20 free spins on registration no deposit, and the part of a turn nobody can play

1

The one shape of award that has no remainder in it

Twenty is a whole number and it stays whole whatever happens next. That looks like a small observation and it is the hinge of this card, because almost nothing else in the transaction behaves that way. A reel sells a turn entire. It will not sell three-quarters of one, it will not carry a balance forward into a fraction, and it will not let a sum of money that falls short of one stake buy anything at all. So every point where money has to become turns, or turns have to become money, is a division, and divisions leave remainders.

A cashier that writes a count into an award has stepped round the first of those divisions. Twenty turns are twenty turns at any price on the ladder, and nobody has to work out whether the sum behind them goes in evenly. Write the same award as a credit instead, two pounds of free play rather than twenty free turns, and the question appears immediately: two pounds buys twenty turns at ten pence and sixteen turns at twelve, with eight pence left that cannot be spent on a seventeenth.

This card follows the remainder through three places it turns up. One is that first division, which an award quoted as a count avoids and an award quoted as a credit does not. One is the foot of a balance during play, where a sum smaller than a stake is money a reader holds and cannot use. One is the top of a play-through, where a required turnover rarely lands on a whole number of turns either. Two of the three cost a reader something measurable. The third turns out to be genuinely negligible, and sorting the one from the others is the work here, since the trade calls all three noise and the name fits exactly one.

The award weighed here is twenty turns for registering, nothing paid in, with the winnings carrying twenty-five times before they can be taken out a count and a multiple this card takes as typical rather than reading anywhere. What registering costs in the first place is a separate question with its own answer, and the card at 25 free spins on registration no deposit solves it; nothing here re-prices it.

2

Three floors in one family, and what a credit divides into

The divisor in all of this is the price of one turn, and the machine publishes it as a ladder. Twenty-eight coin values are on offer for Big Bass Bonanza, each one carried over ten paylines, so that a round is priced at 0.10 at the cheapest, 250.00 at the dearest and 2.00 when a session opens game data, claim 25. Only the bottom of that is for sale to a British reader, the regulations SI 2025 No. 215, regulation 5(2) holding one round to £5 and to £2 again for a player under twenty-five.

The family does not have one ladder, which is what makes the division interesting rather than arithmetical. Three ladders serve the thirty-five slots in it: a floor of 0.10 on thirty-one of them, 0.12 on the pair laid over twelve lines rather than ten, and 0.20 on the pair of Megaways titles game sheet, claim 75f. Ten and twenty pence go into round sums of money; twelve pence very often does not. The drawing below takes one title off each of the three ladders and divides three credits by each.

Divide each floor by the number of lines it is spread over and the three come out the same. Ten lines at a floor of 0.10, twelve at 0.12, twenty at 0.20: a penny a line in every case this card’s own division of two columns of the sheet’s own table. So the family has one coin step and three ladders, and which ladder a title sits on is settled entirely by how many lines the studio laid across it. That is the whole mechanism behind the remainders on this page. A credit divides into whole turns when the line count divides the credit, and twelve does not divide a round sum of pence as readily as ten or twenty do.

Read the middle column of the drawing against the other two. Two pounds at twelve pence a turn is sixteen whole turns and eight pence that will not stretch to a seventeenth. Five pounds is forty-one turns and the same eight pence. Ten pounds is eighty-three turns and four pence. Nothing is left over on either side of that column at any of the three credits, because ten and twenty both go evenly into a round sum of pence and twelve does not. A reader handed a credit has therefore been handed a different number of whole turns depending on a figure the credit does not name, and has been handed a stranded remainder or no remainder for the same reason.

3

Twenty turns at ten pence, worked from end to end

Take the cheapest rung, which is where this card works ten pence a turn, supposed here and not read off any offer. Twenty turns at that price lay £2.00 of stake over the reel, and a published 96.71 per cent the sheet, claims 20 and 21 hands £1.93 of it back. Seven pence stays with the house. That is the one division on the whole card that comes out exactly, and it does so only because ten pence goes into two pounds twenty times.

