200% deposit bonus, and the second quantity it doubles

1

A headline doubles two quantities and charges for one of them

Read a percentage headline slowly and it turns out to be an instruction performed on two separate things. The first is the credit, which goes up by whatever the percentage says and arrives in the account as a number a reader can look at. The second is hidden in the clause underneath, and it is the quantity of staking the credit has to perform before it may be taken out as money. Where that clause is written against the credit, as the shape supposed on this card writes it supposed, in the offer’s own units, the staking goes up by the same percentage. Both quantities therefore respond to the headline. Only one of them is charged for.

Which is where a reel with a published figure stops being decoration. Credit is handed over once, at face value, and nothing takes a cut of the handing over. Staking is different: it is money pushed through a machine whose return is under a hundred per cent, so every pound of it is expected to come back slightly smaller, and the shortfall is the complement of the published figure. For the original it stands at 96.71 per cent the game’s own data and the maker’s description alike, leaving 3.29 points of whatever gets staked expected to remain with the house. That rate belongs to the title. No headline, and no clause, reaches it.

So the two quantities a headline doubles are charged at rates that are not in the same units at all. The credit is charged at nothing. The staking is charged at 3.29 points of itself, and it is charged on the whole of itself rather than once at the end, because the requirement is satisfied by turnover and turnover is the sum of what every turn put across the reels. Double the headline and both numbers double, and the arithmetic that follows is the subtraction of a doubled cost from a doubled credit. Whether that leaves a reader better or worse off is settled before any of it, by one comparison this card keeps coming back to.

It is worth saying what this card is not about, because the neighbouring percentages on this domain take it up. It is not about whether the multiple stands over the credit alone or over the credit with the payment added to it, which is a question about one noun in one clause. It is about what the headline does to the staking once the base of the multiple has been settled, and that question has an answer with a figure in it.

2

Eight hundred pounds across the reels, and what the reel expects to keep

Take the supposed offer at its word. Pay in twenty pounds, receive forty, and stake twenty times the forty. The product of those last two figures is £800.00 of turnover, with the named game taken as counting in full. Eight hundred pounds is a large number to find beside a twenty pound payment, and it is the first figure in the transaction nobody advertises, being the product of two figures that are advertised separately and never multiplied together in a headline.

What that sum costs is a question only the machine can answer. At the published 96.71 per cent, 3.29 points of £800.00 is £26.32, and that is the expected cost of satisfying the clause, as distinct from the cost of losing, which is a different thing and is not what is being measured. The expectation is E = B × (1 − W × (1 − RTP) ∕ g). Begin with g, the weighting, which is the share of a stake that a particular game is allowed to contribute towards the requirement and is taken here at 100 per cent as clauses of this shape commonly set it; then W, the twenty times; then RTP, the figure off the game sheet; and B last of all, since the credit is the only one of the four terms that an advertisement ever prints.

Run it and the credit closes at £13.68. Two-thirds of what was advertised has gone into the expected cost of its own conditions, and not one pound of it went anywhere a reader could see it going, because the cost arrives as a return under a hundred per cent rather than as a fee. A fee of £26.32 on a £40.00 credit would be remarkable. The same sum levied at 3.29 points over £800.00 of turnover is invisible.

Every row of that table doubles, which is the whole of the demonstration and also the whole of the trap. A reader who sees two doubled quantities assumes the doubling was neutral, and in proportion it was. In money it was not, because the two quantities started at different sizes and the subtraction between them is what a reader receives.

3

What the second hundred per cent actually bought

Here is the asymmetry with figures against it. The second hundred per cent of the headline added £20.00 to the credit. It also added £400.00 to the staking, because the clause is a multiple of the credit and the credit grew. The reel expects to keep 3.29 points of that extra turnover, which is £13.16. So the twenty pounds arrived carrying a thirteen pound sixteen obligation, and what the second hundred per cent was worth is £6.84.

