The rounds that are already money, and £69.94 added over eight rows of nine

1

What an absent term does to the house expression, and why six come back whole

Six of the nine guides here rest on terms that ask nothing of the proceeds, and what that absence does to the arithmetic is worth seeing in letters before it is seen in pounds. Put W at nought in E = B × (1 − W × (1 − RTP) ∕ g) and the second term inside the bracket has a nought on top of it, so the term disappears for any return and any qualifying share. The bracket is then one, and the count comes to whatever reached the balance.

What each of those six comes to is therefore its own count at ten pence with the return applied once and nothing taken off afterwards. The paid side is one subtraction: the identical rounds funded by the reader stake the same face and give back the same balance, so the cost is whatever the return keeps. Added, the two carry the return with opposite signs and it drops straight out of the expression, which is why each of those six distances is its own count’s face value rather than a share of it.

In pounds: the six carry £57.00 of face between them and report £57.00 of distance. Fifty rounds, seventy, thirty, a hundred, a hundred and twenty and two hundred, each at the ten pence this publisher states and keeps stating this section’s own figure, give £5.00, £7.00, £3.00, £10.00, £12.00 and £20.00. Those six figures are the face values of those six counts, in that order, with nothing between the two columns at all.

One letter deserves a word before it is assumed away. The qualifying share is a contribution rate and nothing behind these keys fixes one, so it is read at full weight and said to be. On those six rows that generosity is free of charge: with a nought on top of the second term, whatever sits underneath it cannot matter, and the finding is identical at full weight and at a third of it. It is the one place in this network where an unpublished quantity has no work to do at all, and a reader who distrusts an assumption deserves to be told which one is idle.

Two cautions keep the £57.00 honest. It is an expectation over 570 rounds and not a prediction about one of them, so finishing a run with nothing is not evidence of anything having gone wrong. And it is money only where the written terms carry the absence rather than the headline carrying it; where terms are silent on staking, the quantity the sum needs is missing and no total can be struck at all.

2

The two rows publishing no term, and the £8.06 a ceiling takes off them

Two of the eight added rows are not like the six. A count of ten rounds and a count of two hundred sit under keys that name a quantity of free rounds and publish no staking term of any kind, which leaves them in the position almost every other key on this domain is in rather than the position the rest of this heading is in.

For those two the free column has to stand on something, and the only number with a publisher behind it is the British cap. Ten times is the upper limit on a staking requirement over bonus funds under a British licence, effective 19 January 2026 off the rule sheet. It is a ceiling and never an offer’s term, nothing binds a cashier outside that licence, and the footing has to be stated: a cap written about bonus funds reaches the winnings of a count once those winnings sit in a balance of that kind off the rule sheet, while whether a free round is itself such a balance is published in neither direction.

Worked: those two counts carry £21.00 of face and hand back £20.16 of balance. The bracket at ten times and full weight closes at six tenths, so £12.10 survives and £8.06 is taken. Their paid side costs 84p, and the two distances are 62p and £12.32, which is £12.94 between them. Set that beside the £57.00 the six contribute and the closing figure is £69.94.

Which way that bound runs is worked out here rather than borrowed, and worked on those two rows alone. At no term at all the pair would stand £21.00 apart, the whole of their face. At five times the bracket is eight tenths, £16.13 survives and the pair stand £16.97 apart. At ten times £12.10 survives and they stand £12.94 apart. The free column falls as the term rises and the distance falls with it, so a ceiling, being the heaviest term the law allows, yields the narrowest distance of any lawful term. The 62p and the £12.32 are therefore floors, and a real term under the cap would leave both rows wider rather than narrower.

3

The booking taken here, and the £78.00 this heading did not print

Those two rows can be booked two ways and the two are not interchangeable, so the choice is made in the open and the figure it was not given is printed beside the figure it was. Booked at the ceiling, as part two works them, they contribute 62p and £12.32 and the eight rows close at £69.94. Booked instead at the reading this heading is about, with nothing asked of either count, they contribute £1.00 and £20.00 and the eight rows close at £78.00, which is the face value of all eight exactly.

