How long a balance lasts on it, and the quantity deciding that with no publisher at all

1

Which of this reel’s quantities has a publisher, and which has none

Take an inventory before taking a view. The return to player is the best-documented figure this reel has. The maker sets it in a block that holds one item and no second one, and a field inside the opening session carries the identical 96.71 per cent claims 20 and 21. Five reels by three rows, and ten lines across them, come from that same session and from the maker’s internal symbol for the game, while the page the maker keeps for this title offers neither of them claims 22, 24 and 109. The price list is the same story: twenty-eight steps between a tenth of a pound and £250.00, from the session data, with the maker’s page stating no range at all claim 25. The ceiling on one turn, the published 2,100 of one stake, is in that data twice over in two differently named fields, and is absent from the maker’s page for this title claims 27 and 28. One arrival rate exists for the family and it belongs to that ceiling, at 1 in 3,880,481 turns claim 29.

So six quantities, six readings, two primary sources between them, and a reader who goes looking can check every one. The seventh is the scatter, and it is the reason this section exists. The word for it appears on none of the thirty-six game pages the maker’s own site carries, and nothing a session sends down has a field it could occupy claim 104. That is not a gap in this publisher’s research. It is a gap in what anybody has published, and the ten guides below all had to work round it.

The board at the head of this page makes that visible without being asked to. Each row carries the house label for whichever of the reel’s quantities its finding turns on, and the set of labels runs to six. Five of them are spoken for, two rows apiece in three cases. The sixth stood empty across all ten rows, because a label wants a finding under it and no guide could reach one for a quantity nothing states.

2

The scatter derived, and why it comes out as two walls and not a figure

A guide in another section, A balance in a moving unit, settles the centre of how long a balance survives and stops there, saying in terms that the width is this section’s to find and naming the three published things it would have to be built from. Those are the paytable, the ceiling and the top arrival rate, and they are enough to put walls on either side of the width without stating it.

Exactly one outcome of this reel arrives with its size and its frequency both on record, which is all the derivation takes. A turn returning 2,100 of one stake once in 3,880,481 turns puts 1.1365 into the average of the squared outcomes by itself, and the whole of it is paid for out of the published return by 0.00054 of one stake. Everything else the reel does carries the remaining 0.966559 of one stake, and the tightest that remainder could possibly be is every single non-ceiling turn handing back the same 0.966559, which adds a further 0.9340. Subtract the square of the published return, 0.9353, and take the root: the scatter of one turn of this reel cannot be below 1.0656 of one stake. The arithmetic puts a floor under it and no observation is involved.

The other wall comes off the paytable. Its highest paying value is 2,000, which the maker’s own prose for the game states as the most a money symbol can carry claims 39 and 49, so no turn below the ceiling can be worth more than that. Pile every remaining penny of the published return onto that one value, which is the widest arrangement the published figures permit, and the average of the squared outcomes reaches 1,934.25. The same subtraction and the same root give 43.97 of one stake. Between the two walls there is a factor of 41.26, and nothing inside it has a publisher.

Put that at a price. At a turn costing 10p, which this page supposes because it is the cheapest rung the reel’s own list carries, one turn is expected to hand back 9.67p, and the scatter about that is somewhere between 10.66p and £4.40. The low wall is already larger than the thing it is scattered about. Carry it to the largest count this section weighs and a thousand such turns expect £96.71 back, with the scatter of that total standing between £3.37 and £139.02, the upper of the two being £42.31 bigger than the sum it surrounds.

The expectation under every figure on the board is E = B × (1 − W × (1 − RTP) ∕ g). In it g is one all the way through, no term in this class stating a weighting at all; W runs from nothing up to forty; B is either the £1,000.00 the credit advertises or, where a grant is a count of turns, that count multiplied by what one turn costs and then by the published return; and RTP is the 96.71 per cent nine of the ten guides weighed against. Nothing in the expression carries the scatter, and that is the point of this whole page: the formula answers where a balance is expected to end and is silent on how far from there it will actually land.

