Nothing asked of two hundred turns, and the hours that ask it anyway

1

Two hundred turns at a twelve pence floor

The reel weighed here is Bigger Bass Bonanza, and the first thing to settle about it is not its return but the price of entry. Its own session response runs the coin steps across twelve lines rather than ten lines and coin steps, off that response, so the cheapest turn it will sell is 12p and not the 10p most of the family starts at. This card therefore spends 12p a turn supposed, at that title’s own floor, and says so again in each later sentence that spends it, because a worked example resting on a turn the machine does not offer is pricing a purchase nobody can make.

Two hundred turns at that price put £24.00 across the reel. None of the £24.00 is the reader’s: it is the grant, and what comes back out of it is what the arrangement is about. Against the 96.71 per cent printed for this title, the expected sum coming back is £23.21, and the 79 pence between £24.00 and £23.21 is the reel’s share, taken before any condition has been written, read or argued about.

That 79 pence is worth looking at once, because it is the only subtraction this arrangement performs on its own. Every other figure below is the same subtraction repeated on a larger turnover, which is the whole of what a play-through is and the whole of what carrying on at the machine is. A reader who understands the 79 pence needs nothing else explained.

The second row shows what the first one is a choice inside, and it is also where this card says what it cannot do. Between those two ends the sheet gives this title no list of steps and no default either, so a price quoted anywhere in the middle would be a turn nobody here can show the reel sells. A licensed cycle is capped at £5.00, which sits inside the range as money without having to be a step of it, since £5.00 across twelve lines is not a coin value anybody has published. So everything below is worked at the foot, which is confirmed, and the head is printed to show how wide a choice the offer never mentions really is.

2

The close when nothing is asked, which is the whole of it

The house expectation on this site is E = B × (1 − W × (1 − RTP) ∕ g), and the plainest way to meet it is on a card where one of its letters is nought. W here is nought, the grant asking no play-through at all. B is the £23.21 those two hundred turns should produce and not the £24.00 they put across the reel, which is where a spins headline most often misleads itself. RTP is the maker’s 96.71 per cent for this title, and g, the weight a slot is granted towards a requirement, never gets to do anything on this card, there being no requirement for it to weigh a term of the grant, not of the reel.

With W at nought the bracket collapses to one and the close is B. So £23.21 is the expected close of this arrangement, and it is the largest close any grant of two hundred turns at 12p can have, since every condition anybody could attach can only subtract. That is the sentence the headline is selling, and it is true.

It is also the end of what the offer contributes. Once the multiple is gone the only figures left in the arithmetic belong to the reel, and the family does not hold them still. Two titles are sold from twelve pence rather than ten, because both run their coin steps across twelve lines, and the returns their maker prints for the pair are not the same figure.

Fifteen pence, on a grant of two hundred turns, is what the whole published distance between the two twelve-line titles is worth while nothing is asked. That is the point of putting the table here rather than later: with no multiple in the arithmetic the return is applied exactly once, so the family’s spread arrives at the reader divided by nothing. The break-even column is where the two figures stop being near neighbours, and what lives in that gap is the subject of everything below.

3

One toll charged two ways, by the clause and by the turn

A play-through and a decision to carry on are the same transaction wearing two different labels. Both put money across a reel returning less than the whole, and 3.29 points of anything crossing it stays behind. The difference is only who wrote the sentence: a clause says how much turnover has to happen, and a reader staying at the machine supplies turnover without being asked.

Price them both and the identity is exact. A ten-times clause on this grant would require £232.10 of turnover, which costs £7.64 at 3.29 points and would leave £15.57 of the £23.21 standing. Now take the same reel with no clause on it: one turn at 12p costs a hair under four tenths of a penny in expectation, being twelve pence times the reel’s share. Divide £7.64 by that and the answer is 1,934 turns. A reader who played 1,934 turns of their own accord, with nothing obliging them to, has paid what the clause would have charged, to the penny.

