Free daily spins: ten turns a day, against three hundred in one sitting

1

Three hundred turns, priced twice over by one published figure

A grant of turns is not a grant of money, and the difference shows up as the reel’s published return being applied twice rather than once. First the turns themselves have to cross the reel. Ten turns a day for thirty days is 300 turns, and 300 turns at the 10p this card supposes the foot of the published range, supposed here and promised by nobody puts £30.00 of stake across the machine. At 96.71 per cent the expected sum coming back out is £29.01, and that is the first and only moment the reader has anything at all: the £30.00 was never theirs to lose.

Then the condition arrives, and it is written against the £29.01 rather than against the £30.00. Thirty times £29.01 is £870.30 of staking to be done before anything may leave, and the reel charges 3.29 points on staking the complement of the maker’s own figure. Three point two nine points of £870.30 is £28.63 of expected toll, so of the £29.01 the turns were expected to produce, £0.38 is expected to survive. One published figure, used twice, is the whole of the arithmetic.

Written as one line, with g standing for whatever weight an offer gives a named slot against its own requirement:

E = B × (1 − W × (1 − RTP) ∕ g)

On this card B is the £29.01 the turns are expected to yield rather than the £30.00 of stake they consume, which is the one substitution a grant of turns forces on the line; W is thirty; RTP carries the maker’s figure of 96.71 per cent; and the weighting g stands at one, a weighting being something an offer does to a game and not a quantity the game sheet holds any view about a term of the grant, not a figure of the reel. Put those in and the answer is 38p, which on a three-hundred-turn headline is an eighth of a penny a turn.

The two rows carry the identical grant and the identical condition, and £5.57 separates them. Section eight is about why the gap is so large for so small a difference of return, and the short answer is that thirty times happens to fall between the two break-evens.

2

Twelve minutes of grant against six hours of condition

Turn both halves of the arrangement into time and the shape of it becomes plain. A licensed build has to leave a gap of 2.5 seconds between one cycle opening and the next the pace floor written for a reel, so no hour will hold more than 1,440 turns. The grant is 300 turns, which is twelve minutes and thirty seconds at that floor. The condition is £870.30 of staking, which at 10p a turn is 8,703 turns, and 8,703 turns is six hours and three minutes to the nearest minute.

So the advertised thing takes a quarter of an hour to use and the thing attached to it takes a working day’s morning. That ratio is not a feature of the terms; it falls out of the two figures multiplied together, and it would be the same ratio at any turn price, since both sides of it are counted in turns. What the turn price decides is how much money crosses the reel while those six hours pass: £870.30 at 10p, and twenty times that at £2.00 a turn, with the close moving in exactly the same proportion.

One more conversion is worth having before the rest of the card. A day of the grant is ten turns, which is twenty-five seconds. Thirty such days amount to twelve and a half minutes of play distributed over a month, and a reader who opens an account, signs in and finds the grant waiting has spent longer doing that than playing. Nothing on this site has measured how long signing in takes, and nothing here supposes a figure for it; the point is only that the published pace floor makes a ten-turn day a twenty-five second event, and no arrangement of the terms can make it longer.

3

Why instalments and a lump close on the same penny

Expectation adds. Three hundred turns have an expected yield of 300 multiplied by the turn price multiplied by 96.71 per cent, and multiplication does not care in what order or on what days the three hundred happen. Ten lots of thirty turns, thirty lots of ten, sixty lots of five and one lot of three hundred all come to £29.01 at the turn price this card supposes, and the condition written against that sum takes the same £28.63 of expected toll in every case. There is no arrangement of a calendar that makes the mean move.

That is worth stating flatly because the opposite is widely believed, and the belief has a reasonable-sounding basis: a run spread over a month feels as though it must be safer, and a reader who has watched a single sitting disappear in twelve minutes will say so. The feeling is about dispersion and it is not wrong about dispersion. It is wrong about the mean, and the two get confused because nobody prints either.

Read the closing row as a bill rather than as a benefit. Spreading the count buys twenty-nine extra occasions and twenty-nine extra days, takes twelve minutes and five seconds of play away from each of them, and leaves the close reading no change. Occasions and days are real quantities and a reader may genuinely want both. Neither of them is money, and the money is the column that refused to budge.

