Crypto casino: the unit moves and the price list does not

1

Two currencies, one price list, and the same steps in both

Start with the measurement, because it is the one piece of primary evidence on this subject and it is small enough to state exactly. The figures this site uses for the machine were read out of the response the maker’s own server sends a game client when a session opens. Those taken across the family were opened in pounds. The first reading of the original was opened in dollars. The stake steps that came back were identical in both claim 16, the caution on currency.

That is a narrow finding and it carries further than it looks. So the list of prices the machine offers is a list of numbers rather than a list of sums, and it is not converted at the door: the same twenty-eight coin values appear, multiplied by the same ten lines, giving the same ends at 0.10 and 250.00 whichever currency the session was counted in. A reel asked to price itself in a second unit did not re-price. It printed the same numbers and left somebody else to say what they meant.

The reading came out of the response the maker’s own server sends a game client when a session opens, and the screen a player reads inside the game is drawn from that same response, so the page and the player are looking at one source rather than two the method standing behind anything this card calls the game’s own. That is why a figure of this kind outranks a review of the machine: it is not a description of the build, it is the build’s own account of itself.

It is worth being precise about what a session is, since the whole of this part rests on one. A session is an opening: a client asks the maker’s server for a game, and the server answers with the figures that game will run on. Everything this site states about the machine came out of answers of that kind, and the currency the question was asked in is the only thing that differed between the two readings compared here.

A reader may reasonably ask whether a commercial deployment would answer differently from a free-play one, and the honest answer is that this site does not know and will not guess. What it has is two readings, one in each of two currencies, agreeing on the steps. What it does not have is a reading from anywhere a person could put money, because obtaining one would mean naming a place of play, which this site does not do.

The family makes the point again from a second direction. Most of the slot reels in it take the same cheapest step, three of the twelve-line titles begin a step higher, and the pair built on the Megaways layout begin higher again the stake ranges in the family table, so the price list is not even one list across the family. What all of those lists have in common is that no currency appears in any of them.

Two cautions come attached and both are the sheet’s own. These are the steps a free-play server offers, not a statement that any casino anywhere offers that range, and the top of it is in any case out of reach on a licensed British site, where one cycle is capped. Nothing in this first part is a claim about what a place of play puts in front of a particular person. It is a claim about what the machine does when the unit of account changes, which is nothing.

2

Not one figure the reel publishes is a sum of money

Go through what the machine states about itself and the pattern in part one turns out to be the general case. A return of 96.71 per cent is a ratio and nothing else. The ceiling on one turn, which the data puts at 2,100 stakes, is a ratio as well. The rate at which that ceiling arrives is 1 in 3,880,481, which is a probability. The layout is five reels and three rows with ten paylines, which are counts. The price list is twenty-eight steps between two ends, which are numbers waiting for a unit every one of them off the game’s own data.

Not one of those is a sum of money, and that is not an accident of presentation. A machine of this kind is built to be sold into many markets, so its figures are written in the only forms that survive the journey: ratios, multiples, probabilities and counts. The money appears when somebody opens a session and says what the unit is, and it appears on the account rather than on the reel.

The offer side is where the denomination lives, and it is worth listing what sits there. A credit is written in a unit. A deposit floor is written in a unit. A ceiling on a withdrawal is written in a unit. A charge for moving money is written in a unit. Every one of those is a term somebody drafted, and every one means a different quantity of value if the unit underneath it moves while the terms stay still.

So the instrument this site uses has one column that cannot be denominated and one column that is nothing but denomination, which is the clearest statement of where a rail acts. It acts on the right-hand column, after the multiplication rather than inside it.

The consequence for this domain’s method is worth stating plainly, because the method is a multiplication of two figures and only one of them has ever been in money. What the machine states is unitless. What an offer states, a credit, a floor, a ceiling, is denominated by whoever wrote it. So every sum on this site is a unitless figure meeting a denominated one, and a rail that changes the unit changes exactly one of the two.