Two things about that figure are worth more than the figure. The first is that the price of a turn drops out of it. The clause’s cost rises with the stake because the turnover does, and the cost of one unforced turn rises with the stake by exactly the same factor, so the two cancel: the count is 1,934 at 12p, 1,934 at the top end of the range this title publishes, and 1,934 at every price the reel sells in between. The second is that the reel’s own share drops out too. It appears once in the clause’s bill and once in the per-turn bill, and the division removes it. What is left is a count of turns multiplied by a published return multiplied by a multiple, and nothing else at all.

1,934 turns of play nobody asked for cost what a ten-times clause would have cost on this grant, and the figure does not move when the price of a turn moves

4

The absent clause, priced in turns instead of pounds

Section three settles the method, so the rest is arithmetic. The count of unforced turns that costs what a clause of W times would cost is the granted count times the published return times W. On two hundred turns at 96.71 per cent that comes to 193.42 turns for every single time the clause asks, which is the most portable small figure on this card: each extra multiple a cashier might have written is worth a hundred and ninety-three turns of staying put, give or take a third of one.

The third row is the one that shows why the deletion matters at all. Forty times would take £30.54 out of a grant holding £23.21, so the close would be a cost of £7.33 and the reader would be finishing the condition with their own money. The grant cannot pay that bill, which is why a large multiple is not a smaller gift but an arrangement of another kind altogether. Deleting the multiple removes that, and removes it completely.

What the deletion does not remove is the reel. Read down the fourth column instead of the third and the three clauses become one hour twenty, two hours forty-one and five hours twenty-two of ordinary play at the fastest a licensed build may be driven. A reader who takes the grant, keeps the £23.21 and then spends an afternoon at the same title has handed back what the harshest of the three clauses would have taken, with nobody having written a word of it down.

5

Where the whole grant goes, and why it is break-even in disguise

Carry the column one step further and it arrives somewhere exact. Keep adding unforced turns and the expected close falls by four tenths of a penny each time until there is nothing left to fall, and the turn on which it runs out is turn 5,879. That is a little under four hours and five minutes of unbroken play, measured at the pace ceiling a licence imposes, starting from the moment the grant finished.

5,879 is not an arbitrary number. The count of unforced turns is the granted count times the return times the multiple, so setting the whole grant as the bill means setting the multiple to the one value that empties it, and that value is the reciprocal of the reel’s share. It is the break-even play-through, 30.4 times on this title, which the returns table above has been carrying since entry two. Two hundred turns times 96.71 per cent times 30.4 is 5,879.

So break-even, which every other card on this domain meets as a multiple a cashier might write, turns up here as a length of play. On a grant with no clause on it the break-even figure has not stopped being relevant: it has changed units. It is the number of turns after which an unconditional grant has been given back, and on the lower of the two twelve-line titles it is 4,902 turns rather than 5,879, because a bigger share per turn empties the same grant sooner.

That is the answer to the ground this card stands on. Every condition has been removed and the outcome is still not good, and the reason is not that the arithmetic is hiding anything. The arithmetic is as good as it gets: £23.21 out of £24.00, nothing asked, nothing capped. The outcome is not good because what the clause used to supply, besides a bill, was a moment at which the arrangement was over. Delete it and the arrangement has no end written into it anywhere, and the reel charges four tenths of a penny a turn for however long that takes.

6

Eight minutes to hand over, four hours to undo

Both of the clocks on this card come from the same rule and run in opposite directions. A licensed build holds 2.5 seconds under the interval from one cycle to the next, wants its own fresh press for each of them, and may not play itself the pace floor, RTS 14D. Two hundred turns therefore cannot be used in less than 500 seconds, so the advertised part of this arrangement is eight minutes and twenty seconds long at the outside pace.

The same floor caps an hour at 1,440 turns, and 1,440 turns at 12p is £172.80 of turnover, on which the reel’s expected share is £5.69. So an hour of unforced play at this title and this price costs £5.69 of a grant worth £23.21, which is a shade under a quarter of it an hour. Four hours and five minutes is the whole of it, as entry five works out, and the ratio between the two clocks is the finding: the thing being advertised takes eight minutes to deliver and a little over four hours to cancel.

