Free Play Arena: eighty-five findings on seven boards, and £1,082.32 added across seven unlike things

1

One question asked eighty-five times, and the two columns every answer has

Eighty-five guides stand under this address and every one is set the same task: price a quantity of play as the free version somebody is handing over, price it again with a reader’s own money behind it, and print what lies between. Nobody at this publisher has played anything to reach either number. Each is arithmetic on a quantity somebody else printed, or on an assumption named where it is spent. One figure for a free round would answer half of that, leaving out the comparison a reader is actually making, which is against money already in an account.

Three kinds of answer came back. Mostly a sum, where a free version exists and some of it survives whatever is asked of it. Sometimes a nought, where the only free version is a simulation and no route exists by which money leaves one. Twice the answer is that no free version exists at all, which settles something harder: nothing was priced, rather than something being priced at nothing.

The seven sections sort those eighty-five by the shape of the thing rather than by its name: whether a free version is to be had, what a published condition takes back, what a payment at the door buys, what alters when the offer is credit, and what survives where a register cannot reach the seller. Each read its own guides and printed a board, and this page reads those boards.

2

The four quantities settled before any of the eighty-two could be struck

Four quantities had to be settled before any of the eighty-two findings could be struck, and three of the four quantities came from this publisher. A reader meeting the figures first is owed them first.

The stake comes ahead of the rest. A count of free rounds holds no money until a value is put on one round, nothing obliges a cashier to print one, and so every count here is priced at a figure stated on the page spending it. Eleven values are in use, the smallest five pence and the largest a whole pound, and ten pence carries more rows than any other this bill’s own figures. So a board can be rescaled by anybody who prefers a different one.

The last line wants a sentence of its own, because putting a limit drafted for bonus funds over a count of rounds assumes something nobody has settled. The limit covers whatever a count wins once those winnings are entered as bonus funds off the rule sheet, and no source reachable from here says whether a free round produces such an entry, one way or the other. The ceiling is taken on that footing and no page here goes past it. Nothing binding reaches a cashier outside the licence in any case, and no sentence here says any offer asks ten times.

Where an offer prints a demand of its own, that figure is used instead: one board has six rows of exactly that shape, which are the control for the remaining seventy-six keys. All four quantities enter one expression, E = B × (1 − W × (1 − RTP) ∕ g), standing on every guide and every board, and the only letter that changes character from section to section is the first of them.

3

Why the seven add, and what the £1,082.32 is a sum of

Seven section totals, every one a quantity of pounds and pence, and pounds add. £44.00, £177.30, £69.94, £48.66, £560.00, £92.86 and £89.56 make £1,082.32, which anybody can confirm without opening a section. That half wants no defending.

The other half does, because the sum invites a sentence it will not carry. These seven are not seven readings of one quantity. One section prices advances of credit, which are sums handed into an account with nothing having happened to them. Four price counts of rounds, which have already crossed a machine before anybody looks at the balance. Two price both kinds side by side. So a pound of distance in one place came off a sum that paid no margin going in, and a pound in another off a face value the reels had already taken their share of. The denominations match and the things denominated do not.

The honest statement is therefore narrow and belongs in the same breath as the figure. £1,082.32 is an addition of money across seven different things. It is not the worth of free play in Britain, not a market, not an average, and dividing it by eighty-two would give a figure standing for nothing.

What it is good for is worth as much as what it is not. It gives the scale in one number, which no guide and no section can reach, and over half of it belongs to one section. It reconciles two ways, which makes it a check. The tidy move here would be to drop the three findings that do not fit and print one clean total. The result would be larger, rounder and worth less: a total that has swallowed its exceptions can be rebuilt by nobody.

4

Three findings outside the seven totals, and one inside with no bound

Three of the eighty-five findings are not inside the £1,082.32, the sections that made them having refused to put them there, and a fourth sits inside its own total carrying a warning its number cannot show. All four findings are repeated here rather than dropped, for the reason part three closes on.

The first is a rate. A count arriving each day is reported at 31 pence a day, every term behind it carrying those three words with no way of prising them off. A sum wants one further quantity, the run of days the thing lasts, which no offer of that shape prints. Dropped into a money column it would read as 31 pence once, wrong for a fortnight and wrong for a year.