4

What spreading the count leaves exactly as it was

Whatever one round of this reel may hand over at once is capped at 2,100 stakes the win limit the session data carries, and the game times that one outcome and nothing else: it lands on average once every 3,880,481 turns. At the 10p this card supposes, the cap is £210.00, and that figure is the same on the thirtieth day of a run as it is in the ninth minute of a sitting, because it depends on the turn price alone.

So does the chance of meeting it. A grant of 300 turns is 300 draws against a rate of one in 3,880,481, however those draws are spaced, which means roughly 12,935 readers would have to take the same grant on the same reel for one of them to see the limit land while using it. Spacing the draws across a month does not add a draw and does not shorten the rate. A reader who believes a daily run gives the big outcome more chances to appear has confused the number of occasions with the number of turns, and only the turns are counted.

What the ceiling contributes to the published return can be priced as well, and that figure is the one to carry away from this section. A cap of 2,100 stakes arriving once every 3,880,481 turns contributes a little over half of one stake per thousand turns, which at 10p across 300 turns comes to £0.02. Of the £29.01 the grant is expected to yield, in other words, two pence is the win limit and £28.99 is everything else. The outcome that makes the reel worth advertising accounts for about one part in eighteen hundred of what it is expected to pay.

That is how dispersion gets handled here, and the reason for taking that route rather than a shorter one is worth putting on the page. No volatility figure is published for any of the thirty-six titles the maker lists: not one of its game pages uses the word, and the data a game hands its client has nowhere to put such a thing, so nobody has published the quantity a reader most wants here and this card states none. What is published is the paytable, the win limit and the rate above, and those three are enough to show the shape without naming it. The top paying row of the paytable runs 2000, 200, 50 and 5 against five, four, three and two of its own symbol, which is four hundred to one inside a single row. A machine whose own paytable spreads four hundred to one, and whose round may reach 2,100 stakes at a rate of one in 3,880,481 turns, is a machine where almost every reader finishes below the mean. The mean is £29.01. Almost nobody gets £29.01.

5

What spreading the count changes, which is survival

Here is what the instalments genuinely buy, stated as the quantity they buy rather than as a feeling. A balance that is refilled every morning cannot run out while the run lasts. Ten turns a day for thirty days guarantees thirty occasions on which there is something to play with, whatever happened on the twenty-nine before, because the next morning’s ten turns do not depend on the last morning’s result. A single sitting of 300 turns guarantees exactly one occasion, and if it goes badly it is over in twelve and a half minutes. Survival time is the one column in section three that the instalments move, and it is the only thing a reader is actually choosing between.

Put a clock on it and the scale of the choice appears. Reaching a single hour of play on a ten-turn daily grant takes 144 days, because an hour is 1,440 turns at the published floor and ten a day divides into it 144 times. Reaching the 3,880,481 turns the win limit is timed at takes 388,048 days of a ten-turn grant, which is past a thousand years. The same 3,880,481 turns are 12,935 sittings of three hundred. Neither route gets anybody there. What separates them is that one takes a month to fail and the other takes a quarter of an hour.

£870.30 of staking asked of a grant advertised as three hundred free turns, which is 8,703 turns at the 10p a turn this card supposes, or six hours of play at the floor under a turn’s length

There is a second thing the spacing changes and it runs the other way. Thirty occasions are thirty separate decisions to sign in, and the condition does not pause between them. A reader clearing £870.30 of staking at 10p a turn has 8,703 turns of work to do, and ten turns a day contributes ten turns a day to it: on the arithmetic of the grant alone, the staking cannot be discharged inside the month at all, and a reader who intends to clear it will be buying turns with their own money while the free ones trickle in. That is not a criticism of any particular terms. It is a consequence of a grant of 300 turns carrying a condition of 8,703, and the ratio between those two counts is 29 to one, which is the thirty times less the reel’s own retention.

So the two deliveries are not two prices for one thing. They are two different things at one price. The lump is a short, high-variance event with a long obligation attached. The instalments are a month of short events with the identical obligation attached, and the obligation is the part nobody advertises in turns.

6

One day of the run, priced on its own

Divide the whole arrangement by thirty and the daily unit comes out. Ten turns at the 10p this card supposes is £1.00 of stake, and £1.00 at 96.71 per cent yields an expected £0.97. That £0.97 then carries thirty times itself in staking, £29.01, on which the reel’s 3.29 points take £0.95, and what survives one day is one and three tenths of a penny. The staking on one day and the expected yield of the whole month are the same £29.01, which is not a coincidence worth reading anything into: the month is thirty days of ten turns and the multiple happens to be thirty as well. Thirty such days come to the 38p on the card at the head of this page, which is the arithmetic closing on itself.