Then the requirement. Winnings landing as bonus funds have to be staked twenty-five times over before anything can leave, and what survives is E = B × (1 − W × (1 − RTP) ∕ g). Start from the multiple: W is the twenty-five. Under it, g is what the offer reckons a round of the slot contributes towards clearing, a whole round wherever the terms stay quiet at full value, in the terms. RTP is the published figure of whichever reel the staking is made to cross. And B is the £1.93 the twenty turns are expected to produce in the first place.

Put the four together at this title’s own figure and the award closes at £0.34. Thirty-four pence is three whole turns at the price supposed here, with four pence over, and those four pence are the first of this card’s remainders to appear in the open.

4

A close that will not buy one more turn

Carry the same award on to a second reel and something happens that is worth a table of its own. Big Bass Christmas – Frozen Lake carries 96.07 per cent, sixty-four hundredths of a point beneath the title above it game sheet, claim 74. Its page is also the one page in thirty-six that prints its return without a per cent sign beside it, a formatting slip the sheet records at claim 75k so that nobody mistakes it for a different kind of figure. On a card about figures that will not divide, a figure printed without its unit is at least in keeping.

Three pence. The second row is not a smaller prize of the same kind as the first; it is a sum that cannot be put back into the machine that produced it, because the cheapest round on that reel costs ten pence and three pence will not reach it. An award whose expected close falls under one stake has arrived, in the ordinary case, at a balance that is unplayable on its own terms. Nothing in the table says so, because a table of money cannot: it takes the price of a turn standing beside the money to make the point visible at all.

The reason the second row is so much smaller is the break-even column rather than the return column. One over the house edge puts break-even at 30.4 times on the upper reel and at 25.4 on the lower, and the requirement is twenty-five, which sits comfortably under the first and a fifth of a multiple under the second. A requirement that close to break-even leaves almost nothing however good the return is, and the thirty-one pence between the two rows is what sixty-four hundredths of a point is worth once a multiple has had twenty-five goes at it.

5

The band at the foot of a balance, one stake wide

Now the remainder this card exists to price. Play stops when a balance will no longer buy a round, and a balance will no longer buy a round as soon as it falls under one stake. So there is a band at the bottom of every balance, running from nothing up to a penny short of the price of a turn, inside which money is held and unplayable. At ten pence a turn that band is nine pence wide. At the 2.00 a fresh session opens on it is £1.99 wide. At the £5 a British licensed round is held to it is £4.99, and at the top of the published ladder it is £249.99.

How much of it is actually stranded in a given case depends on where a balance happens to stop, and nothing published says anything about that. This card supposes that no resting point inside the band is favoured over another a supposition about where play ends, made here and sourced nowhere, which puts the stranded amount at about half a stake on average. Five pence, then, at the price this card works at.

Five pence sounds like nothing until it is set against what the award is expected to be worth, which is thirty-four pence. The stranded remainder is about a seventh of the close. And the two move together: the close of a twenty-turn award at twenty-five times is a fixed multiple of whatever one turn costs, and so is half a stake, so the fraction one makes of the other does not shift as a reader moves up the ladder. Take the award to the coin value a fresh session opens at and it closes at £6.87 with the band’s midpoint at £1.00, the same seventh over again to the second decimal place.

There is a sharper version of the same thing wherever a requirement is still running. A sum under one stake cannot be put across the reel, and a sum that cannot be put across the reel contributes nothing towards clearing, so a balance that falls into the band with the requirement unfinished has stopped moving in both senses at once. Seven pence left and twenty-five times still outstanding is not a small setback: it is an arithmetically closed position, in which the money is held, the condition is unmet, and no sequence of further events can change either. Nothing in an offer’s terms describes that state, and nothing has to, because it is a property of a machine that sells whole turns rather than a term anybody wrote.

About a seventh of what a twenty-turn award is expected to be worth sits below the price of one more turn, and the share is identical at every rung of the ladder

That is the finding this card was written to produce, and it is why rounding on a machine is not the kind of rounding that can be waved away. A rounding error shrinks as the quantities grow. This one does not shrink at all, because the thing being rounded to is the same thing every figure on the card is built from. A reader who moves to a dearer turn to make the award worth more has moved the dead band up by exactly the same factor.

