These are not estimates. A ball's path through a pin field is a sequence of coin flips, so every landing chance follows directly from the binomial distribution.
At each row the ball moves left or right. With sixteen rows that is sixteen decisions, and the slot it lands in depends on how many went right. One path leads to the far edge; 12 870 lead to the centre.
| Landing spot | Chance per drop | Roughly once in |
|---|---|---|
| far edge | 0.0015% | 65 536 |
| slot 1 from the edge | 0.0244% | 4 096 |
| slot 2 from the edge | 0.1831% | 546 |
| slot 3 from the edge | 0.8545% | 117 |
| slot 4 from the edge | 2.78% | 36 |
| slot 5 from the edge | 6.67% | 15 |
| slot 6 from the edge | 12.22% | 8 |
| slot 7 from the edge | 17.46% | 6 |
| centre | 19.64% | 5 |
The table shows one half of the board; the other is a mirror. Add both sides for the chance of landing that far out in either direction.
| Landing spot | Chance per drop | Roughly once in |
|---|---|---|
| far edge | 0.0244% | 4 096 |
| slot 1 from the edge | 0.2930% | 341 |
| slot 2 from the edge | 1.61% | 62 |
| slot 3 from the edge | 5.37% | 19 |
| slot 4 from the edge | 12.08% | 8 |
| slot 5 from the edge | 19.34% | 5 |
| centre | 22.56% | 4 |
| Landing spot | Chance per drop | Roughly once in |
|---|---|---|
| far edge | 0.3906% | 256 |
| slot 1 from the edge | 3.12% | 32 |
| slot 2 from the edge | 10.94% | 9 |
| slot 3 from the edge | 21.88% | 5 |
| centre | 27.34% | 4 |
On sixteen rows at high risk the headline multiplier sits behind odds of one in sixty-five thousand. At one drop every four seconds without pause, that is roughly once every three days. Meanwhile the centre slots — paying below the stake on that setting — take the large majority of every session.