1.3p of expected close in one day of a ten-turn grant at the 10p a turn this card supposes, which is what an unbroken run of visits is worth for a day of it

One and three tenths of a penny is the figure a reader should have before deciding how much a streak is worth protecting. A daily grant is built to make an unbroken run feel valuable, and the mechanism for that is usually a window: the turns land, they are good for that day, and a day missed is a day gone. Suppose a window of exactly one day, supposed here by this card alone and chosen because it is the commonest shape a recurring grant takes. A reader who misses a day has given up 1.3p of expected close. A reader who misses ten days of a thirty-day run has given up 13p. A reader who misses the whole month has given up 38p, which is the entire value of the arrangement and is less than the cost of four turns at the turn price this card has been spending.

Set that beside what the reel is doing while the run lasts. Each day’s ten turns put £1.00 across the machine, so thirty days put £30.00 across it, and the staking on the winnings adds £870.30 more. The reader’s expected keep from all of that is 38p. The expected retention of the reel across the same traffic is £28.63 on the staking plus £0.99 on the turns themselves, and a reader who wants the single number for what the month is worth to the machine rather than to them can have £29.62 of expected retention against 38p of expected close.

None of that makes the run a bad use of a morning or a good one, and this card has nothing to say about how anybody should spend a month. What it has to say is that the figure a daily grant trains a reader to protect, the unbroken sequence of visits, is worth a penny and three tenths a day once the reel and the condition have both had their turn at it, and that nobody anywhere publishes that figure. It takes a published return, a published pace floor and two suppositions stated in the open to get at it, and the answer is small enough to be worth having before the first morning rather than after the thirtieth.

7

The feature round is larger than the daily allowance

The reel’s own feature round opens on a count of scatters, three, four or five, and the award set against them is ten turns, fifteen turns or twenty a map both primary sources carry identically. Hold that against the grant. The smallest award the round makes is ten turns, which is an entire day of a ten-turn allowance, and the largest is twenty, which is two days of it. A single event inside the machine therefore hands over as much as the offer hands over in a day or two, and the offer’s daily unit is smaller than the machine’s own smallest extra.

The round can also extend itself, and the extension is bigger again. A retrigger comes on every fourth wild and adds ten turns, and the multiplier climbs 2x on the first retrigger, 3x on the second and 10x on the third. Count that out: the top rung is the third retrigger, which is the twelfth wild, by which point the round has been handed thirty extra turns on top of whatever it opened with. A round that has reached the 10x rung has therefore run for at least forty turns, which is four days of the grant, and no ten-turn day can contain one. What the 10x multiplies is not stated by the maker for this title: its page gives the ladder without saying what the ladder applies to, and it names the object only in its description of a different title in the family, so this card does not carry that description across.

The frequency of the trigger is the figure a reader would want next, and it is not published. Neither the maker’s page nor the data the game hands its client states how often three scatters land, and the only hit rate in that data is the one for the win limit. Two figures for it circulate on review sites, they disagree with one another by more than half as much again, and the game’s own data carries neither, so no figure for it appears on this card. What can be said without one is the part that matters here: a ten-turn day is a very small sample of anything, and a round whose own award is ten to twenty turns cannot be fitted into it without spilling over into turns the grant did not give.

That spill is the dispersion of a daily grant stated properly. The distribution of a ten-turn day is almost entirely nothing, with a thin tail where a round opens and the day is suddenly worth several days. A reader meeting thirty such days in a row meets mostly nothing and occasionally a day that behaves like a week. The mean of all thirty is 97p of yield a day, and the median day, with no round in it, returns a good deal less than the mean. That gap is a property of the machine and not of the offer, and the offer cannot narrow it: the paytable, the win limit and the trigger map belong to the reel, and a calendar laid over them changes when they happen rather than how widely they are spread.

8

Thirty times falls between two of the family’s break-evens

Break-even is the house edge inverted, so it travels with the published return, and the family publishes a dozen different returns across its titles. On the original, 3.29 points of edge inverts to 30.4 times. Where the printed figure is 96.07 per cent, which covers nine titles, 3.93 points inverts to 25.4 instead. The condition this card has priced is thirty times, which sits inside the first and outside the second, and that single accident is why £5.57 separates the two rows in section one.

