Plinko RTP, derived from scratch.

Every multiplier on the Plinko simulator comes from one formula: a coin-flip probability, priced by a studio to hit a target return. Here's the full binomial derivation — no shortcuts, every number computed live on this page.

01 / The binomial distribution

A ball is just n coin flips in a row.

At every peg, the ball bounces left or right with equal (50/50) probability — exactly like a fair coin. Over n rows, the ball has made n independent left/right decisions, and the number of ways it can land in bucket k (k rights out of n flips) is the binomial coefficient C(n,k) — the same count used in Pascal's triangle. Divide by the total number of paths, 2ⁿ, and you get the exact landing probability for every bucket.

8 rows — path counts per bucket, C(8,k)

Bucket 0 — C(8,0)1 of 256 paths (0.39%)

Bucket 1 — C(8,1)8 of 256 paths (3.13%)

Bucket 2 — C(8,2)28 of 256 paths (10.94%)

Bucket 3 — C(8,3)56 of 256 paths (21.88%)

Bucket 4 — C(8,4)70 of 256 paths (27.34%)

Bucket 5 — C(8,5)56 of 256 paths (21.88%)

Bucket 6 — C(8,6)28 of 256 paths (10.94%)

Bucket 7 — C(8,7)8 of 256 paths (3.13%)

Bucket 8 — C(8,8)1 of 256 paths (0.39%)

Notice the shape: it peaks in the centre (bucket 4, reachable 70 ways) and shrinks toward the edges (bucket 0 or 8, reachable only 1 way each). That shape is fixed by the coin-flip math — no studio can change it without changing the number of rows.

02 / Full derivation — 12 rows, medium risk

Every bucket's contribution, added up to one RTP.

RTP is just Σ P(k)·multiplier(k) — the probability of each bucket, times its payout, summed across every bucket. Here's that sum computed in full for the 12-row, medium-risk table.

Bucket	Ways, C(12,k)	P(k)	Multiplier	Contribution
0	1	0.024%	33×	0.806%
1	12	0.293%	11×	3.223%
2	66	1.611%	4×	6.445%
3	220	5.371%	2×	10.742%
4	495	12.085%	1.1×	13.293%
5	792	19.336%	0.6×	11.602%
6	924	22.559%	0.3×	6.768%
7	792	19.336%	0.6×	11.602%
8	495	12.085%	1.1×	13.293%
9	220	5.371%	2×	10.742%
10	66	1.611%	4×	6.445%
11	12	0.293%	11×	3.223%
12	1	0.024%	33×	0.806%

Sum of the contribution column98.99% RTP

03 / Why it always lands near 99%

It's not a coincidence — it's the design goal.

The path probabilities (P(k)) are fixed by the coin-flip math and can't be changed. What a studio does control is the multiplier attached to each bucket — and they pick those numbers specifically so the weighted sum lands near a target RTP, almost always ~99% for Plinko. That's why every row/risk combination on this site clusters so tightly around the same figure: it's engineered to, not a lucky accident of the math.

Probabilities are fixed

C(n,k) ÷ 2ⁿ never changes for a given row count — it's pure combinatorics, the same for every casino.

Multipliers are chosen

A studio solves backward from a target RTP to find multiplier values that make Σ P(k)·multiplier(k) hit that target.

Different studios, different numbers

Stake, BC.Game and BGaming each solve that equation independently — same target, different specific multiplier tables.

04 / Full breakdown — 16 rows, high risk

The widest spread on this site, bucket by bucket.

Bucket	P(k)	Multiplier
0	0.0015%	1,000×
1	0.02%	130×
2	0.18%	26×
3	0.85%	9×
4	2.78%	4×
5	6.67%	2×
6	12.22%	0.2×
7	17.46%	0.2×
8	19.64%	0.2×
9	17.46%	0.2×
10	12.22%	0.2×
11	6.67%	2×
12	2.78%	4×
13	0.85%	9×
14	0.18%	26×
15	0.02%	130×
16	0.0015%	1,000×

The 1000× bucket lands only 0.0015% of the time — roughly 1 in 65,536 drops. What that drought actually feels like in a session is covered in the variance walkthrough.98.98% RTP

05 / Platform guides