£20.00 of extra credit arrives with £400.00 of extra staking, and 3.29 points of that staking is £13.16, so the second hundred per cent is worth £6.84

Six pounds eighty-four against a headline reading twenty pounds is a ratio worth carrying about, and nothing in it accuses anybody of anything. Nothing has been concealed: the credit really is twenty pounds larger and the clause really is printed. What has been left unperformed is a multiplication, and the only figure missing from it belongs to the machine rather than to whoever drafted the terms. A reader holding the published return can finish it in one line.

The symmetry inside the figure is the part that generalises. Six pounds eighty-four is also exactly what the first hundred per cent was worth, because a credit of £20.00 under the same clause closes at £6.84 on the same reel. Two halves of one headline, each worth the same, and together worth the £13.68 the card above carries. A percentage headline is an instruction to repeat a transaction, and the value of the repetition is the value of the thing repeated.

That has a consequence for reading any of these headlines. If the first hundred per cent is worth having on a given reel under a given clause, the second is worth exactly as much, and so would a third or a fourth be. If the first is worth less than nothing, each further one subtracts the same amount again. The headline cannot rescue a clause and cannot spoil one. It can only repeat whatever the clause and the reel have already settled between them, which is what this card was opened to establish.

4

The fraction no percentage in a headline can shift

Set the headline aside and write the credit as the payment multiplied by whatever the percentage comes to. The expectation then reads as that product standing outside a bracket, and inside the bracket there is no percentage at all. So the share of a credit which survives its own conditions is a quantity with no headline anywhere in it, and on this reel under this clause that share is a little over a third.

Inside the bracket there are only two figures, and they are both ratios. One is the play-through the terms ask. The other is the multiple at which the expected cost of staking equals the credit exactly, which is the reciprocal of the house’s share and comes to 30.4 times on the original. Divide the first by the second and the answer is the proportion of the credit the conditions consume. Twenty divided by 30.4 is a little under two-thirds, so a little over a third survives, and £13.68 is that fraction of £40.00.

Written that way, a deposit match reduces to one comparison: the multiple asked against the multiple the reel will bear. Everything else in the offer is scale. A reader can use that, since the multiple asked is printed in the terms and the multiple the reel will bear follows from the return the maker publishes for whatever title the turnover is going to be done on. Two numbers, one division, and the percentage in the headline turns out to be the least informative quantity on offer.

It also explains why these pages do not rank percentages against one another. A headline of two hundred is not better or worse than one of three or four hundred in any sense the arithmetic recognises. It is larger, and larger multiplies whatever sign the bracket already had. The sign lives in the clause and in the reel, and the reel is the half of it that no document in the transaction mentions.

5

One credit against three of the family’s published returns

The studio’s own site carries 36 Big Bass game pages and the returns printed on them are not one figure. Twelve distinct figures appear across the family off the game sheet’s own table, which means the rate at which staking is charged is chosen, without anybody intending to choose it, by whichever tile in a lobby a reader opens. Below is the same £40.00 credit under the same twenty times, worked at three of those published figures.

Five pounds twelve separates the ends of that table, on one credit, under terms that did not change by a word. Hold it beside the £6.84 the second hundred per cent was worth and the ordering is uncomfortable: picking a lower-returning title of the same family can take away three-quarters of what the extra hundred per cent handed over. A reader who went looking for a bigger headline and then opened whichever Big Bass tile was nearest has very possibly undone their own bargain without touching a clause.

Every reading in that table is a figure the maker prints about itself, one to a title, and the axis they travel along is the name on a lobby tile. Nobody choosing a tile believes they are choosing a rate at which turnover will be charged, and that is precisely what has been chosen. The claim this trade repeats instead, that one title runs at several returns picked by whoever is running it, has nothing primary behind it: 36 game pages print a single figure apiece, seven jurisdiction values opened against the maker’s own server came back with the same figure, and no statement from the maker, a regulator or a testing house was found. So this card leaves that claim alone in both directions and prices the axis that is printed.