3

An hour, counted in units rather than in pounds

Now the arithmetic, done once in units and once in money so that the difference between the two is visible. A licensed build will not start a second cycle quickly enough for an hour to hold more than 1,440 turns RTS 14D, off the rule sheet. At the cheapest step the list carries, which is 0.10 and which this card spends throughout the house stake, named wherever it goes, that hour puts 144.00 units across the reel. On this reel the machine is then expected to keep 3.29 points of that turnover, which comes to 4.74 units.

Written in pounds those are £144.00 and £4.74. Written in any other unit they are the same two numbers with a different name after them, and the reason is the one part one established: the steps did not change when the currency did. A reader who moves from one unit to another has not changed the count of steps, has not changed the ratio applied to them, and has therefore not changed either figure.

The hour in a second unit is worth writing out in full once, because the temptation is to assume a conversion has happened somewhere inside it. One thousand four hundred and forty turns at a step of 0.10 is 144.00 of the unit. The machine keeps 3.29 points of that, which is 4.74 of the unit. Nothing in either sentence refers to a currency, and no exchange rate was applied at any point, because there was nothing in the arithmetic for one to apply to.

If that seems like a small claim, set it against how this subject is usually written about, where a machine is described as costing so much a spin and the figure is quoted in whichever currency the writer had in mind. That is a conversion performed silently, and it is the thing this card exists to take apart.

What they have changed is the thing neither figure mentions. Four point seven four units is a quantity of money only once somebody says what a unit fetches, and that statement is made outside the machine, by a market rather than by a maker. So the same hour has one cost in units, which is fixed and published-derivable, and a second cost in money, which is whatever the first one is multiplied by a number this site has no source for.

Take the arithmetic of a credit as well, because it comes out the same way. A credit of 50.00 units at a play-through of ten times, worked against the 96.71 per cent the maker publishes and with the slot weighted at one, closes at 33.55 units in expectation. Write the credit in pounds and the close is £33.55; write it in anything else and the close is 33.55 of that, every term in the expression being either a ratio or carried in the unit the credit was written in.

The shape of that expression is worth one line, so that it is clear across the section. The house expectation is E = B × (1 − W × (1 − RTP) ∕ g), where B is the sum advertised, W the multiple asked of it, RTP whatever the reel publishes and g the weight the terms put on a named slot. Every term in it is either unitless or in the unit B is written in, so the whole expression carries the unit of the credit and nothing else. A moving unit does not enter the formula. It operates on the answer.

4

What the rail does change, and over what span

If the rail does not touch the price list, the return or the ceiling, what does it touch? One thing: what a held balance is worth, for as long as it is held. That is not a small thing, and it has a shape worth drawing out, because it behaves differently from everything else this site prices.

The machine’s cost is proportional to turnover. Put 144.00 units across the reel and expect to lose 4.74 of them, and the figure does not care how long it took. The unit’s cost, in either direction, is proportional to the balance held and to the time it is held for. Those are different bases entirely: one is measured by how much is staked, the other by how much is sitting still and for how long. A reader who treats the second as a version of the first will get the size of it wrong in both directions.

Put numbers on the two bases and the difference stops being abstract. A reader holding 1,000.00 units and playing an hour at the least step puts 144.00 of them across the reel, so the machine’s share is 4.74 units and the remaining 855.26 are sitting still. The machine cannot touch what is sitting still, and the unit cannot distinguish what is sitting still from what is being staked. One cost is charged on the part moving through the reel and the other on the whole of what is held.

Which means the ratio between the two costs is set by something neither the machine nor the rail publishes: how much of a balance somebody puts through in an hour. At the least step that is a seventh of the thousand. At the stake the machine opens on it would be the whole of it nearly three times over, except that a balance cannot be staked faster than the floor permits.

This is where the section’s own quantity does the work, because the time a balance spends in the unit is not a free variable on a licensed build. The floor under a turn fixes how many turns an hour holds, so an hour of continuous play is an hour of exposure, and the count of turns and the count of minutes rise together. Take the floor away and they come apart: the same 1,440 turns can be got through in less time, so the same turnover is exposed to less movement, and the same hour holds more turnover and more cost from the machine. Neither effect has a published size, because the count of turns on an unlicensed build is published by nobody.

