Rows, balls and probability

The plinko casino game: rows, risk and what the table shows

A ball falls through a field of pins and lands in a cell with a multiplier. Here is how the rows govern the probability, and why the risk level only swaps out the figures at the bottom.

Plinko is a house game where a ball is dropped from the top of a triangle of pins. At each row the ball bounces either left or right, and in the end it lands in one of the cells along the bottom. Each cell has a multiplier, and your stake is multiplied by the figure where the ball stops.

The game looks random and lively, but behind the animation lies a fairly simple distribution. Once you understand it, you can read the payout table yourself and see what you are actually choosing when you change the number of rows or the risk. All the house games and the operators that offer them are gathered in full on the home page of kryptospill.

Plinko: the ball's route through the board

At every row of pins the ball is pushed either left or right. The cell at the bottom is the sum of all those small choices of direction. The animation illustrates the mechanics and reproduces no real round.

How plinko is built up: pins, rows and cells

The board consists of rows of pins that get wider towards the bottom. With 8 rows there are 9 cells at the bottom, with 16 rows there are 17. The rule is always the same: the number of cells is the number of rows plus one.

You make three choices before every round:

The stake in the coin your balance is held in.
The number of rows, usually a range from around 8 to 16.
The risk level, often called low, medium and high.

The ball has no memory. A bounce to the right in row three says nothing about what happens in row four, and the previous round does not affect the next. It is precisely that independence that makes the mathematics so tidy.

The distribution: why the middle is hit most often

Think of each row as a coin toss. To end up at the far left the ball has to go left in every single row. To end up in the middle it is enough for it to go roughly the same number of times each way, and there are a great many paths there. Statisticians call this a binomial distribution.

The probability for a cell is the number of paths to the cell divided by all possible paths. With 8 rows there are 2 to the power of 8, so 256 paths in all.

A worked example: 8 rows

The figures below were worked out by us as an example, with an equal chance of left and right in each row:

The outermost cell on each side: 1 path out of 256, roughly 0.39%.
The next one in: 8 paths, roughly 3.13%.
The third from the edge: 28 paths, roughly 10.94%.
The fourth from the edge: 56 paths, roughly 21.88%.
The middle cell: 70 paths, roughly 27.34%.

Add both sides together and the ball ends in one of the three middle cells in over 71% of rounds.

A worked example: 16 rows

With 16 rows there are 65,536 possible paths, and the edges become extremely rare. Each of the two outermost cells is reached in only one way, so around once per 65,536 drops. The middle cell has 12,870 paths and is hit in roughly 19.6% of rounds, and the five middle cells together account for well over half.

More rows do not give more large wins, then. They give a greater distance between the ordinary and the rare, and that is why the table can set much higher figures at the edges.

A worked example for sixteen rows where each pin sends the ball left or right with equal chance. Almost every drop lands near the middle; the large multipliers at the edges are rarely hit, and that is why they can be large.

The risk level changes the table, not the ball

Many believe that high risk makes the ball behave more wildly. It does not. The distribution from the section above is exactly the same at every risk level; the only thing swapped out is the multipliers at the bottom.

Here are two invented tables for 8 rows, made only to show the principle:

Low risk (example): 13× – 3× – 1.3× – 0.7× – 0.4× – 0.7× – 1.3× – 3× – 13×
High risk (example): 29× – 4× – 1.5× – 0.3× – 0.2× – 0.3× – 1.5× – 4× – 29×

Multiply each multiplier by the probability for the cell and add them up, and low risk comes out at roughly 98.9% and high risk at roughly 99.1% back on average. The expectation is nearly the same. The difference is how the money is spread: in both tables the ball lands below 1× in around 71% of rounds, but with high risk you lose more each time, while the rare edges pay more.

What the margin means in a session

A small calculation, also as an example: you drop 200 balls with 0.0001 BTC on each. You have then staked 0.02 BTC in all. With a return of 99% the expected loss is 1% of that, so 0.0002 BTC. That seems little, but automatic play can give many hundreds of drops in a short time, and then it is the turnover that decides the bill, not the balance you started with. In one single session the result can still land far above or below the average.

That is the same sum that lies behind the term return to player. If you want to see how such a percentage is calculated and why it says nothing about one evening, it is in the walk-through of the return and the house's share.