6

The same obligation counted in turns instead of pounds

Eight hundred pounds of turnover is not a sum anybody pays, which is why it reads as abstract. It is a sum anybody stakes, over and over, and the unit it is actually spent in is a turn of the reel. The game’s data lists 28 coin values, each of them staked across ten lines, which makes the cheapest turn 0.10 and the dearest 250.00 the game’s data, where a range has to be read from. This card buys its turns at the bottom of that, ten pence apiece supposed, off the published foot. Eight hundred pounds of turnover is then 8,000 turns.

Put a clock on it and the figure changes character. No licensed cycle may restart inside 2.5 seconds RTS 14D, which is 1,440 turns in an hour at the outside, so 8,000 of them will not fit inside five and a half hours anywhere that rule holds. Half of those turns, 4,000 of them, arrived with the second hundred per cent, in exchange for the £6.84 priced in entry three. Run at that ceiling, the expected cost of the whole £800.00 comes to a little under eight pence for every minute spent in front of the reel.

That conversion matters for one reason beyond its own arithmetic. The cap on pace belongs to the British licence, and a cashier advertising a match of this size does not hold one, so nothing in the sourced regulatory record holds the clock for it. A faster build does not change the £26.32, which depends on the turnover and the return and on nothing else. It changes how little time a reader has to notice the turnover accumulating, which is a different kind of consequence and not one this card can put a figure on.

Raise the stake and the count falls in proportion while the money stands still. At the 2.00 total stake the game’s own data opens on, the same obligation is 400 turns rather than 8,000, and the expected cost is £26.32 either way. A reader choosing a stake is choosing how long the obligation takes and not what it costs, and that is one of the few things in this transaction that the reel hands entirely to them.

7

Which of these figures a Great Britain licence would have moved

Go along the figures on this card and ask, one at a time, what a British licence reaches. The published return: nothing. Big Bass Bonanza carries 96.71 per cent wherever it is run, and the arithmetic resting on that figure comes out identically on either side of the licensing line. That is what lets one unit measure terms on both sides of the line honestly.

The credit: nothing directly. No sourced rule says what percentage a match may advertise or what sum a cashier may hand over. The clause, though, is a different matter, and it is where the whole of the difference on this card lives.

So the single figure a licence would have moved is the multiple, and moving it is worth £13.16 on this one credit. That is the honest shape of the loss: not that the offer is forbidden, and not that nothing out here is regulated, but that one number in one clause is bounded in one place and unbounded in the other, and the bound is worth a third of what the credit closes at.

8

Where a bigger headline stops helping and starts costing

Everything above rests on twenty times, which sits comfortably under the 30.4 times the original will bear. Lift the multiple and the bracket narrows, and somewhere it closes. The exact place is the reciprocal of the house’s share, and because the share is a different figure on different titles of the family, so is the place: 30.4 times on the original, 28.7 on Big Bass Reel Repeat, 25.4 on Big Bass Day at the Races. Past the figure for whichever title the turnover is done on, a credit’s expected close is below nothing and the headline is multiplying a cost.

That is the asymmetry read from the other end, and it is why entry three insisted the headline cannot rescue a clause. At twenty times on the original, each hundred per cent is worth £6.84 and a reader wants more of them. At forty times on the same reel, each hundred per cent would be worth less than nothing by a similar margin, and a larger headline would be a larger subtraction. The two cases look identical in an advertisement, since an advertisement prints the percentage large and the multiple small, and they are opposite in arithmetic.

A reader who wants one test rather than a method can have this one. Take the published return of the title the staking will be done on, subtract it from a hundred, and divide the answer into a hundred. What comes back is the multiple at which a credit of whatever size closes at nothing. Compare it with the multiple printed. If the printed multiple is smaller, a bigger headline is worth having in proportion; if it is larger, a bigger headline costs more. No figure in that test came from an advertisement, and two of the three came off a page the studio publishes about its own game.

Which leaves the thing a reader should probably do first, and it has nothing to do with percentages. Look up the return for the actual title before looking at the headline, because the table in entry five moves one credit by £5.12 on a swing of 0.64 points of return, and no part of that swing is printed anywhere in an offer.