One more consequence follows from the two bases, and it is the one most often got backwards. A reader who stops playing has stopped the machine’s cost entirely, since no turnover is crossing the reel, and has not stopped the unit’s cost at all, since the balance is still held. Those two sentences are the practical difference between a cost on a flow and a cost on a stock, and no arrangement of the terms makes them behave alike.

The reverse holds as well. A reader who converts a balance out of the moving unit has stopped the second cost and left the first untouched, because the reel goes on keeping its published proportion of whatever crosses it, in whatever the balance is now denominated in.

There is a third thing in the sheet worth setting beside those two, and it is about where the figure a player sees comes from. The return shown on a game’s own information screen is drawn from the same session response the figures on this card came out of an inference from the protocol, labelled as one, so a screen and a sheet agree by construction rather than by luck. That makes the screen the one place a reader can check a return without taking anybody’s word for it, and the duty requiring something of the kind to be within reach before anybody commits was written into the licence, not into the build.

So the honest description of what a rail adds is a second cost, acting on a different base, over a span that a duty about the clock is the only thing fixing. That is the consequence this card prices, and part five is the only way it can be priced without supplying a figure nobody published.

5

The movement that comes to exactly one hour of edge

Here is the one computation on this subject that needs nothing from outside. Take a reader holding a balance equal to one hour’s turnover at the cheapest step, which is 144.00 units. Over that hour the machine is expected to take 3.29 points of the turnover, which is 4.74 units. Ask what movement in the unit would cost the same, and the answer is 3.29 per cent, because the balance and the turnover are the same number and the same proportion of each is the same quantity.

That is a conversion rather than a prediction, and it is the useful form of the question. It says: on this reel, at this step, over one licensed hour, holding a balance the size of the hour’s turnover, a unit that moves by the house edge has cost exactly what the house edge cost. Everything beyond that follows by proportion. A balance twice the size doubles the unit’s share and leaves the machine’s share alone. An hour at half the step halves the machine’s share and leaves the unit’s alone, if the balance has not changed.

The equivalence does not depend on which step is taken, which is worth checking rather than asserting. Run the same hour at the stake the machine opens on, 2.00 a turn, and the turnover is 2,880.00 units with an expected cost of 94.75. A movement of 3.29 per cent on a balance of 2,880.00 units is 94.75 as well. The step cancels out of both sides, because both are proportions of the same number.

Two things make that equivalence worth printing rather than asserting. The first is that it gives a reader a yardstick made entirely of published figures: the edge is the machine’s own, the count of turns is the floor’s, and the balance is the reader’s own choice. The second is that it shows the two costs are not of the same kind. The machine’s is a rate on a flow; the unit’s is a rate on a stock. They happen to meet at one number, under one assumption about the balance, and they part company the moment that assumption changes.

Scale the balance and the yardstick scales with it, which is the practical form of this part. Double the balance and the movement matching an hour of edge halves, because the same cost is being spread over twice the stock. Halve the balance and it doubles. The machine’s share has not moved in any of those cases, the turnover not having moved, and that asymmetry is the whole of the structural difference between the two costs.

4.74 units an hour is the machine’s share whatever the unit, and a unit moving by 3.29 per cent over the same hour costs the same again on a balance the size of that hour’s turnover

6

Two reels, one price list, two different costs

The price list is not the only thing that stays put when a unit changes. The return does too, and since the family publishes a dozen distinct returns, two reels sharing the identical price list produce different costs for the identical hour. The table works the same hour against the original and against Big Bass Vegas 1000, a later reel of the family whose page and whose data both give 96.53 per cent both figures off the family table.

Twenty-six pence over an hour is a small figure and it is a published one, which is the only reason it is here. Set it against the second cost from part five and the comparison does the work this card exists to do: a movement of a fifth of one per cent in the unit, over the same hour and on a balance the size of its turnover, comes to about the same money as choosing the lower-returning of two reels. One of those two quantities is printed by the maker of the machine. The other is printed by nobody this site may cite.

The second row of the table is a later reel of the same family and it is there for a reason beyond arithmetic. It takes the identical steps, so a reader moving between the two is not changing the price of a turn by a penny. What changes is the proportion kept, and the proportion is the one figure the maker prints for each title on its own page.