How to read the plinko table in the game

Nearly every version shows the multipliers directly on the board, and many also have an info button with a table for each row count and risk level. Do this before you stake anything:

Choose the row count and the risk, and write down the multipliers.
Find the probability per cell with the method above, or use the figures from the examples.
Multiply and add. The sum is the return the table gives.
Compare it with the return figure the game states itself. If the figures are far apart, it is the table on the screen that matters to you.

If you want to practise this with no stake, the demo version with play money is a good place to count cells and compare risk levels.

Is the round decided beforehand?

In house games at crypto casinos the outcome is often decided by a combination of a server seed, a client seed and a round number. The hash of the server seed is shown before you play, and once it has been swapped out you can recalculate every round. For plinko that means the whole path through the rows can be verified.

Such a check shows that the round was not altered after the stake. It says nothing about whether the table is favourable or whether your account is handled tidily. The whole procedure is explained step by step in the article on seed checking.

Plinko for real money: check the account rules first

Many of those searching for plinko for real money are really wondering what happens on the day they want the win out. The answer is not in the game but in the operator's terms. Three things are worth finding before a first deposit.

When the ID check comes. At Vave ID can be demanded before any payout (cl. 8.7), and the same holds at Rocketpot at a withdrawal request (cl. 11.4 and 12.4). At Bitcasino.io the check is triggered by an event (cl. 3.13 and 6.6).

Which amount triggers a document requirement. Bitcasino.io writes €2,500 or the value in crypto (cl. 6.6). Rocketpot gives $2,000–$2,500 in two different clauses.

Caps per period. Wild Fortune has ceilings of €1,000 per day, €5,000 per week and €15,000 per month for withdrawals (cl. 11.8). Wolfbet sets $8,000 a week and $30,000 per calendar month (cl. 15 §5). Metaspins has no upper cap but can pay large amounts in instalments (cl. 12.5).

The periods for documents vary too. Rainbet gives a period of 72 hours for the documents (cl. 20.1), Metaspins 30 days (cl. 9.10). Read this before you play plinko for real money and you will avoid surprises once the balance has grown. How the payout itself is done with the address and the network is described in the step-by-step guide to withdrawals.

How to choose a plinko casino

Which operators have the game you see in their lobby. We do not assess casinos by the number of games or the size of a bonus, but by five points in the terms and the register.

When choosing a plinko casino you can use the same questions:

Do the terms say that identity can be checked?
Does it say when the check starts?
Is an amount stated?
Is there a period for sending documents?
Does the licence register show the operator's own domain?

A plinko casino that answers yes to all five makes it easier to know what is expected of you. The scores for the twelve operators we have worked through, with their licences and files, are in the overview of crypto casinos.

Scams and fake plinko apps

The plinko board is easy to copy. There are apps and adverts showing a falling ball and large figures but lacking a licence, a seed panel and a table. A typical mark is a promise of certain income, or a demand to pay a «fee» before the win is released. We work through such signs on the page about fake plinko offers.

Play with limits

Plinko runs at a high pace, and many rounds in a short time let the house's small margin take effect. Set an amount you can bear to lose before you start, and take breaks. If you feel play getting out of hand, you can get free help at Hjelpelinjen on hjelpelinjen.no. You have to be 18 to play.

Frequently asked questions

Can I influence where the ball lands in plinko?

No. You choose the stake, the number of rows and the risk level, but the path through the pins itself is decided by the random number generator or the seed combination. The moment you press, how many balls you drop at once and what happened in the previous round make no difference. The distribution is the same every time, and the only thing you change is which multipliers stand in the cells at the bottom.

Do 16 rows give a better chance than 8 rows?

Not in the form of a higher expected return. More rows make the edges much rarer, and so the table can show higher figures there. At the same time the middle becomes more dominant. In our worked example the outermost cell is hit around once per 256 drops with 8 rows, but only around once per 65,536 drops with 16 rows. Which suits you depends on how large you want the swings to be.

What does high risk mean in plinko?

High risk means the multipliers at the bottom are spread further apart: the edges pay more, and the cells in the middle pay less. The ball falls exactly as it does on low risk. In the examples on this page both tables come out around 99% in return, but with high risk the losses per round in the middle are larger and the wins at the edges rarer and bigger.

Where do I find the rules for withdrawals before I play?

In the operator's terms, often under headings such as withdrawals, verification or the account. Look for when ID can be demanded, which amount triggers a document requirement, whether there are ceilings per day, week or month, and what period you have for sending documents. Note the clause number, and you will find it again if the question comes up later.