Mines Odds and Payouts

Four figures on a mines game's rules or help screen decide what its chart looks like. The RTP is the portion of every amount wagered that comes back over a very long run, and on a formula-priced board it fixes every multiplier. The board size sets how many squares there are, usually 25, though some games let the player shrink or enlarge the grid. The mine range says how many mines may be hidden, from a single one up to every square but one on most games, while a few titles fix the count. The maximum win is the ceiling on what one round can pay, stated either as a multiplier or as an amount of money.

Some games list the multiplier for every step in advance, others reveal only the next one as the round goes on; either way, the figure on screen is the one to hold against the chart below. A multiplier is displayed to two decimals and a payout lands in whole cents, and both steps can shave a little off the stated return.

Picture 25 closed squares with 3 mines hidden among them. The first click finds a safe square with a chance of 22 in 25, or 88.00%. The second click then picks from one square fewer, with one safe square fewer among them, and getting through both clicks succeeds 77.00% of the time. Each further click multiplies in another fraction of the same kind, safe squares left over squares left.

The fair multiplier is one divided by that chance: the payout at which a bet would, on average, return exactly its stake. For the first click with 3 mines that is 1.14x. A studio that sets the game at 97% pays 97% of the fair figure, so the same click shows 1.10x, and two clicks show 1.26x where the fair price would be 1.30x.

Every chart on this page applies to games priced this way, which covers most studio boards. Games with their own step prices, and games built as a ladder rather than a board, follow other numbers, described at the end of the page.

Each row is a round that stops after that many safe squares, with a single mine hidden among 25. The chance falls by the same step at every click, so the multiplier creeps up for most of the board and then leaps over the final few squares. Multipliers in the last column are rounded to the nearest hundredth.

Three mines is a common default setting. A round of 5 clicks is close to a coin toss at 49.57%, and by 10 clicks the chance has dropped to 19.78% while the multiplier has reached 4.90x.

With 5 mines the first click is safe 80.00% of the time, and every later click gives up a larger share of the chance than the one before: 5 clicks succeed 29.18% of the time and 10 clicks only 5.65%.

Each safe square at 10 mines multiplies the payout by a larger factor than the last, because the mines make up a growing share of the squares still closed. On a capped game the bottom rows are rarely paid in full, as the section on caps shows.

Once mines outnumber safe squares, a round seldom survives more than a handful of clicks. These setups trade a small chance for a large multiplier at once, rather than building it up step by step.

Every multiplier scales with the return, so another version of the same game moves each row by the same proportion; the figures at 97% are in the charts above.

The largest figure a 25-square board can show does not belong to the setup with the most mines. With 24 mines there is a single safe square, so the round ends after one click, found 4.00% of the time and worth 25.00x at a fair price. The peak sits in the middle of the range: with 12 mines, revealing all 13 safe squares happens once in 5,200,300 rounds, for a fair multiplier of 5,200,300x.

On a game with a maximum win, the payout stops climbing long before that point, so the real ceiling of a board is its cap rather than its chart.

On a formula board the multiplier is the RTP divided by the chance of reaching it. Multiply the two back together and the average result of any bet is the RTP itself, whatever the mine count and however many clicks the player takes, as long as the multiplier is paid with all of its decimals.

A game that pays the multiplier it shows, to two decimals, pays a slightly different number. Rounded down, the setup of 2 mines, 3 clicks has an exact multiplier of 1.2597x but shows 1.25x, and that missing fraction of a hundredth lowers its return from 97% to 96.250%. Across all 300 setups of a 25-square board set at 97%, the average return falls to 96.928%, 238 setups pay back less than stated, and not one pays more.

Small multipliers lose most, because a hundredth is a bigger slice of a small number. The 39 setups that pay less than double the stake average 96.674% when rounded down. Rounding to the nearest hundredth spreads the error both ways instead, as the comparison below sets out.

The key number: Rounded down to two decimals, a board set at 97% returns 96.928% averaged over its setups, and only 96.250% on the worst of them.