This heading prints £69.94. The reason is not that the ceiling is the better guess about what the terms behind those two counts require, because this heading says nothing whatever about that. It is that a board reads its guides and prints what they found, and those two guides close on 62p and £12.32 on their own instruments. A head that re-priced two of its own rows to fit the heading they sit under would be inventing a finding on the one page whose job is to refuse exactly that, and the invention would be the more tempting for producing a rounder number.

The £78.00 is worth printing all the same, because the two bookings answer two different questions and a reader may want the second one. £69.94 is what these eight counts are worth on the terms they publish, with two of them standing on a lawful ceiling. £78.00 is what eight counts of this size would be worth if every one of them published what six of them do. The gap between the two bookings is £8.06, and £8.06 is four tenths of the £20.16 of balance those two counts hand back, which is precisely the bite a ceiling takes when a term is absent from the page rather than absent from the offer.

Said as a ratio rather than as a sum: £69.94 is 89.7 per cent of the £78.00 of face, where the six unconditional rows alone come to 100 per cent of theirs. A reader looking for the single number this heading supplies and the rest of the domain cannot should take that one, because it is the price of publishing a term rather than of asking one.

4

A rate is not a sum, and the one row standing outside the closing figure

The ninth guide reports a count of rounds arriving each day, and its finding is 31 pence a day. The row keeps its place on the board, is set back off the measure, and is outside the £69.94, and the reason is arithmetical rather than editorial.

Worked at this heading’s own stake, five rounds a day carry 50 pence of face, hand back 48 pence of balance, and come out of a ceiling of ten times at 29 pence. Five rounds funded by the reader instead cost two pence a day. So the distance is 31 pence a day, and every quantity in that sentence has the words a day attached to it and cannot be separated from them.

To turn 31 pence a day into a sum of money the arithmetic wants one further quantity, the number of days the thing runs, and no offer of this shape publishes one. There is no usual figure for it either, and a usual figure would be this publisher’s invention rather than a measurement. So the quantity is named as missing and the row is left as a rate, which is a complete and checkable finding about a day and no finding whatever about a year.

Adding it anyway would do visible damage. Dropped into the money column the 31 pence would read as 31 pence once, which understates a daily offer that runs for a month and overstates one withdrawn tomorrow, and in both cases it would produce a closing figure standing for nothing. Dropped into the rounds column, five rounds a day would sit beside 699.4 rounds of distance as though the two were the same kind of thing. A board that added either would have printed a total nobody could rebuild, which is the one thing a closing figure on this domain must never be.

So the closing sentence under the board says eight rows were added and one was left outside, and says why in the same breath. That is the whole of the mechanism: the figure names its own scope, and a reader can check the scope against the nine rows above it without working any of the arithmetic again.

5

How the £69.94 was added, and which eight rows went into it

Each of the eight findings in the closing figure was taken off the guide that reported it, at the figure that guide’s own instrument closes on, and added without being rounded first. Six of them are £5.00, £7.00, £3.00, £12.00, £10.00 and £20.00, which is £57.00. Two of them are 62p and £12.32, which is £12.94. Added, £69.94.

The same closing figure comes out of the columns as well as out of the rows, which is what makes it checkable twice over. £78.00 of face across 780 rounds hands back £74.88 at the return assumed here. The ceiling takes £8.06, and it takes it off two rows and not off eight, so the free column closes at £66.82. The paid column is four pence in each pound of £78.00, which is £3.12. £66.82 beside £3.12 is £69.94, and that is the second road to the same answer.

One row is shown to the nearest penny and it does not move the total. A distance of 61.6 pence stands on its own guide as 62p, so the exact arithmetic across the eight gives £69.936 and the printed arithmetic gives £69.94. Those are the same figure to the penny this domain prints in, and the rounding is reported here rather than left for a reader to find in a column that would not quite add.

Nothing else stands outside the £69.94 and nothing is waiting to be filled in. All nine guides under this heading have reported, so the board carries no row saying a finding is not in yet, and the only row outside the addition is the rate dealt with in part four.

