Mathematics · no guesswork
RTP and odds in mines: how much the grid pays, and who pays more
In a slot the return is hidden inside a bonus game and cannot be checked. In mines there is a 25-tile grid and a mine count, and the multiplier for every click is computed from those two numbers by one formula. We derived it, computed it for every version in the set and checked it against the table the developer itself published. Below: the curves, seven RTP values compared on one scenario, and an honest answer to how much an evening costs in each version.
The formula behind every multiplier
Say the grid has N tiles, M of them mines, and you want to open k safe ones in a row. The chance that all k are clean is the number of ways to choose k tiles among the safe ones divided by the number of ways to choose k among all of them. The inverse of that chance is the fair multiplier: what the game would pay if it kept nothing. Multiply it by the RTP and you get what stands in the payout table.
The extreme case convinces faster than any lecture. Twenty-four mines, one safe tile. The chance of hitting it is one in twenty-five, that is 4 percent; the fair multiplier is 25; at RTP 95 the game pays 23.75x. That is exactly the number in the table InOut Games published. It matched at 3 mines, at 5 and at 10 as well - all four rows the studio showed, our computation reproduced digit for digit.
The second confirmation is the Mines+ ceiling from Pragmatic Play. Stated: 5070293x. The number of ways to choose 12 mines from 25 tiles is 5200300; multiply by 0.975 and you get 5070293 without a spare digit. The formula is one for the whole industry; studios differ only in the share they keep and in how they round the last digit.
How the multiplier grows: four curves on one grid
RTP 97.5, as in Mines+. The multiplier axis is logarithmic; otherwise the ten-mine curve would not fit on any screen.
One mine is almost a straight line: twenty-four safe tiles, and fifteen open ones pay only 2.44x. Three mines is a gentle arc, 18.69x by the fifteenth tile. Five mines is noticeably steeper: 205.6x on the same fifteenth. And ten mines is a wall: the third tile 4.93x, the fifth 17.25x, the tenth 1061x, and on the fifteenth the ladder simply ends, because there are no safe tiles left.
The point of the curves is not which one is higher. All four deliver the same return - 97.5 - over a long run. The point is the shape: the steeper the curve, the less often you climb it and the sooner it ends. Choosing a mine count is choosing the curve you prefer to walk, not choosing an advantage.
One grid, seven versions: what each pays for the same click
Five scenarios and every stated RTP in the set. The "fair" column is the multiplier with no house share; the difference from it is what the studio keeps.
| Scenario | Odds | Fair | RTP 92 | RTP 94 | RTP 95 | RTP 96 | RTP 97 | RTP 97.5 | RTP 98.4 |
|---|---|---|---|---|---|---|---|---|---|
| 3 mines · 5 tiles | 49.6% | x2.02 | x1.86 | x1.90 | x1.92 | x1.94 | x1.96 | x1.97 | x1.99 |
| 5 mines · 5 tiles | 29.2% | x3.43 | x3.15 | x3.22 | x3.26 | x3.29 | x3.32 | x3.34 | x3.37 |
| 10 mines · 3 tiles | 19.8% | x5.05 | x4.65 | x4.75 | x4.80 | x4.85 | x4.90 | x4.93 | x4.97 |
| 1 mines · 10 tiles | 60.0% | x1.67 | x1.53 | x1.57 | x1.58 | x1.60 | x1.62 | x1.63 | x1.64 |
| 24 mines · 1 tiles | 4.00% | x25.00 | x23.00 | x23.50 | x23.75 | x24.00 | x24.25 | x24.38 | x24.60 |
Take the first row: three mines, five tiles open, a 49.6 percent chance of getting there. The fair price of such a round is 2.02x. Minesweeper at 98.4 would pay 1.99x, Mines+ at 97.5 pays 1.97x, versions at 95 such as Mines by Turbo Games pay 1.92x (InOut truncates the tail in its own table and prints 1.91x), and Mines Supreme at 92 pays 1.86x. The gap between the extremes is thirteen hundredths on every such round, and it does not depend on luck.
The caveat about Minesweeper is an honest one: BGaming has a path instead of a grid, and the row "3 mines, 5 tiles" literally does not exist there - the column shows what its return would give on the classic grid. For the other six values the scenario is real: Hot Mines at 97 against Mines by InOut at 95 is the same 5x5 from the same studio, the same three mines and different 1.95x and 1.91x (the table above shows 1.96x and 1.92x: InOut truncates the last digit rather than rounding).