The same effect appears at every return level. At 99%, rounding down leaves an average of 98.928% and a worst setup at 98.280%. The screen does not reveal whether a title settles at the displayed figure or carries more decimals behind it, so these numbers describe a game that pays exactly the multiplier it shows.

Both columns describe a 97% game on 25 squares, counted over all 300 combinations of mines and clicks, each weighted equally. Rounding down can only take; rounding to the nearest hundredth takes about as often as it gives, so its average sits almost on the stated figure.

Rows run from the setups that lose most to those that lose nothing. Where the exact multiplier falls just short of the next hundredth, rounding down costs the most; where it already ends near a whole hundredth, neither kind of rounding matters.

A maximum win comes in two forms. A multiplier cap stops the payout growing at a set multiple of the stake, the same for every bet size. A money cap limits the amount a single round can pay, so the multiplier it allows depends on the stake, and dividing the cap by the stake gives it. A setup whose multiplier would pass the cap is paid only the cap, and its return drops by the share cut off.

Take a game with a money cap of 10,000 in its currency, played at a stake of 100.00. That cap is worth 100x the stake. With 3 mines at 97%, the chart crosses that line at 19 safe clicks, where the setup returns 86.957% instead of 97%, and a player who clears every safe square gets back just 4.3478% of the amount staked over the long run. At a stake of 10.00, the same money cap is worth 1,000x, and clearing that board returns 43.4783%.

The rule: Beyond the point where a setup meets the cap, every further click adds risk without adding pay, so the return of the round only falls.

Each cell gives the first number of safe clicks that is paid less than the formula at 97%, and the return of that setup; every click after it loses more. Boards with a single mine or with 24 mines never reach any of these caps, since their largest multiplier is small.

Figures at 97%, with every combination of mines and clicks counted once. A player who keeps to short rounds never meets the cap at all.

A payout has to be a whole number of cents. If a game rounds the multiplier down to two decimals and then rounds the payout down to the cent, a very small stake loses part of almost every win. At a stake of 0.01 with a single mine, a win on the first click pays 0.01, a return of 96.00%, and a round of 3 clicks pays the same 0.01, a return of 88.00%: the multiplier rises but the payout cannot reach the next cent.

On the smallest stake, a 97% game averages a return of 90.474% and 286 of the 300 setups lose something. The worst, 3 mines, 5 clicks, returns 49.565%, because a multiplier of 1.95x on that stake still pays out a single cent.

The loss fades quickly as the stake grows. At 0.10 the average is 96.314%, and at 1.00 cent rounding adds nothing beyond what two-decimal rounding already takes.

Figures for a 97% game that truncates the multiplier at the second decimal and then cuts each payout to the cent, with stakes in currency units. A game that carries more decimals loses less; the bottom row is the cost of two-decimal rounding alone.

Some studios let the player change the grid as well as the mine count, from a small three-by-three board up to larger ones. The counting does not change: each click succeeds with the share of closed squares that are still safe. With the same 3 mines, a small board makes every click far riskier and a large one far gentler, and the multipliers stretch or shrink to match.

All four rows hide 3 mines. The last column is the fair price before the studio applies its return, which a 97% version pays that share of. Larger boards follow the same rule, and their top multipliers grow faster still.

Not every mines game follows the formula. Some studios publish their own payout table, in which the return can differ from one setup to the next, so the choice of mines and clicks changes the price of a round and not only its swing. Others build the game as a ladder: rows of tiles climbed one at a time, each row hiding its own hazard, which is a different count altogether. None of the charts on this page describes these games, and their figures come only from the game's own screens.

A short calculation tells the two kinds apart. Divide the RTP on the rules screen by the multiplier the game shows for a setup: on a formula board the result is the chance of reaching that step, and it agrees with the chart. When it does not, that step is priced by the game's own table, and its true return is the shown multiplier times the chance from the chart, which can sit well below the headline figure.