The second is a rate of another shape. One key sets the word free beside no quantity whatever, so its guide prices the unit any quantity would have been counting. Each pound of face stands 61.6 pence from the same pound bought, or 6.16 rounds, and multiplying that by whatever face a headline eventually names gives that headline’s distance. The multiplier is what is missing, and supplying it was the key’s job.

The third is neither a rate nor a nought. A guide about a dealt table reports that no free version of such a play has ever existed, for a reason in the structure rather than in anybody’s pricing: staking is the only element of a live hand that could be imitated, and imitating that alone leaves an empty chair. So the funded side stands alone at £6.00 over a hundred and fifty hands, with nothing to take it from. A nought is a measurement that came to nothing; an absence is the finding that there was nothing to measure.

The fourth is bounded in neither direction, alone among the eighty-five in that. Its £3.70 was worked at the ceiling like the eleven beside it, and above it sits a cap on what the offer will ever hand over. A cap of that sort is money rather than a multiple, which puts it outside the ten-times limit altogether; nothing published sets a lowest lawful one; and the British term barring such a cap is drafted against money a reader paid in, which on a no-deposit key is nil. So the word least appears nowhere beside it, and it stays inside its section’s total, the figure being money like the rest.

5

Why £1,082.32 is a least and not a middle, derived on seven boards

Almost nothing under these keys prints the staking it asks, so the free column rests on a published limit instead, and where in the range that puts the answer is the first thing to want to know. Seven writers worked it separately over seven balances: hold a balance where it is, hold the return where it is, and turn only the staking demanded.

Every line of that drops from left to right, on seven boards worked by seven hands, and not one runs the other way. The reason is a single sentence. Each turn of the staking sends more of the identical balance back through the games, the house keeps its share of every pound so sent, and less survives to be set beside the price of buying the play outright. Ten times is the furthest British law lets a licensee go, so that right-hand column is the thinnest free side any lawful staking leaves. Every figure resting on it is accordingly a least: the eighty-two stand at least as far from buying the same play as the boards say, and a real demand under the limit leaves them wider than printed.

Two of those lines cover part of a board and say so on their own pages. The first covers three advanced counts out of fifteen rows, twelve of the fifteen offering nothing but a simulation, which is nought under every demand there is. The third covers two rows of eight, the other six publishing that nothing is owed. Both boards close higher than their line here.

Two unstated quantities share that bracket and pull against one another, which is how either gets read as the other. A staked pound is credited in full, the most generous reading, since any lesser credit leaves less behind; the staking is read at the limit, the least generous. That pairing cannot overstate an offer at a reader’s expense.

Two qualifications go with the least. The first is the finding with a cap over its payout, set out in part four. The second is a whole board rather than one row: the section about keys a register does not reach states plainly that its £89.56 is the reading at the published edge rather than a least, the licence setting that edge not reaching the sellers those keys are about, and nothing there ruling out twenty times or sixty. That is the narrower claim, that section stands behind it, and this page prints it instead of flattening it into the other six.

6

How the eighty-two were added, and the two tenths of a penny inside it

Each of the seven came up from the section that reported it, at the number that board closes on, with its decimals intact. No figure was re-struck to fit, no row re-priced to suit a heading, and nothing here computed from an offer, which is how one page of a hundred comes to carry no finding of its own.

How many guides stand inside each figure is worth setting down. Fifteen of sixteen on the first board, the dealt table held out; twelve of thirteen on the second, a rate held out; eight of nine on the third, a daily count held out. Then seven of seven, twelve of twelve, fifteen of fifteen and thirteen of thirteen, those four having nothing to leave outside. Added, eighty-two, which against eighty-five leaves the three of part four.

It reconciles down the columns as well as across the rows, so neither road is taken on trust. The free sides are £20.16, £162.60, £66.82, £45.50, £525.00, £86.83 and £83.76, which is £990.67. The paid sides are £23.84, £14.70, £3.12, £3.16, £35.00, £6.03 and £5.80, which is £91.65. £990.67 beside £91.65 is £1,082.32, and that is the figure the seven distances give as well.

One rounding is in it and is printed rather than smoothed. Three of the seven sections close between pennies and show the nearer one: their free sides are exactly £45.504, £66.816 and £86.832 where the pages read £45.50, £66.82 and £86.83. Worked exactly, the free column is £990.672 and the distance £1,082.322; worked from the printed figures, £990.67 and £1,082.32. Two tenths of a penny lies between the routes and both print alike, which is luck rather than a rule, and it is said here so that nobody goes looking for an error in a column that already adds.