It is worth being precise about how unusual that is. A condition of ten times is inside break-even on every title the maker publishes, so the choice of title changes the close but never its sign. A condition of forty times is outside break-even on every one of them, so again the sign is fixed and only the size of the loss moves. Thirty times is in the narrow band where the sign itself depends on which name a reader picked off a lobby tile, and the band is less than five times wide. A recurring grant asking around thirty times is therefore the one shape of offer on this site where the title does not merely cost a reader money: it decides whether the arrangement has any value at all.

The spread itself is small and wholly published. Out of thirty-six game pages the maker lists, six print 96.71 per cent. Nine titles are printed at 96.07, a gap of 0.64 points. Eleven are at 96.50, where break-even is 28.6 times and thirty is just outside it, closing at minus £1.45 on the same grant. So the same recurring offer, word for word, closes at 38p, at minus £1.45 or at minus £5.19 depending on nothing but which title of one family it is spent on, and the offer itself has no opinion on that because an offer is written about an account.

There is a second axis along which a published return genuinely moves, and it is not this one. The data most titles hand their clients carries a separate return for each bet mode, regular play against ante-bet play against each bonus-buy level, and those figures are primary and may be used freely. They are also a few hundredths of a point apart within any one title, which is a tenth of the gap that matters here, so a bet mode is the wrong place to look for anything a recurring grant would notice. A bet mode is a choice the reader makes at the machine. The title is a choice the reader makes in a lobby. Neither of them is anybody else’s choice about the machine, and the trade’s claim that a choice of returns is on offer to whoever installs a title has no primary source at all behind it: each of the thirty-six pages prints one figure, not one of them says that figure can vary, and what is left is affiliate reviews contradicting each other. This card prints no figure from that claim and works every close at the published one.

9

What a recurring grant is actually buying

Collect the figures. Three hundred turns at 10p put £30.00 across the reel and are expected to yield £29.01. Thirty times that yield is £870.30 of staking, costing £28.63 in expected retention and leaving £0.38. A day of the run is worth a penny and three tenths of that. The grant takes twelve minutes and thirty seconds of play to use and the condition takes six hours and three minutes to discharge. The win limit is £210.00 at that turn price, arrives on average once every 3,880,481 turns, and accounts for two pence of the £29.01. Inside the British licence the condition could only have asked ten times, closing at £19.47, so the licence is worth £19.09 here.

Set against a single sitting of the same 300 turns, the recurring version buys twenty-nine extra occasions and twenty-nine extra days, and buys nothing else. Not a better return, not a longer tail, not a cheaper condition, not a greater chance of the win limit, not a penny of close. A reader who wants a month of short sessions rather than a quarter of an hour of a long one is being offered exactly that and is paying nothing extra for it, which is a genuine thing to want and is not what the headline count is advertising.

And a reader who wants the money should look at the two figures the arrangement does not print side by side: 300 turns given, 8,703 turns required. Those two counts are the offer, and everything else on it is presentation. The reel supplies the 96.71 per cent that converts between them, the pace floor that turns both into hours, the 2,100 stakes that cap a single round and the one in 3,880,481 that times it. The grant supplies a count and a multiple. Where the two sets of figures meet is where this card has been working, and what it found is that the calendar is free and the condition is not.

None of the above describes any particular place of play. A condition of thirty times is more than treble the ceiling a British licence puts on bonus funds, so a cashier writing one is by definition a cashier outside the Great Britain licence, and the duties listed in section two depart along with it: the ten-times ceiling, the rule against pressing a reader into a settled rhythm, the rule against working on somebody who has said they are finished, the £5 and £2 caps on what a cycle may take, the gap required between one cycle and the next, and a listing in the national self-exclusion scheme. The reel is identical either way. The reel is the only part of this that is.

Which leaves one sentence worth more than any of the figures above it. A recurring grant is the only shape of offer on this card whose advertised quantity is a unit of time rather than a unit of money: thirty days is the thing being handed over, and the three hundred turns are how the thirty days are filled. Price the days and the arrangement is honest enough, at a penny and three tenths of expected close each. Price the turns and the answer is 38p against 8,703 turns of required staking. Both sums are correct, they describe one arrangement, and the headline carries just the first. A reader who wants to know which they are being sold can settle it with a single question, which is whether the grant stops when the month does. If it does, the days were the product. If the staking carries on past the last morning, the turns were.