Peg Drop

Reading the peg board’s distribution

Twelve coin flips in a row

The ball enters at the top and passes twelve rows of pegs. At each row it goes left or right, and after twelve such decisions it lands in one of thirteen slots — one for each possible count of right-hand bounces from zero through twelve.

That structure is exactly twelve coin flips. Landing in the leftmost slot requires twelve consecutive lefts, which happens once in 4,096 drops. Landing in the centre requires six of each in any order, and there are 924 different ways to arrange that — which is why the middle is so much more common.

The multipliers mirror this: the edges pay 50× and the centre pays 0.2×. The board is priced against the distribution, not against how the drop looks.

There is nothing to decide, and that is the lesson

Every ball enters at the same point and no input affects the bounces, so there is no strategy in the ordinary sense. The only variable you control is your stake.

What is genuinely worth taking from this game is the shape of the distribution, because it explains an enormous amount about probability generally. The most likely single outcome — the centre slot — is a loss of eighty percent of your stake. The outcome that pays 50× is real, reachable, and will not happen in a typical session.

The counter-intuitive part is that the board is close to fair in aggregate despite feeling relentless. A theoretical return of just over ninety-five percent is spread across a distribution where you lose a little most of the time and win enormously almost never. That mismatch between what a game feels like and what it returns is the single most useful thing to internalise about casino mathematics.

Every slot, with its true odds

The number of ways to reach each slot is a row of Pascal’s triangle, and the chance of any slot is that count divided by 4,096. The theoretical return of 95.0879 percent is not a target — it is what you get when you multiply each multiplier by its exact probability and add them up.

Common mistakes

The board invites pattern-seeking precisely because you can watch every bounce happen.

• Expecting the edges because they are visible. A 50× slot is reached once in 4,096 drops — you can see it on the board and still never reach it in a session.
• Reading a run of centre landings as due for a change. Each drop is twelve fresh independent bounces with no memory of the last ball.
• Thinking the ball can be influenced. Every drop starts identically and nothing you do changes the bounces.
• Treating the centre as a small loss. At 0.2× it returns a fifth of your stake, and it is the single most likely outcome on the board.

What is different about this version

Each bounce is an independent random decision rather than a physics approximation tuned to produce a target distribution. That means the slot probabilities are genuinely binomial — the counts in the table above are Pascal’s triangle exactly, not an approximation of it, and the published return follows arithmetically from them.

The full path is recorded and drawn, so you can see all twelve decisions that produced the result. That transparency is unusual: it means the distribution is not something you have to take on trust, because every drop shows its own derivation.

Written by the Silverweb Games team from this game’s own implementation. Last reviewed July 31, 2026.