Both rows hold the stake at 10p because both titles publish that rung as the foot of their own range, and the fourth column prices the section’s 2,440 granted turns as one grant, which is a quantity no guide beneath this page holds. Read the closing row carefully. Moving the whole section from one title to the other is worth £1.56 on what the turns hand back, and £264.77 once the ten play-throughs have acted on that same 0.64 of a point. Of that £264.77, however, £224.00 belongs to the single four-figure credit and is already reported on its own card, leaving £40.77 spread across the other nine. A clause multiplies a difference in the return; it cannot multiply a difference in the scatter, because there is no published figure there for it to act on.

3

What each quantity was worth across the ten, and the one worth nothing

Sort the board by its labels instead of by its figures and the section states its own case. Under the stake range sit two rows, coming to −£141.58. Under the published return sit three, coming to £21.58. The cycle time holds two at −£7.35, the maximum win holds two at £2.18, and the feature trigger holds one at £3.43. Added in that order the five come back to the same −£121.74 the board closes on, which is what a regrouping ought to do. The sixth label has no row, no figure and no subtotal, and the absence is not an oversight anywhere: it is the finding.

The largest of those five subtotals wants reading with care, because what made it large is not the range of stakes at all. One of the ten guides weighs a four-figure credit, and that single card is −£151.50 of the −£141.58. Lift that one out and the stake range is worth £9.92 instead, and the nine remaining closes add to £29.76 rather than to −£121.74. One row is therefore worth £151.50 of swing on its own, which is more than the whole section comes to either way.

That row still counts towards the closing figure, and the reason is worth stating because it is the test the board applies. A row is set aside when its card prices a different quantity, not when its card prices a large one. All ten of these cards print a close in pounds in the third column, so all ten are the same quantity and all ten add. What a dominant row earns is a sentence, which it now has, rather than a place outside the measure.

4

What the missing quantity costs a reader across this whole class

Three of the ten close under nothing, at −£151.50, −£30.56 and −£4.59, which is −£186.65 standing against the £64.91 the other seven come to. Each of the three asks a multiple past the crossing point of 30.4 times that this title’s published return sets, and each is therefore expected to finish having taken money rather than given any. A guide can say that much. What no guide can say, because no guide sees ten at once, is what the absent quantity is worth across a whole class of grant, and that is this page’s own figure.

Work it on the four-figure count. Its granted turns are expected to hand back £96.71 and the forty times asked of those winnings is expected to cost £127.27, which is £30.56 more than the turns produce and is how that card reaches −£30.56. Now set the two walls from part two beside the £127.27. At the low wall the scatter of those thousand turns is £3.37, about a thirty-eighth of what the condition costs, and a reader may treat the expected close as very nearly the outcome. At the high wall it is £139.02, exceeding everything the condition is expected to cost, and the expected close then settles almost nothing about where any one reader finishes. Both walls rest on published figures only. Nothing published chooses between them.

So the cost of the missing quantity, put as flatly as the arithmetic allows, is that nobody reading can tell which of those two accounts of their own grant is the one they are in. Every figure on the board is honest and every figure on the board is an expectation. Whether an expectation is a forecast or a curiosity depends entirely on the width around it, and the width is the one thing on this page nobody will supply. That holds for all ten grants, and it holds whatever a reader pays for a turn, because the walls are quoted in stakes and scale with the price exactly as the expectation does.

£1,248.00 advertised across this section, closing at −£121.74 once every stated condition has crossed the reel, with the scatter around that figure pinned no closer than between 1.0656 and 43.97 of one stake per turn

5

Where the closing figure came from, what it added and what it omits

The figure under the board is ten figures added, and each one is the third column of the card that produced it rather than a recomputation performed here. That distinction matters by a penny or two: a card rounds its expected winnings to the penny before any multiple is applied to them, as the network’s own arithmetic appendix instructs, so adding the printed figures and re-deriving them from scratch are not quite the same operation. The board adds what the cards print, and a reader with a pencil can repeat that addition.