£78.00 of face across eight reported findings, worth £66.82 on the booking taken here and costing £3.12 funded by the reader, so £69.94 of distance and 699.4 rounds in hand

6

The one heading on this domain where the second unit adds, at 699.4 rounds

Every finding across this domain is given in two units, money and a count of rounds, because a reader parts with one and plays in the other. On most of this domain the second saying is a per-row statement and nothing more, since the counts on one board were divided by several different stakes and will not add. This heading is the exception, and the exception is worth printing because it is the only one.

All eight added rows here are worked at ten pence a round. One stake produced all eight counts, so the eight counts of distance are the same kind of quantity and the column adds: 50, 70, 30, 120, 100, 200, 6.2 and 123.2 rounds come to 699.4 rounds, and 699.4 rounds at ten pence is £69.94. Both are printed because a reader who cannot picture £69.94 can picture seven hundred rounds.

The count is also the more durable of the two. Shift the stake and every sum on this page shifts with it, while the count of rounds in the distance holds still on the six unconditional rows. Fifty rounds of distance stays fifty rounds of distance however much a round stakes, the distance there being a face value and a face value being a count at a stake. On the two rows standing on the ceiling the count does move, 6.2 rounds and 123.2 rounds being six tenths of a balance plus a margin rather than a whole face, and that difference between the two kinds of row is visible in the figures without any working.

Two cautions. A stake is frequently the offer’s choice and not the reader’s, so the sums above show how far the money depends on a figure the offer may have settled instead. And 699.4 rounds is a distance rather than a quantity of play: it is how many more rounds a reader holds by being given these counts instead of buying them, not a number of rounds anybody has to play through.

7

What still stands between £66.82 and a bank once nothing is owed

The whole claim of this heading is that £66.82 is spendable rather than held behind a condition, so the things that can still stand in front of it deserve naming as plainly as the figure does. A staking term is gone on six rows and capped on two. What is not gone is everything that happens at the cashier’s end when a reader asks for the money.

Three of those belong to a British licence and to nothing an offer of this kind is bound by, which is the point of listing them.

That last point is the sharpest thing this heading has to say about itself. A count of ten rounds reports 62p of distance, and a payout floor of ten pounds over a balance of 58p holds the whole of it in place indefinitely. The term that was absent cost nothing and the floor that was present costs everything, so a reader comparing two counts on their staking terms alone is comparing them on the condition that happens to be published.

Nothing in this part describes a way round anything, and there is nothing to describe. The statement is what is lost: four duties that a licensed cashier owes and an unlicensed one does not, priced against the figures this heading has already worked out.

8

Why the stake moves all of the £69.94 and the return only £12.94 of it

Two assumptions carry this heading, the ten pence a round and the 96 per cent, and they behave quite differently. The stake is a straight multiplier on everything. Halve every stake and the eight rows close at £34.97; double every stake and they close at £139.87. The count of rounds in the distance is untouched by either, staying at 699.4.

The return behaves differently, and on four fifths of this closing figure it does not behave at all. On the six rows where nothing is asked the return cancels exactly, paying the free side and charging the paid side in equal measure, so £57.00 of the £69.94 is six face values with no return inside them. That is 81.5 per cent of the total. The return survives only on the two rows standing on a ceiling, where the free column is a fraction of a balance the return itself produced.

Worked on those two: at 94 per cent the bracket shuts at four tenths instead of six, so the pair stand £9.16 apart and the eight close at £66.16. At 97 per cent it shuts at seven tenths, the pair stand £14.89 apart and the eight close at £71.89. The return moves those two rows twice over, once as the balance they hand back and once inside the bracket, and both movements run the same way, so a better return widens them. A three point swing therefore moves the closing figure by £5.73, all of it inside £12.94 of the £69.94 and none of it inside the other £57.00.

That immovable column is why these nine keys are read as the control for the other seventy-six. Everywhere else a free round is worth a part of its face, the part turns on a term somebody chose and a return nobody prints, and comparing two counts means comparing two assumptions. Here, on six rows out of nine, neither assumption is needed: a count with nothing asked of it hands over its own face value, whatever a round stakes and whatever a machine gives back.