Your board
The maths of this board
| Slot | Multiplier | Chance | About 1 in | Share of RTP |
|---|
The ball goes left or right at every peg with equal chance, so the chance of slot k (counted from 0 on the left) on a board with n rows is C(n, k) ÷ 2^n. RTP = the sum of each chance × its multiplier. The chance of being ahead uses a normal approximation, which is rough for a few drops on a high-risk board. The sample tables are our own, not any casino's.
- Maths reviewed by Josh Miller
- Tested by Diana Westfield
On a 16-row Plinko board, the far left slot is a 1 in 65,536 shot. The middle slot is about 1 in 5. The CasinoCalcs Plinko calculator above works out the exact chance of every slot for 8 to 16 rows, then uses the multipliers to give you the RTP, the house edge, and how much a session of drops is likely to swing. It’s free. Start from one of our sample tables or type in the multipliers your game shows.
Plinko probability chart
The ball bounces left or right at every peg with a 50/50 chance, so where it lands follows a binomial curve. Slots in the middle are hit constantly; slots at the edge almost never.
| Rows | Middle slot | Next to middle | Each edge slot |
|---|---|---|---|
| 8 | 27.3% | 21.9% | 1 in 256 |
| 10 | 24.6% | 20.5% | 1 in 1,024 |
| 12 | 22.6% | 19.3% | 1 in 4,096 |
| 14 | 20.9% | 18.3% | 1 in 16,384 |
| 16 | 19.6% | 17.5% | 1 in 65,536 |
Each extra row halves the chance of hitting an edge slot. That’s why the biggest multipliers sit on 16-row high-risk boards: the game can afford to show 1,000x when it lands once in 65,536 drops.
Working out the RTP
RTP is each slot’s chance times its multiplier, added up. Take a made-up 8-row table: 5.6, 2.1, 1.1, 1, 0.5, 1, 1.1, 2.1, 5.6. The chances are 1, 8, 28, 56, 70, 56, 28, 8, 1 out of 256. So the RTP is (2 × 5.6 + 16 × 2.1 + 56 × 1.1 + 112 × 1 + 70 × 0.5) ÷ 256 = 98.98%. House edge 1.02%. You don’t need to do that by hand: paste the numbers into the slot boxes above and the calculator shows it, plus each slot’s share of the return.
The share column is the interesting one. On a high-risk table, a big chunk of the RTP comes from slots you’ll rarely see. On our 16-row high-risk sample, more than a fifth of the RTP comes from the eight outer slots, which catch about 1 ball in 47 between them. That’s not a trick, just how high variance works, but it explains why a high-risk session usually feels worse than the RTP suggests.
Risk level changes the swings, not the price
Our sample tables all return about 99%. On 16 rows, low risk pays more than your bet on 45% of drops, high risk on just 21%. The typical swing over 500 drops at £1 is around ±£8 on low and ±£41 on high, while the average cost is about £4 to £6 either way. Same price, very different ride. The “chance of being ahead” line shows it best.
To watch it happen ball by ball, drop a few hundred on the Plinko simulator. For the other crypto-style games, see the crash game calculator and the mines calculator.
Plinko is fast. A few hundred drops go by in minutes, and so does the money. BeGambleAware.org has free support if it’s getting out of hand.