400% deposit bonus, found past where a credit stops being worth anything

1

Deriving the point where a credit has paid for itself

Start with nothing but the reel. A machine whose published return sits under a hundred per cent is expected to hand back a fraction of what crosses it, and the part it does not hand back is the complement of that figure. For the original the maker prints 96.71 per cent the maker’s game page, with the game’s own data agreeing, so 3.29 points of any turnover is expected to remain where it was staked. That is a rate, and a rate multiplied by a quantity gives a sum.

Now bring in a credit, and ask one question about it. A credit carries a condition requiring some quantity of turnover before anything may leave, and performing that turnover has an expected cost of 3.29 points of the turnover. There must therefore be a quantity of turnover whose expected cost equals the credit exactly. Below it, the credit still has something left in it. Above it, satisfying the condition is expected to swallow more than the credit ever held, which makes the arrangement a purchase rather than a gift.

Solving for that quantity needs no algebra beyond a division. If the cost is 3.29 points of the turnover and the cost is to equal the credit, the turnover is the credit divided by 3.29 points, which is the credit multiplied by a hundred over 3.29. A hundred divided by 3.29 is 30.4, to the one decimal place this card prints. So the turnover at which a credit has been wholly paid for is 30.4 times the credit, on this title, and the figure came out of the reel without consulting a single offer.

Two things about that derivation are worth pausing on. The first is that the credit cancelled. Whatever the credit is, the crossing sits at the same multiple of it, so a four-hundred-per-cent headline does not push the crossing further away and a hundred-per-cent headline does not pull it nearer. The second is that the figure is not a constant of the trade, only a constant of the title, since the complement of 96.71 per cent is not the complement of every return the maker publishes. Entry five takes that up with figures.

2

The crossing named twice, as a multiple and as a sum of turnover

A multiple is a convenient form for the crossing and a bad form for reading a document, because a document prints a multiple of its own and the two look alike enough to be confused. So it is worth having the crossing in pounds as well. The offer supposed on this card matches a £12.00 payment four times over supposed, as the shape of the headline, giving £48.00 of credit. Forty-eight pounds divided by 3.29 points is £1,458.97, and that is the crossing stated as turnover.

Both forms are the same fact and each catches a different reader. Somebody comparing terms wants 30.4 times, so that a clause reading thirty-five times can be seen at a glance to be past it. Somebody who has already committed wants £1,458.97, because that is the figure a cashier’s own running total of turnover can be held against as it climbs. The second form has the further merit of not depending on how the requirement was written, since a requirement expressed against the payment, against the credit or against both reduces to a sum of turnover in the end.

The house expectation closes the loop. It is E = B × (1 − W × (1 − RTP) ∕ g). The bracket reaches nought when the play-through W equals the weighting g divided by the complement of the return, and with the named game counting in full that is simply the reciprocal of 3.29 points. Where a clause counts a slot at less than its full stake, the crossing moves in proportion to the weighting, which is the only term in the formula that an offer can use to shift a point otherwise fixed by the reel.

£1,458.97 of turnover is the crossing for a £48.00 credit on the original, and the clause supposed here asks £1,680.00, which is £221.03 beyond it

3

How far past it this clause stands, and what the overshoot costs

Thirty-five times £48.00 is £1,680.00 of turnover. Against a crossing at £1,458.97 that leaves £221.03 standing beyond the point where the credit ran out, and the expected cost of £221.03 at 3.29 points is £7.27. So the credit closes at £7.27 below nothing, and the minus sign is doing no rhetorical work: the arithmetic is reporting that the conditions attached to a credit are expected to cost more than the credit holds.

It helps to see how quickly the last few multiples do their work. At thirty times the credit the close is 62 pence, which is almost exactly break-even and would strike most readers as a thin but real gift. Five more times of play-through adds £240.00 of turnover, the expected cost of which is £7.90, and that single step is what carries the figure from 62 pence to £7.27 below nothing. Nothing in the headline changed and the credit is still £48.00.

Read down the last column and the credit loses roughly £7.90 for every five times added, which is 3.29 points of £240.00 and will go on being that for as long as the credit stays at £48.00. A reader who has grasped the crossing has therefore grasped the gradient as well, because the gradient is the credit multiplied by the house’s share and does not vary with where on the scale the clause happens to sit.

None of which says the arrangement is a trap. A credit with an expected close below nothing can still be a reasonable thing to accept, if what somebody wants is a quantity of play rather than a quantity of money, and £1,680.00 of turnover at ten pence a turn supposed, off the published foot is 16,800 turns of a named reel. What the arithmetic refuses is only the word that usually sits beside the headline. This is a purchase of play with a discount attached, and the discount here is a negative number.

4

The biggest thing the reel can do in one turn, held against the obligation

A reader looking at £1,680.00 of required turnover sometimes reaches for a thought that feels like a rescue: one good turn and it is all paid off. The game publishes the figure that settles this. Its own data puts a ceiling of 2,100 stakes on a single round the game’s data, the maker’s page naming no ceiling whatever, and a turn costing ten pence makes that ceiling £210.00.

Eight. That is how many times £210.00 goes into £1,680.00, exactly, so the largest single event the machine is capable of would discharge an eighth of the obligation and no more. There is no outcome on the paytable that satisfies this clause in one turn, which means the turnover has to be performed, turn by turn, and every turn of it is charged at 3.29 points. The overshoot cannot be outrun by a good result, because the overshoot is a property of the clause and not of the sequence of outcomes.

The frequency is worth setting beside the size, and the game publishes exactly one hit rate: the maximum win lands once in 3,880,481 turns the only hit figure in the game’s data. No base-game frequency and no feature frequency is published anywhere this site may cite, so nothing further can be said about how often anything else happens, and this card says that rather than borrowing a figure from a review. What can be said is that an eighth of an obligation, available once in nearly four million turns, is not a plan.