6

The remainder at the top of a requirement, which really is noise

The third division runs the other way and deserves the same treatment, if only to show that not every remainder is worth a paragraph. A twenty-five-times requirement on winnings of £1.93 asks for £48.25 of turnover. Turnover is bought a turn at a time, so the question is how many whole turns reach it. At ten pence each the answer is 482 turns and a half, which means 483 turns are needed and the last one carries the balance five pence past the line.

Take it to a reel whose floor does not divide the sum and the overshoot grows a little. At twelve pence a turn, £48.25 of turnover needs 403 rounds rather than the 402 and a tenth the division gives, and 403 rounds stake £48.36, which is eleven pence more than the requirement asked for. Eleven pence of extra staking costs a reader eleven pence multiplied by the house edge, which is about a third of a penny in expectation.

A third of a penny is noise, and it is worth saying so plainly on a card that has just spent three paragraphs refusing to say it about something else. The difference between the two is not size but behaviour. The overshoot at the top is bounded by one stake and then divided by the house edge, so it is a few hundredths of a stake. The stranding at the foot is bounded by one stake and divided by nothing, so it is half a stake. The second is roughly thirty times the first, and it is the one the trade ignores.

7

Which way each of the three roundings runs

Set the three side by side and ask, of each, who gains by the fraction that goes missing. The answers are not the same and the differences are instructive.

The first rounding, a credit divided into whole turns, runs against the reader and in nobody’s favour. The eight pence that will not buy a seventeenth turn at twelve pence is not taken by the house; it simply sits in an account doing nothing. Where the credit carries a play-through it is worse than nothing, because a sum that cannot be staked cannot contribute towards clearing, so a requirement written over the whole credit can be arithmetically impossible to finish. An award quoted as a count of turns, which is the shape on this card, sidesteps the whole of that.

The second, the band at the foot of a balance, runs against the reader and in the house’s favour by default rather than by design. Money a player cannot stake is money the house keeps unless the player withdraws it, and the sums are small enough that a great many readers will not bother. Nothing in the published rules says a cashier must do anything about it, and nothing this site has read suggests a cashier does.

The third, the overshoot at the top of a requirement, runs against the reader in form and is negligible in substance, as entry six worked out. Of the three roundings it is where arithmetic and intuition finish up agreeing.

None of the three is a term anybody writes down. They are consequences of a machine that sells whole turns meeting a cashier that writes round numbers, and the fact that neither party chose them is exactly why nobody prices them. A reader looking for the cost of an award in its terms will not find these, because they are not in the terms and never were.

8

What the rounding comes to once it is added up

Add the measurable pieces at the price this card works at. About five pence stranded below one stake when play ends, on the supposition that no resting point is favoured; about a third of a penny lost to the overshoot at the top of the requirement; and nothing at all from the first division, because twenty is a count and a count has no remainder. Call it five pence and a third, against an expected close of thirty-four pence.

Two things follow and both are worth carrying away. The first is that the figure does not shrink with scale: at the coin value the game opens on, the same three pieces come to about a pound and seven pence against a close of £6.87, which is the same proportion to the penny. Rounding on this machine is a fixed share of the answer rather than a vanishing one, and a page that calls it noise has not divided anything.

The second is that the only way to make it disappear is to choose a stake that divides the balance it will have to be spent from, and no reader can do that, because the balance is unknown in advance and the ladder is the machine’s rather than theirs. A cashier could do it, by quoting an award in turns and settling the price, which is what the better-written awards of this shape already do, and a reason for preferring them that the headline count says nothing about.

So the honest summary of this card is narrow. Twenty turns on registration are worth thirty-four pence at ten pence a turn and three pence on a reel published lower in the family, where three pence will not buy another round. Round numbers of turns behave well and round numbers of money do not, the band at the foot of a balance is the piece worth pricing, and the share it takes is the same whatever one turn costs.