In Plinko, a ball falls through a triangle of pegs and makes one left-or-right bounce at each row. Where it lands depends only on how many of those bounces went right, which is why the landing slots follow a binomial distribution: the middle is common, the edges are rare.
This guide explains the board, shows exactly where the slot odds come from, and gives the full probability table for 8, 12 and 16 rows. Every figure here was recomputed with a short script before publishing.
The board in one paragraph
An online Plinko board has a number of rows of pegs, usually somewhere between 8 and 16. Under the last row is a line of slots, and each slot shows a multiplier. You set a stake, drop a ball, and are paid stake × the multiplier of the slot it lands in. A board with n rows always has n + 1 slots. Large multipliers sit at the edges; small ones (often below 1×) sit in the middle.
Most games also offer a risk level (low, medium, high). Risk doesn't move the ball; it changes the multipliers printed on the slots. We cover that in Plinko risk levels and multiplier tables.
One bounce per row
Treat each row as a coin flip: the ball goes left or right, 50/50, and each bounce is unaffected by the last. After n rows, the ball has made n choices.
The slot it lands in is simply the number of right bounces, counting slots from 0 on the far left. Zero rights means the far-left slot. All rights means the far-right slot. Four rights out of eight means the centre slot on an 8-row board.
That's the whole model. Online games don't simulate physics; they draw random left/right decisions (or a single random slot with the same odds) and then animate a ball to match.
Counting paths
Every specific sequence of bounces is equally likely. With 8 rows there are 2⁸ = 256 sequences, each with probability 1/256.
The question is how many of those sequences end in each slot. The number of ways to choose k rights out of n rows is the binomial coefficient C(n, k). So:
P(slot k) = C(n, k) ÷ 2ⁿ
Worked example: 8 rows
- Edge slot (k = 0). Only one path: left eight times. C(8, 0) = 1, so the chance is 1/256 = 0.39%.
- Next slot (k = 1). One right bounce, which can happen at any of the 8 rows. C(8, 1) = 8, so 8/256 = 3.13%.
- Centre slot (k = 4). C(8, 4) = 70 paths, so 70/256 = 27.34%.
The centre is 70 times more likely than either edge, purely because more paths lead there. Nothing about the pegs is "pulling" the ball to the middle.
Slot probability tables
The tables below list every slot, numbered from the left edge. Boards are symmetric, so slot k and slot n − k always have the same odds.
8 rows (9 slots)
| Slot | Paths C(8,k) | Probability | About 1 in |
|---|---|---|---|
| 0 / 8 | 1 | 0.391% | 256 |
| 1 / 7 | 8 | 3.125% | 32 |
| 2 / 6 | 28 | 10.938% | 9.1 |
| 3 / 5 | 56 | 21.875% | 4.6 |
| 4 (centre) | 70 | 27.344% | 3.7 |
| Total | 256 | 100% |
(The total counts each mirrored pair twice: 2 × (1 + 8 + 28 + 56) + 70 = 256.)
12 rows (13 slots)
| Slot | Paths C(12,k) | Probability | About 1 in |
|---|---|---|---|
| 0 / 12 | 1 | 0.0244% | 4,096 |
| 1 / 11 | 12 | 0.293% | 341 |
| 2 / 10 | 66 | 1.611% | 62 |
| 3 / 9 | 220 | 5.371% | 18.6 |
| 4 / 8 | 495 | 12.085% | 8.3 |
| 5 / 7 | 792 | 19.336% | 5.2 |
| 6 (centre) | 924 | 22.559% | 4.4 |
| Total | 4,096 | 100% |
16 rows (17 slots)
| Slot | Paths C(16,k) | Probability | About 1 in |
|---|---|---|---|
| 0 / 16 | 1 | 0.0015% | 65,536 |
| 1 / 15 | 16 | 0.0244% | 4,096 |
| 2 / 14 | 120 | 0.183% | 546 |
| 3 / 13 | 560 | 0.854% | 117 |
| 4 / 12 | 1,820 | 2.777% | 36 |
| 5 / 11 | 4,368 | 6.665% | 15 |
| 6 / 10 | 8,008 | 12.219% | 8.2 |
| 7 / 9 | 11,440 | 17.456% | 5.7 |
| 8 (centre) | 12,870 | 19.638% | 5.1 |
| Total | 65,536 | 100% |
What the tables tell you
More rows, rarer edges. Each extra row halves the chance of any one edge slot. On 16 rows, a single edge slot comes up about once in 65,536 drops. That's why 16-row boards can print enormous edge multipliers: they almost never pay them.
More rows, wider spread, flatter middle. The centre slot falls from 27.3% (8 rows) to 19.6% (16 rows), but the ball still lands in the middle few slots most of the time. On 16 rows, the five central slots (6 to 10) take about 79% of all drops.
The shape doesn't decide the return. The binomial odds are the same on every fair board with the same row count. What changes between games, and between risk levels, is the pay table. The return (RTP) is the probability-weighted average of the multipliers, which we calculate step by step in Expected value and variance of a Plinko drop.
A quick reality check (fictional session)
Fictional example. Say a player drops 200 balls on an 8-row board. Using the 8-row table, the expected counts are roughly: 55 in the centre slot, 87 in slots 3 and 5 together, 44 in slots 2 and 6, 12–13 in slots 1 and 7, and about 1.6 across both edges. A real session will scatter around those numbers. Seeing zero edge hits in 200 drops is normal: the chance of that is (1 − 2/256)²⁰⁰ ≈ 21%.
Before you play: a short checklist
- Find the row count and risk level you're on, and the multipliers for every slot.
- Look for the published RTP for that exact combination. If none is shown, treat that as a warning sign.
- Know where 1× is. Count how many slots pay below your stake; on many tables most drops lose part of the stake.
- Check the fairness info. See how provably fair Plinko maps a hash to a path.
- Set a limit first. Plinko is gambling. Over many drops the pay table's built-in edge works against you.
Summary
Plinko is a sequence of left/right coin flips drawn as a pegboard. The landing slot is the number of right bounces, so slot odds follow C(n, k) ÷ 2ⁿ. The middle is common, the edges are very rare, and the pay table, not the board, sets your long-run return. For the most common misunderstandings, read Plinko myths, checked against the math.
FAQ
Why do most Plinko balls land in the middle?
Because there are many more left/right paths that end in the middle than at the edges. With 8 rows, 70 of the 256 equally likely paths end in the centre slot, but only one path ends in each edge slot.
How often does a ball land in an edge slot?
With fair 50/50 bounces, a given edge slot is hit once in 256 drops on 8 rows, once in 4,096 on 12 rows and once in 65,536 on 16 rows. Either edge doubles those chances.
Does adding rows change the house edge?
Not by itself. Rows change the shape of the distribution; the house edge comes from the pay table that is set for each row count. Each row/risk combination has its own table and its own return.
Is online Plinko a real physical board?
No. Online Plinko is a random number generator drawn as a board. The animation shows a result that the number generator has already decided.