What an evening costs: the house edge in money
A hundred bets of ten units is an ordinary evening. The right column is the expected loss on such a series - an average, not a guarantee.
| RTP | House edge | Expected loss over 100 bets of 10 | Games in the set |
|---|---|---|---|
| 92 | 8% | 80 | Mines Supreme 92% |
| 94 | 6% | 60 | Mines 94% |
| 95 | 5% | 50 | Mines, Mines, Turbo Mines, Book of Mines, Mines Blast |
| 96 | 4% | 40 | Lucky Mines, 1Tap Mines |
| 97 | 3% | 30 | Hot Mines, Jackpot Mines, Mummy Mines, Mini Mines |
| 97.5 | 2.5% | 25 | Mines+ |
| 98.4 | 1.6% | 16 | Minesweeper, Minesweeper XY |
A hundred bets of ten is a turnover of a thousand. A game at RTP 98.4 keeps on average 16 of that thousand, a game at 92 keeps 80. The mechanics are identical down to the tile, and you cannot feel the difference over an evening: one lucky round covers it with room to spare. It shows only over the long run - and it always shows.
Look at the 92 row. Hacksaw Gaming put the RTP right in the game's name, and that is rare honesty: the value is usually buried in the help screen. It is also a hint: since the studio ships a build at 94 and a build at 92, the casino chooses which one to install. Our platform carries both, and each says which one it is.
Where the mathematics ends and the ceiling begins
The theoretical multiplier and what the game will actually pay are different numbers. At Hacksaw Gaming the ceiling is hard and set in stakes: 10000, and the game does not count beyond it. At InOut Games it is in money, 20000 USD, so it depends on the stake: on a small one it is out of reach, on a large one it kicks in before the theoretical maximum. Pragmatic Play states a 5070293 multiplier, the highest in the set; Turbo Games 805001 for its big grids and 456660 for the classic one.
The practical meaning: the 3105322 multiplier in the row "10 mines, 15 tiles" is a real quantity, but the game will almost never be able to pay it. The chance of getting there is below a thousandth of a percent, and the ceiling intervenes earlier. So when choosing a game for a big multiplier, look not at the table row but at the stated ceiling: every studio has its own, and in the tables on the game pages the cells above it are marked as such.
Provably fair: making sure the mines were not moved
At Turbo Games and BGaming a round works like this: before the first click the game shows a hash - a fingerprint of the layout - and after the round it reveals the key the fingerprint was made from. Recompute the hash yourself: if it matches, the mines were where they are shown before you clicked. The other studios have no such key on screen; fairness there is backed by a licence and an audit. Both forms are legitimate; the second just requires trust, and the first a calculator.
See the curve on a live grid
The BGaming, Turbo Games and Belatra demos open without an account - run ten rounds at three mines and at ten.
What people ask about RTP and odds
Does RTP change with the number of mines
No. Multipliers are rescaled so the return stays the same. Check the extreme case: at 24 mines there is one safe tile, a 4 percent chance of hitting it, a fair multiplier of 25, and a game at RTP 95 pays 23.75. At 3 mines and 22 open tiles the chance is 0.043 percent and the game pays 2185x - the same share, just different steps.
How is the multiplier in mines computed
The chance of opening k safe tiles in a row equals a ratio of combinations: how many sets of k tiles can be drawn from the safe ones, divided by how many can be drawn from all 25. The fair multiplier is the inverse of that chance; the real one equals the fair one multiplied by the RTP.
Why does one game have RTP 92 and another 98.4
Because they are different games from different studios, and each sets its own share. Minesweeper by BGaming keeps 1.6 percent of turnover, Mines Supreme by Hacksaw Gaming keeps 8. A 6.4-point gap means that on the same series of bets the second game eats money five times faster.
What is a payout ceiling and when does it get in the way
It is the upper limit beyond which the game does not pay, whatever the multiplier. For Hacksaw Gaming games it is 10000 stakes; for InOut Games it is set in money at 20000 USD. The theoretical multiplier at 10 mines reaches 3105322 but hits the ceiling long before that number.
Can I pick a profitable mode from the table
There is no profitable mode in the table: every row gives the same expected return. What you can pick from it is frequency. If a round that ends on the first click forty times in a hundred does not suit you, 10 mines is not your mode, however attractive the multiplier looks.
What does provably fair mean and how do I check it
The game publishes a hash of the layout before the round and the key itself after it. Recomputing the hash from the revealed key confirms the mines were where they are shown before your first click. Turbo Games and BGaming work this way; for the others fairness is backed by a licence and audit rather than a key on screen.
Return understood? Pick a version
Every version from the comparison above is on the platform: from Minesweeper at 98.4 to Mines+ with a 5070293x ceiling.