All ten rows count towards it, and that is less usual than it reads. A board sets a row back from its measure when the card under it prices some other quantity: an hour, a turnover, or a cost spread over a span. Add one of those to a close and the answer is a quantity of nothing at all. Here every one of the ten third columns holds pounds surviving a condition. Four of the grants ask nothing of the winnings, so on those four cards the yield and the close are one figure and the same figure; six carry a multiple and close behind their yield. Both shapes are closes, so the addition is sound and nothing stands apart.

What the figure leaves out divides in two. The first part is ordinary: a turn costing 10p is this publisher’s supposition, named afresh wherever it is spent, and one of the ten guides spends twelve pence instead because the title it weighs begins its own range there claim 75f. Change the supposition and nine of the ten figures move together, which is why it is stated rather than assumed quietly.

The second part is this section’s whole subject. The closing figure is a sum of expectations and it says nothing whatever about dispersion, which is the quantity this section is named after. A board cannot print what no source publishes, and the honest form of that is a figure with its limits written beside it rather than a figure with an adjective. Nothing to do with a document check at the exit, a refused withdrawal or the days a cashier takes is in the closing figure either, none of those being quantities of a machine.

6

The word nobody can avoid, and the three answers in circulation

Everything above has been written round a word with no publisher behind it, and the word is volatility. It is avoidable here only because no publisher states a figure for it, so there is nothing to print; it is unavoidable in the trade, where every review of this reel carries one. Three secondary sources were read for the game sheet and they answer three different ways claim 121. The first puts it on the high side of medium and scores it four out of five. The second says it is low. The third says high inside a table of specifications while its own prose, on that same page, calls the reel medium to highly volatile, so that source does not agree with itself.

Each of those is a reviewer’s characterisation and belongs to the reviewer who made it, which is why this page attributes all three and prints none as a property of the reel. The maker publishes no figure of that kind for any of the thirty-six titles its own site lists, so there is nothing for a review to be right or wrong against. What makes the three-way disagreement worth a paragraph rather than a footnote is how exactly it matches the working in part two. A quantity loose by a factor of 41.26 is a quantity three careful readers can describe three ways without any of them having made a mistake, and one of them can contradict itself in a single page without anything being available to catch it.

The derived walls do not settle the question and are not offered as settling it. They do something a word cannot, which is to state what is known and where the knowing stops. A reader told that a reel is highly volatile has been handed somebody’s impression. A reader told that one turn of it scatters by at least 1.0656 of one stake and at most 43.97 has been handed two subtractions they can perform themselves, from three figures they can go and read.

7

Why the working is about one title and will not travel across the family

The walls in part two were built for Big Bass Bonanza and describe that reel only. Two of the three ingredients are specific to it in ways worth spelling out, because a derivation carried quietly onto a sibling title would be the sort of invented figure this whole site is arranged to avoid.

The ceiling is the first. Counted off the family table, the thirty-five slot titles carry seven different limits on what one turn may hand over: 2,100 of one stake on four of them, 4,000 on three, 5,000 on eighteen, 10,000 on five, 15,000 on one, 20,000 on three and 25,000 on one claim 74. The thirty-sixth title on the maker’s list is not a reel at all and no limit could be read for it claim 75d. The 2,100 above is therefore one of seven answers, and it is shared by only three other titles claim 75i.

The arrival rate is the second and it is scarcer still. One rate exists across the whole family and it belongs to the original’s own ceiling. A floor under the scatter needs a size and a rate in the same hand, so the lower wall can be built for exactly one of the thirty-six titles, and for the rest there is no arithmetic to perform.

Which has a consequence inside this section. That figure of 96.71 per cent stands on six pages of the maker’s own site claim 75b, and across those six the limit on one turn takes three of its seven values, the largest being nearly two and a half times the smallest. One of the ten guides here weighs a title that shares the original’s published return exactly and carries 4,000 of one stake rather than 2,100, so the walls derived above do not describe the reel that guide weighed, even though the figure in its machine column is identical. An identical return is not an identical machine, and nowhere else across this domain does the gap between those two sentences carry the whole of a section’s argument.