how far

On the narrow base the point where a match becomes worthless does not depend on the headline at all. Credit enters the expression as B and leaves it again, so the share that survives is a function of the turnovers and the weighting and nothing else, and it reaches nought at twenty-five turnovers. Twenty-five is therefore the break point for a treble, for a double, and for a match at four hundred per cent, which is the most useful single fact about the whole family.

On the wider base that stops being true, and it stops being true in a direction worth knowing. Sweeping the payment in multiplies the effective turnovers by the ratio of the whole balance to the credit, and that ratio depends on the percentage: four thirds on a treble, three halves on a double, two on a one-to-one match. Divide twenty-five by the ratio and the break point comes out at eighteen and three quarters for a treble, sixteen and two thirds for a double, and twelve and a half where credit and payment are equal.

Read the third column against the fourth and one base makes the family uniform while the other orders it. Under the narrow base a reader has one number to check, the turnovers, and the percentage is a matter of appetite. Under the wider base the percentage becomes part of the arithmetic, and the surprise is which way round it goes: the larger the ratio, the later the break point arrives. A treble on the wider base survives to eighteen and three quarter turnovers where a one-to-one match has already died at twelve and a half.

Weighting does more damage than either base. Work the expression once more with g reduced to the thirty-pence contribution the British regulator set down in consultation taken off the rule sheet: ten turnovers then wants £1,500.00 of play rather than £450.00, the surviving share goes below nothing and floors at nought, and the break point falls to seven and a half turnovers on the narrow base. A reader who has found the base and the multiple and not the weighting has two thirds of the arithmetic.

6

Why a larger ratio suffers least from a wider base

The result in part five is counter-intuitive enough to be worth taking apart. Sweeping a payment into the base hurts in proportion to how large the payment is next to the credit. At a one-to-one match the payment equals the credit, so the base doubles and the play owed doubles. At a treble the payment is a third of the credit, so the base grows by a third and the play owed grows by a third. The bigger the headline, the smaller the payment behind each pound of credit, and the less there is to sweep in.

In money, on a £15.00 payment at each ratio: a one-to-one match drops from £9.00 to £3.00, a double from £18.00 to £12.00, this bill’s treble from £27.00 to £21.00, and a quadruple from £36.00 to £30.00. The absolute loss is £6.00 in all four cases, because the swept-in quantity is the same £15.00 every time and the margin on ten turnovers of £15.00 is £6.00. It is the proportion that differs, and the proportion is what a reader comparing offers is actually sensitive to.

Which gives a narrow but genuine piece of guidance, arrived at by arithmetic rather than by opinion. Where two offers differ only in their headline ratio, the base term matters less on the larger one. Where two offers differ in their base, the narrow base is worth a sixth of the finding on a quadruple and two thirds of it on a one-to-one match. And in neither case does the ratio on the front of the offer tell a reader which base they are being asked to accept.

7

A practice balance of forty-five pounds and the nought it hands over

A fourth way of putting £45.00 in front of a reader asks for no arithmetic. A practice balance showing £45.00 hands over nought. Nought is not a rounding of £27.00 and not £27.00 waiting on a condition somebody has declined to print. Nothing comes out of a practice balance because nothing in one is money, and that holds at £45.00, at £450.00 and at five hundred pounds alike.

Put a practice balance through this bill’s own instrument and the free column reads nought on every row it has. The distance then becomes the paid figure of minus £1.80 and nothing else, which is the finding rather than the absence of one. Three hours of turning a practice £45.00 into £700.00 teaches a reader the controls and settles nothing whatever about £450.00 of real play, because a practice balance cannot carry the one quantity this bill exists to print.

So four arrangements can show £45.00 and mean £27.00, £21.00, minus £1.80 or nought, with nothing on the screen to tell them apart. The balance is the least informative quantity in the transaction. What decides which of the four a reader is in is a paragraph of terms, and the paragraph is shorter than this one.

8

The term that settles it, and why no total is struck without it

This bill carries two findings and will not reduce them to one, because the figure that would choose between them is a term rather than a calculation. Where the condition covers the credited sum alone, £45.00 comes to £27.00. Where it covers the £15.00 as well, £45.00 comes to £21.00. Both are worked from the same return and the same ten turnovers, and the only thing separating them is a phrase in a document a headline does not quote. Picking one of the two and printing it as the answer would be passing off a guess as arithmetic.

The other missing quantity is the multiple itself. Three hundred per cent names a shape of offer rather than a particular one, so no document anywhere states the turnovers a given reader will be asked for. Ten was used throughout because it is the ceiling a British licence sets, and a cashier of this kind does not hold one, so ten is the friendliest possible reading. Where neither the base nor the multiple is published, this bill values £45.00 over a span of multiples and will not settle on one figure, since a reader can check a stated absence and nobody at all can check an invented quantity.

What kind of figure £28.80 is matters as much as its size. Ten turnovers is the furthest a licensee may lawfully be taken, so no lawful condition brings the distance below it, and a count of five would lift it to £37.80. Outside that regime no ceiling applies, and a heavier condition shuts the gap: £10.80 at twenty turnovers, £1.80 at twenty-five, the last of those being one crossing of the credit. Read as a floor, the pair of findings say credit beats paying by at least £28.80 under anything the law would allow.

The finding comes to five lines. A treble describes what the reader pays in, so £15.00 produces £45.00 of bonus funds and three quarters of the £60.00 on screen is conditional. Ten turnovers of the credited sum leave £27.00 and the same £45.00 staked by the reader costs £1.80, putting the findings £28.80 or 96 rounds apart. Sweep the payment into the base and the same ten turnovers become thirteen and a third, and the finding falls to £21.00. The break point sits at twenty-five turnovers on the narrow base and at eighteen and three quarters on the wider one, so the base is the only thing on a treble that makes the percentage part of the sum. And the weighting, if it is thirty pence in the pound, takes the whole of it to nought.