Twenty-six pence over an hour will strike some readers as too small to bother with, which is the right reaction and the wrong conclusion. Ten hours of the same play multiplies both figures by ten without altering either rate, and the drawing at the foot of this card sets a tenth of an hour, an hour and ten hours side by side for exactly that reason.

The turnover column stands still between the rows, which is why it is printed. Both reels take the same steps, so an hour commits the same count of units on either, and the whole of the difference is what each keeps. Change the unit as well and the column still does not move: it is the same 144.00 in a different name, and the closing row is the same 0.26 in that name too.

7

The figure this card will not supply from anywhere

A reader will have noticed what is missing, and it is missing deliberately. There is no figure on this card for how much any unit moves, over an hour or over a year. The sheets this site is built on carry regulatory fact and fact about the machine, and neither of them publishes anything about the price history of anything at all. An estimate dropped in here would look exactly like the figures beside it, which all carry a claim number, and it would be the only one that did not.

That refusal has a cost and the cost should be admitted. It means this card cannot tell a reader whether the second cost is larger or smaller than the first in any real case. What it can do is give the exchange rate between the two, which is part five, and let anybody who does have a figure for the movement finish the sum in one multiplication. That is the honest division of labour between a page and its reader.

A reader who wants to use that refusal rather than resent it can do so in one step. Find a figure for the movement from a source that publishes one, multiply the balance by it, and set the answer against 4.74 units an hour at the least step or 94.75 at the stake the machine opens on. Those two figures are this card’s whole contribution, and both are published-derivable.

What this card will not do is pretend the second figure is unavailable because it is unknowable. It is perfectly knowable, and it is simply not on either of the two sheets this site is built from, which is a statement about this publisher’s sources rather than about the world.

The same refusal applies in the other direction, and it is the more important of the two. Nothing here says what any place of play charges to move a unit in or out, what it credits, or how long it takes, because nothing read at the primary level for the rule sheet publishes any of that for this part of the market recorded as unverified rather than estimated. A page that filled those in would be describing a route rather than pricing a consequence, which is not what this section is for.

8

What is left standing when the unit is taken away

Strip the unit out of everything above and see what survives, because that is the clearest statement of what this card found. The twenty-eight steps survive. The return survives, being a ratio. The ceiling of 2,100 stakes survives, being a multiple. The rate at which it arrives survives, being a probability. The count of 1,440 turns in an hour survives wherever a floor holds the clock. The expected cost of 4.74 survives, being a ratio applied to a count.

The ceiling behaves the same way and is worth one line of its own. Two thousand one hundred stakes at the least step is 210.00 of the unit, and at the stake the machine opens on it is 4,200.00 of it. Neither figure needed a currency to be computed and neither acquires one until somebody says what the unit fetches.

What does not survive is every sum of money on the page, because not one of them was ever a property of the machine. That is the finding, and it cuts against the way this subject is usually written about. A unit that moves is not a thing that happens to the reel. It is a thing that happens to the account, and the reel goes on printing the same numbers at the same ratio while it happens.

The list of what survives is worth one more reading, because it is the list of everything a reader can rely on when the unit under them is not fixed. Three published ratios, one published probability, a handful of counts and a price list of twenty-eight steps. Everything else written about this subject, here or anywhere, is a sum of money that somebody has converted.

One last quantity survives the loss of a unit, and it is the span of the price list itself. The step at the head is 2,500 times the step at the foot, and a ratio between two numbers on one list is as unit-free as the return is. That factor would still describe this machine if every currency it had ever been quoted in were replaced tomorrow morning.

A reader who wants the shortest version of all of this can have four words: the reel prices in numbers. Everything else on any page about a moving unit, including every sum on this one, is those numbers after somebody has said what they fetch.

Which leaves a reader with one practical sentence. Whatever unit is in use, the count of steps between the ends of the price list is twenty-eight, the proportion the machine keeps is the maker’s published figure, and the only quantity that moves with the rail is what the whole lot is worth once somebody converts it. Keep the two apart and the arithmetic stays honest. Run them together and a page ends up pricing a machine in a unit it never quoted.