Nothing else is outside the £1,082.32 and no row waits to be filled.

eighty-two findings off seven boards, worth £990.67 as rounds and credit somebody else staked and costing £91.65 bought outright, so £1,082.32 of distance, added across seven unlike things and measuring none of them

7

Three objects under one pound sign, and what a pound buys on each

Part three said the seven are unlike and the table under the standfirst shows how. Grouped by what is being priced, the £1,082.32 falls into three pieces of very different sizes, and what separates them is not their size.

Four boards price counted play: forty-five rows, worth £219.31 free against £36.15 to buy the same rounds, so £255.46 between them. A count stakes itself, so the reels have taken their share before any condition turns up, and the condition then bites into a balance the margin is already out of.

One board prices advances of credit: twelve rows, £525.00 against £35.00, so £560.00, over half of what this page closes on and by a wide margin its largest single piece. Credit is handed across as money and has crossed nothing, so the house takes its share once on the way through and the condition lands on the sum flat. Running the return over an advance before the condition is the error that comes naturally, and that board puts £21.00 on it. Two boards price both kinds in one column: twenty-five rows, £246.36 against £20.50, so £266.86, and both set their counted rows out separately from their advanced ones for exactly this reason.

Those two per-pound figures come off the boards rather than from this page, and they differ because they are prices of different objects. A reader adding them has put a pound that went through a machine beside a pound that did not, which is the same fault, differently dressed, that the credit board puts at £48.00 elsewhere: a payment and an advance show on one screen as one balance, and valuing that balance as the advance treats a reader’s money as though it had been given to them.

8

What this page could not add, and printed the absence of instead

Three further totals would have been easy to set down and not one exists. Each is left out with its reason, a stated absence beating a figure nobody can rebuild.

The first is a count of rounds under the money. Every finding here is said twice, in pounds and in the rounds a reader plays, and on six boards the second saying stands against each row and under none, the stakes differing page by page. Nine stakes produced one board, eight another, five another, four another, three another and two another, and two rows on the domain count something other than a round, one in bingo tickets and one in dealt hands. A single board is the exception: the section where nothing is owed worked all eight added rows at ten pence, so its counts total at 699.4 rounds. Seven boards together have no such luck, so no count stands at the foot of this page.

The second is a total of face. Adding what the eighty-two put across the machines would set face values of counts beside sums of credit in one column, which part seven is the whole reason against.

The third is a reading at another return. Six of the seven sections print what their board comes to at ninety-four per cent and at ninety-seven, that assumption being the one most worth arguing with. The seventh prints no such pair, its findings being credit rather than counts, so a figure at domain scale would want a number nobody struck.

A fourth thing this page will not do is not an addition at all. No figure anywhere on this domain is built on a named game or a named maker. Four keys carry such a name and the h1 of those guides carries its key, so the names appear and appear nowhere else. None of the four states a return for a title, orders a catalogue or characterises a studio, and under the question asked here none needed to: what a free round hands back is settled by a count, by a stake, by a return and by a condition, and a name on a lobby is none of those.

9

The one quantity here a reader can spend without knowing a stake

Everything above rests on a stake somebody had to choose, which is a fair thing to distrust. Three of the seven boards print a quantity with no stake inside it at all, and if one number is carried away from this page it should be that one.

At the limit a count keeps six tenths of whatever balance the reels return, and buying the same rounds costs four hundredths of the face they put across. Six tenths of ninety-six pence set against four pence is 14.4, with no stake and no currency anywhere inside it. So a free count of rounds is worth 14.4 times the cost of buying the same count outright, which reads alike on a tenpenny round and on a sixty-penny one. Three boards reached it separately, which is why it stands here rather than being worked out on this page. The credit board carries its own version, part seven’s sixty-four hundredths of whatever was advanced.

Three cautions keep both usable. Each is an expectation over a long run of rounds rather than a prediction about an afternoon, so ending a session with nothing is no evidence of anything. Each is read at the limit, so a real demand under it makes both larger. And neither says the money arrives.

That last caution is where this page ends, being the one thing on it the arithmetic cannot supply. £91.65 has been taken by the end of a session. £990.67 stands in accounts somebody else controls, under conditions somebody else wrote, with no British licence behind any of it. Both columns are correct and neither is a version of the other, and a reader who treats them as two certainties of one kind has made the single error that eighty-five guides of arithmetic cannot catch.