The break-even point, and the one number it needs

There is a figure at which a jackpot stops being a bad wager and becomes a good one, and the reference literature gives it a name. Above its "break-even point" a progressive becomes "a positive expectation bet", with a return above 100 per cent (both phrases are the literature's, and not ours). Below it the house holds an edge over every player at the game (every player, and without exception).

So far this is arithmetic and it is sound, but the trouble begins the moment anybody tries to locate the point on an actual slot machine.

Working out a break-even "counter" requires the probability of the jackpot, and on a slot that probability is not published by anybody (we looked, and the search is described on how often these jackpots fall). The literature says the same thing in colder terms, noting that the calculation can be done for card games such as video poker, blackjack and Caribbean Stud, and is "difficult for slot machines because the payback is usually not published".

One of the databases we read adds the practical half of the objection, and it is the half that most pages chasing a big counter ignore. A large number on the screen does not by itself demonstrate "positive expectation", because four other things enter the sum: the size of the "network", the way the chance "scales" with the stake, the "reserve rules" which hold money back, and any division of the prize.

That is why there is no sentence on this site of the form "above X million the game is worth playing", and why you will not find one. Such a sentence cannot be written honestly for a slot, and the rest of this page is the demonstration.

The only game where the sum can actually be done

Caribbean Stud Poker is the exception, and it is the exception for a dull reason: the hands are cards, the combinations are countable, and somebody has done the counting (the figures below come from the one analyst who published them in full, table by table).

The "side bet" (the extra wager, usually a dollar, that buys entry to the progressive) carries an average house edge of 26.46 per cent, which is among the worst prices anywhere in a casino (a slot at 89 per cent is the cheaper wager). The royal flush that collects the whole meter restarts from a "seed" of $10,000, and a straight flush takes 10 per cent of the meter and leaves the remainder standing.

The useful quantity is the rate at which the "meter" buys back that edge: every $10,000 that stands on it adds 0.029242 to the return of the side bet, on the most widely used "paytable", and dividing the one by the other is the only step the sum needs.

It appears, however, in a range rather than at a point, which is the finding this page is built on. The break-even counter falls somewhere between $149,431 and $425,380 (a spread of $275,949), and which end of that range applies depends entirely on the paytable which the table in front of you happens to use.

A factor of fourteen on the same wager

Three worked examples make the spread concrete, and all three are the same game with the same dollar on the same side bet. On the paytable numbered 4 (the tables are numbered in the published study) the wager turns favourable at $176,611.05; on the paytable numbered 12 it turns favourable at $29,491.24; on the paytable numbered 15 it needs $425,380.

That is a factor of fourteen between the easiest table and the hardest, and a player who learned the first figure and applied it at the third would be making a bad bet while believing he had found a good one.

A fourth example adds the house rules on top of the paytable. At one Australian room (Casino Canberra), running paytable 7 with a $50 bonus for the "dead man's hand", break-even arrives at $149,389.47; but if the player must also cover a $5 game minimum to be eligible, the figure moves to $238,716.85, and at a $10 minimum to $328,044.23.

So the expected value of a progressive does not depend on the size of the pot. It depends on the size of the "pot" measured against the particular paytable, the particular house rules and the particular cost of entry at the table in front of you, and three of those four are usually invisible to the person deciding whether to play at all.

The pots now standing above their own average

Why a large counter proves nothing on its own

Read down that table and the pattern is the opposite of the one a reader might expect from the headline percentages. LotsaLoot stands at nearly eleven times the average of everything it has ever paid ($283,836 against $26,035), Fruit Fiesta at more than four times ($107,192 against $24,507) and Jackpot Deuces at almost five ($186,793 against $37,822), and every one of them has gone over three years without a win.

These are not bargains which the market has overlooked, but the games that nobody plays, and the counter is high for exactly that reason: a pot grows with "turnover" and falls with wins (both halves of that are mechanical), so a deserted game produces a large number on the screen and a very small chance of the number landing on anybody at all.

King Cashalot is the sharpest instance in our whole document. The counter stands at $2,224,299 against an average win of $654,283 (the base return is 91 per cent, and the jackpot needs five king wilds on one particular line), which is 45 per cent above the largest prize the game has ever handed to anybody. The last person to collect it did so 9 years 8 weeks ago.