Neither clock is a prediction about a reader. They are both ceilings on pace, which is the useful direction for a bound to run in: a reader who plays more slowly has a longer session and identical arithmetic, and a reader who wants the four hours over faster is not permitted to have that on a licensed build. No reel has been played by anybody here and not one figure rests on watching one.

7

What the ten pounds is doing, and what it is not

The payment is a qualifying condition rather than a price, and the distinction decides where it is allowed to appear. Ten pounds handed to a cashier is still the reader’s ten pounds: it can be staked, and on a licensed site it can be taken back out without a cap on the amount. So it does not belong in the product column of this card, and what does belong there is the only part of it the reel touches.

At 12p a turn, ten pounds buys 83 whole turns and leaves fourpence standing under the price of one, which the arithmetic simply cannot spend. Eighty-three turns put £9.96 across the reel, and at 96.71 per cent they are expected to hand back £9.63, so one pass of the payment through this title is expected to cost 33 pence. That 33 pence is the payment’s real contribution to the weighing, and it is about one part in seventy of what the grant hands over.

Two ratios follow and both are worth keeping. The arrangement sells twenty turns for every pound of payment, which is a number a reader can carry to any offer of this shape and test. And the grant’s expected yield is £2.32 for every pound paid in, which is the figure that makes an unconditional grant attractive and which is perfectly real. What it is not is durable: it is £2.32 a pound at the instant the two hundredth turn ends, £1.75 a pound an hour later and nothing at all after four hours and five minutes, with nobody having broken a promise anywhere along the way.

There is one quantity left that no sum on this card can reach, and the honest thing is to name it rather than to fill it. How widely the outcome of two hundred turns is spread about the expected £23.21 is a property of this reel, and no spread is published for any title in the family. What is published is the ceiling: 4,000 times the stake on this title the win limit, off the session data, which at 12p is £480.00, or 20.7 times what the whole grant is expected to yield. A single turn that can be worth twenty grants is the shape of the answer, and the frequency that would turn that shape into a figure is not something the maker states for this title.

8

What an unconditional grant is actually selling

Collect it. Two hundred turns at the twelve pence this title is sold from commit £24.00 and are expected to return £23.21. Nothing is asked of the £23.21, so £23.21 is the close, and it is the best close a count of that size can have. The qualifying ten pounds is expected to cost 33 pence on one pass of the same reel. Run the identical grant on the other twelve-line title, published 0.63 of a point lower, and the close is £23.06, so the choice between the two is worth fifteen pence. Eight minutes and twenty seconds uses the grant up; four hours and five minutes of play nobody asked for hands the expected close back.

So what is being sold is two hundred turns and a decision. The turns are worth what the arithmetic says and the decision is worth whatever a reader’s own stopping point is worth, and the second of those is the larger figure by some distance. A clause asking ten times would have taken £7.64; an hour and twenty minutes of carrying on takes the same £7.64. A clause asking forty times would have taken more than the grant holds; five hours and twenty-two minutes of carrying on takes the same. The offer has deleted the bill and left the price list in place.

None of that makes the deletion worthless, and the arithmetic will not support saying so. A multiple is compulsory and an afternoon is not, and that difference is real money to a reader who leaves. What the arithmetic will support is the narrower claim, which is that the deleted condition is the only part of this arrangement a reader cannot choose, and everything it used to decide is now theirs to decide instead, at the same rates. The reel’s share does not know whether a turn was required or merely available.

And one figure has not appeared anywhere above, deliberately. Nothing here states the chance of the feature round turning up across two hundred turns, since no arrival rate for it stands on the maker’s pages or in a session’s own data, and the two figures in circulation on review sites disagree with one another. The identity in entry three was built so that it needs no such figure: a count of turns, a published return and a multiple are the whole of it. A card about how long a balance lasts can be written without the rate, and this one is.