These numbers are not estimates. The path of a ball through a pin field is a sequence of coin flips, so the chance of every landing spot follows directly from the binomial distribution.
At each of the rows the ball moves left or right. With sixteen rows there are sixteen such decisions, and the slot it lands in is decided by how many went right. There is exactly one way to go right every single time — which is why the far edge is so rare — and thousands of ways to split evenly, which is why the centre is so common.
The far edge slot, the one carrying the headline multiplier, comes up once in about sixty-five thousand drops.
| Landing spot | Chance per drop | Roughly |
|---|---|---|
| edge | 0.0015% | 1 in 65 536 |
| slot 1 | 0.0244% | 1 in 4 096 |
| slot 2 | 0.1831% | 1 in 546 |
| slot 3 | 0.8545% | 1 in 117 |
| slot 4 | 2.78% | 1 in 36 |
| slot 5 | 6.67% | 1 in 15 |
| slot 6 | 12.22% | 1 in 8 |
| slot 7 | 17.46% | 1 in 6 |
| centre | 19.64% | 1 in 5 |
The table shows one half; the other side is a mirror image. Add both sides together for the chance of landing that far out in either direction.
| Landing spot | Chance per drop | Roughly |
|---|---|---|
| edge | 0.0244% | 1 in 4 096 |
| slot 1 | 0.2930% | 1 in 341 |
| slot 2 | 1.61% | 1 in 62 |
| slot 3 | 5.37% | 1 in 19 |
| slot 4 | 12.08% | 1 in 8 |
| slot 5 | 19.34% | 1 in 5 |
| centre | 22.56% | 1 in 4 |
| Landing spot | Chance per drop | Roughly |
|---|---|---|
| edge | 0.3906% | 1 in 256 |
| slot 1 | 3.12% | 1 in 32 |
| slot 2 | 10.94% | 1 in 9 |
| slot 3 | 21.88% | 1 in 5 |
| centre | 27.34% | 1 in 4 |
On sixteen rows at high risk, the outer slots are where the thousand-times multipliers sit. One in sixty-five thousand drops means that at one drop every four seconds, without pause, you would expect to see it about once every three days. Meanwhile the centre slots — which on high risk usually pay less than the stake — account for the large majority of every session.