Mines and Plinko games: how the multipliers build in the house edge

In Mines and Plinko the fair multiplier is the inverse of the probability of the outcome. The game then pays a fixed share of that figure, such as 97%, and the missing 3% is the house edge. The margin is inside every multiplier, so no tile count or slot choice removes it.

By Nairobi Ultimate Editorial (prepared with AI tools under our editorial policy) · Last updated 2026-10-25

The one rule behind both games

Mines and Plinko look different, but their prices are built the same way. The fair multiplier for an outcome is 1 divided by its probability, and the game pays a fixed share of that. This guide uses a share of 97%, a house edge of 3%, as a choice for illustration, not as the figure of any real game.

The same idea runs through how RTP and house edge work. If a payout is 0.97 times the fair figure, then payout times probability is 0.97, so KES 97 comes back on average per KES 100 staked. Regulation 20(2) of the Conduct of Gambling Operations Regulations, 2026 says a licensee must display rules of games, odds, house edge and average return to the player, and regulation 20(3) applies this to online gambling.

Mines: the probability of each safe pick

Take a grid of 25 tiles hiding m mines. A player opens tiles one at a time and the round ends at the first mine. The chance that the first pick is safe is (25 − m)/25. If it is, 24 tiles remain, 25 − m − 1 of them safe, so the second pick is safe with chance (24 − m)/24, and so on.

P(k safe picks) = (25 − m)/25 × (24 − m)/24 × ... × (25 − m − k + 1)/(25 − k + 1)

The fair multiplier after k picks is 1/P(k). The priced multiplier is 0.97/P(k).

Worked example: 3 mines

Illustrative example, 25 tiles, 3 mines, 3% edge, not the game of any operator. After three safe picks the fair multiplier is 13,800/9,240 = 1.4935, and the priced one is 0.97 times that, or 1.4487, shown as 1.45x. Multiply the priced figure by the chance of getting there and the product is 0.97 on every row.

What this shows about Mines

The edge does not grow or shrink with the number of picks. Whether a player stops after one tile or after five, the average return on the stake is 97 cents per shilling, a point shared with crash games and their cash-out targets. What changes is how often the round ends in a loss and how large the occasional payout is.

More mines raise every multiplier. With 10 mines the first pick is safe with chance 15/25 = 60%, so the fair multiplier is 1.667x and the priced one is 0.97/0.6 = 1.617x. Two safe picks have chance 15/25 × 14/24 = 35%, priced at 0.97/0.35 = 2.771x. Higher multipliers mean a larger spread of results, the idea behind volatility, and the margin is untouched.

Real games show multipliers rounded to two decimals. If a game rounds down, the effective edge is slightly above the stated one, which is a reason to read the published return to player and not infer it.

Plinko: a binomial pattern of slots

In Plinko a ball drops through rows of pegs. At each peg it goes left or right with equal chance, which is the standard model. With 8 rows there are 2^8 = 256 equally likely paths, and the number of paths that finish with j right-bounces is the binomial coefficient C(8, j).

P(slot j) = C(8, j)/256, so the nine slots hold 1, 8, 28, 56, 70, 56, 28, 8, 1 paths

The centre slot is reached by 70 paths, 27.34% of drops. Each outer slot is reached by 1 path, 0.39% of drops. A path count is a count of routes, not a force aimed at a slot.

Fair payout against a priced table

Illustrative example, 8 rows, payouts chosen for this guide and not taken from any real game. The shares add to 248.2/256 = 96.95%, so the house edge of this table is 3.05%. The fair multiplier column, taken per group of slots, is what the table would pay if there were no margin.

Where the edge sits in a Plinko table

A priced table shortchanges the rare slots most. The edge slots in the example pay 5x where the fair figure for that group is 128x, yet they supply only 3.91% of the return, because they are reached in 2 drops out of 256. The frequent slots hold most of the return, so the position of the middle of the table decides the overall price.

The same table returns less than the stake in (70 + 112)/256 = 71.09% of drops. The remaining 28.91% pay 1.4x or more. A pattern of many small losses and occasional larger payouts is how a payout table pays an average of under 100% while still showing the odd large result.

Many Plinko games offer risk settings, often labelled low, medium and high. In the model that means different payout tables on the same peg board. Each table has its own average return, so the published figure for the setting chosen is the one that applies.

What the regulations expect, and what they do not cover

Regulation 45(1) requires game rules to be clearly displayed before a player places a wager. Regulation 45(2) requires the random number generator used for all games of chance to be certified by the Authority or its approved agent to test randomness and theoretical return to player, and regulation 45 also requires that return percentage to be publicly disclosed for each game. See how RNG testing works in Kenya for the testing side.

None of this makes a round predictable. A mine layout or a ball path is generated for each round, independent of the last, which is why the gambler's fallacy misleads and why expected value is a long-run average, not a forecast. Gambling is addictive: play responsibly, and only if you are 18 or older.