The theoretical case for playing it is real, and we are not pretending otherwise. The practical case collapses the moment anybody asks how many spins at 91 per cent a player would have to buy in order to reach a prize whose probability nobody has published, on a game whose own history says it pays once every two and a half years at best.

The one documented case of a prize being divided

The fourth item on the database's list of complications, the division of the prize, is usually treated as a theoretical worry. On one network it is a published rule, and it is worth setting out because it shows how far a counter can mislead.

Pragmatic Play's "Power" Jackpot carries four levels, and the only game carrying it is Wolf Gold (a title which also carries fixed jackpots of its own). The official page gives their "average prizes" rather than their "seeds", a distinction which the supplier makes explicitly and which we keep: €750 at the "Mini", €12,500 at the "Minor", €125,000 at the Major and €4,500,000 at the top. The mechanism attached to that top level is the interesting part.

When the Power level is won, half of the prize goes to the winner and the other half is shared out among the last thousand players of the jackpot game (a published rule, on the supplier's own page). A reader looking at €4,500,000 on a counter is therefore looking at a prize of which, if he were the winner, he would collect about half, and the published figure says nothing about that at all.

It is the clearest proof we have that a counter is not a quantity a player can use without the rules beside it. One network out of the fourteen we have tabled publishes such a rule, and we have no way of knowing how many of the others have one!

What the counter becomes in the hand

One more gap sits between the number on the screen and the money in an account, and it is the gap this trade writes about least. A counter is a "nominal" figure, which means a number written rather than a sum held, and whether the whole of it arrives at once is a question of rules rather than of arithmetic.

The clearest published statement anybody makes of those rules belongs to a regulator rather than to a casino. The Michigan Gaming Control Board writes that "a jackpot of more than $100,000.00 may be paid in installments over a period of not more than 25 years" (R. 432.1841, subsection (g)(iii)), and it requires the machine to display that the prize will be paid that way, how many instalments there are and how far apart they fall.

The same rule obliges the operator of the system to hold a reserve "sufficient to fully fund the present value of all amounts currently reflected on the progressive meters" (subsection (t)(ii)), and the two words carrying the weight there are "present value" (what a future stream of payments is worth today, which is always less than the sum of its parts). The money standing behind a counter is therefore the discounted worth of a series of payments rather than the figure written across it. A winner cannot sell that series either, since the right to the payments may not be assigned or transferred except to an estate on death (subsection (n)).

New Jersey adds a provision worth reading before a large counter starts to look attractive. A licensee removing a progressive payout permanently must set "a time limit of not less than 30 days", and once that limit expires the amount still sitting on the meter may be retained by the licensee (N.J. Admin. Code 13:69D-1.52, subsections (h) and (i)); the money on an abandoned counter does not return to the players who fed it, because nothing in the rule requires that it should.

Those are rules for machines on a floor in two American states and this site lists no American operator, so read them as the clearest description of the mechanism rather than as the terms of your own account. Online the equivalent clause is the house's own "ceiling" on withdrawals, which is the most it will release in a month whatever the balance says, and it is the one line in a set of terms worth finding before a deposit rather than after a win.

The check takes two minutes and you can run it yourself, which is why we set it out here instead of offering a verdict: search the terms for the monthly maximum, then search again for whether a jackpot win is excluded from it. If it is not excluded, do the division before you play rather than afterwards. A ceiling of five thousand a month set against a prize of a million is sixteen years and eight months of waiting, and a prize collected over sixteen years is a different product from the one on the poster!

What we would look at instead

If the break-even point cannot be computed, something has to take its place, and you are entitled to know what we would use instead: a comparison rather than a verdict.

We would read three things together: the "average interval" between wins on that level (the trackers compute it from the whole recorded history of the level), the interval since it last fell (what the trade calls a "drought"), and the average of the prizes the game has actually paid. A pot far above its own average on a level running near its usual interval is a different proposition from the same pot on a level that has been silent for four times as long, and the second case is the common one (King Cashalot is of the second kind).

Then we would read the base return, because that is the price you pay for every spin spent waiting, and on the games in the table above (89 to 92 per cent, every one of them) it is the figure which settles the question before the counter is ever reached. A deficit of nine points a spin is not recovered by patience (Major Millions is published at 89.37 per cent).

And we would treat the whole table as an illustration of how the mechanism works rather than as a shopping list, which is the sentence the trade usually omits and the one we would put first!

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