Hold that against the smaller headlines on this domain and a shape appears. The crossing is a fixed multiple of the credit, so the obligation and the crossing both scale with the headline. The reel’s single-turn ceiling does not scale with anything: it is 2,100 times whatever one turn costs, and at a fixed stake it is a fixed sum of money. So the larger the headline, the smaller a fraction of the obligation one turn could ever cover, and at four hundred per cent that fraction is an eighth.

5

The crossing is not one figure across the series

Everything so far has been worked on one title. Twelve distinct returns appear over the 36 Big Bass pages the maker keeps the sheet’s own table of the family, and the crossing is the reciprocal of whichever of them applies. So the same credit under the same clause meets its crossing in different places depending on which tile the turnover is done on.

Three crossings, 5.1 times apart from end to end, on a swing of 0.67 points of published return. The offer is past every one of them, which is the point of putting three rows up rather than one: at thirty-five times there is no tile in that table that rescues the sign, and the choice of tile decides only the size of the loss. It decides it by £11.26, on a credit of £48.00, and that figure is printed in no document a reader will be shown.

The axis those rows travel along is the title, and the maker publishes it for itself, one figure to a page. It is not the thing this trade keeps repeating, which is that a single title runs at a choice of returns picked by whoever is running it. On that question the record is thin and the sheet says so plainly: no statement from the maker, none from a regulator, none from a testing house, 36 pages printing one figure apiece, and the only sources secondary and in disagreement with each other over whether there are three such figures or five. This card neither asserts the practice nor denies it, and measures what is actually printed.

6

A title whose own two sources put the crossing in two places

The bottom row of that table deserves a paragraph on its own, because the figure in it is not settled even by the maker. The maker’s description of Big Bass Halloween prints 96.04 per cent, while the game itself reports 96.06 when a session opens, and both of those are primary sources belonging to one company. The sheet records the disagreement and does not choose between them, which is the right thing to do and also the inconvenient thing, because the two figures put the crossing in two places.

Work them both. A complement of 3.96 points puts the crossing at 25.3 times; a complement of 3.94 points puts it at 25.4. On a £48.00 credit that is a difference between £1,212.12 and £1,218.27 of turnover, which is about six pounds and would matter to nobody. What matters is the demonstration: a derivation that depends on a published figure inherits whatever uncertainty the published figure has, and on this title the publisher disagrees with itself by 0.02 points.

The close in that row moves with them too, and by very little: £18.53 below nothing on the maker’s page figure and £18.19 below nothing on the game’s own, since 0.02 points of £1,680.00 in turnover is about 34 pence. So the row stands, with a caveat whose size has been stated rather than waved at. That is the discipline this domain runs on. Where two sources differ, print both, record which said which, and then say what the difference is worth in the unit the page is already using.

It also puts a limit on how confidently anybody should read a crossing to the first decimal place. Thirty point four times is the reciprocal of a figure the maker states to two decimals, and the arithmetic cannot be more precise than its input. A reader comparing a clause at thirty-five times against a crossing at 30.4 has a margin wide enough that rounding does not matter. A reader comparing a clause at thirty times against a crossing at 30.4 is inside the margin, and the honest answer there is that the credit is worth about nothing.

7

What a bound on the multiple would be worth on this credit

Everything on this card turns on one number in one clause, and in one jurisdiction that number has a ceiling over it. Pricing the ceiling is a better way of describing what a British licence gives a player than any adjective would be, because the ceiling has a value in pounds on this exact credit and the value can be worked out.

Set the two figures from that block side by side and the honest statement of the loss is short. One number in the terms is bounded in Great Britain and unbounded here, and on this credit the bound is worth more than the credit itself. Nothing about the percentage in the headline is bounded in either place, and nothing in the sourced record says a match may not be four hundred per cent.

Which is why this card does not treat the percentage as the thing to be warned about. The percentage decides the size of the credit and the size of the obligation together. The multiple decides the sign. A reader who gets that ordering the right way round will read a four-hundred-per-cent headline at ten times quite differently from a hundred-per-cent headline at forty, and the arithmetic says they should.

8

Using the crossing before any money has moved

The crossing is the one figure in this transaction that a reader can produce unaided, and producing it takes two numbers and a division. Take the maker’s figure for the title in question, take it away from a hundred, and divide what is left into a hundred. That quotient is the multiple at which a credit has been wholly consumed by its own condition, and it is 30.4 on the original, 28.6 on Big Bass Blast and 25.3 on Big Bass Halloween.

Then read the terms for the multiple, and read them for the base the multiple stands on, because the words come out the same whether the base is the payment, the credit or the two added together. Convert whichever it is into a sum of turnover and hold it against the credit divided by the house’s share. If the turnover asked is smaller, the credit has something in it. If it is larger, whatever the excess turns out to be, the house’s share of it is the price of accepting the credit, and on the figures supposed here the excess is £221.03 and the price is £7.27.

Two cautions on using it. The weighting matters: where a clause counts a slot at less than its full stake, the crossing falls in the same proportion, and a weighting has to come out of the document rather than off the game sheet. And the stake does not matter at all, which surprises people. The obligation and the crossing are both sums of money, so the price of a turn changes only how many turns the obligation takes, never what it costs. At the total stake of 2.00 that the game’s data makes its default, this clause is 840 turns rather than 16,800 and the £7.27 is unmoved.

Last, the thing worth doing before any of it. Find the return for the title itself rather than assuming the series shares one, because the table in entry five moves this credit by £11.26 on nothing but the name on a tile. A reader spending the whole of their attention on the percentage in a headline will have spent none of it on the one figure here that is published by a party holding no stake in the result.