Plinko calculator

Three examples, worked out

1. How likely is an edge hit in 1,000 drops on 16 rows? One specific edge slot comes up with probability 1/65,536. There are two edges, so the chance per drop is 1/32,768. The chance of at least one edge hit in 1,000 drops is 1 − (1 − 1/32,768)¹⁰⁰⁰ ≈ 3.0%. In other words, about 97 out of 100 players who drop 1,000 balls never see an edge slot.

2. What if the big payouts sit on the two outermost slots on each side? Suppose your 16-row High table pays its two biggest multipliers on slots 0, 1, 15 and 16. Together those four slots have a probability of 34/65,536, about 1 in 1,928 per drop. Over 1,000 drops the chance of at least one hit is about 40.5%. Set a target in the Hit chance tab to see which slots of your table pay that much.

3. How many drops for a 50% chance of an edge slot on 16 rows? Solve 1 − (1 − p)ⁿ = 0.5 with p = 1/32,768: about 22,700 drops. For a 90% chance, about 75,500. At $1 per drop, that’s tens of thousands of dollars wagered, with an expected loss of the total wagered times the house edge along the way.

Expected loss in plain words

Expected loss = total wagered × (1 − RTP). With an RTP of 99%, 1,000 bets of $1 cost $10 on average. That’s the average across many players. Your own session can end far above or far below it; the Bankroll tab shows the typical range, and the simulator shows the full picture including the chance of going bust.

The formulas

• Probability of slot k on n rows: P(k) = C(n, k) / 2ⁿ
• RTP: Σ P(k) × multiplier(k)
• At least one hit in N drops: 1 − (1 − p)ᴺ
• Drops needed for a target chance q: N = ln(1 − q) / ln(1 − p)

Choose the event before calculating a hit chance

A slot, either edge and a target multiplier are different events. When several slots pay at least your target, their probabilities are added before calculating the session chance. A threshold absent from the selected table has zero hit probability, even if another operator offers that multiplier. Match the rows, risk and captured table before comparing results.

A profitable drop returns more than the stake. A payout below 1× still credits something, but it is a net loss on that drop. RTP includes every total-return multiplier, while expected net profit subtracts the original stake. These distinctions explain why a frequent payout and a favourable average return are not the same statistic.

Know when to use a simulation instead

The chance of a target hit over a fixed number of independent drops does not include a bankroll stopping rule. If you cannot fund all planned drops, actual exposure can be lower. The Bankroll tab uses an approximation; rare payouts can make its range unreliable for a short session. Use the fixed-bet simulator to inspect early stopping and the spread of ending balances, and keep its sampling estimates separate from the exact board probabilities.