OneTaskBy Tim King · Updated
Plinko Game
Drop Balls Down a Peg Board and Watch Where They Land
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How the Plinko Game works
This Plinko game drops balls through a field of pegs. Click above the pegs to drop a ball and watch it clatter down to one of the bins at the bottom, or press Drop 100 balls and watch the bins fill up. Each bin shows a running count and the panel on the right keeps the totals. Change the number of rows, the ball size and how bouncy the balls are while it runs, drag any ball with the mouse, and go fullscreen to fill the screen.
Plinko game: what it does and why
Plinko is the peg board from The Price Is Right, and its older name is the Galton board or bean machine, built by Francis Galton in 1873 to show how a bell curve appears out of pure chance. A ball hitting a peg bounces left or right with roughly equal odds, so after twelve rows it has made twelve coin flips. The bin it lands in is the number of rightward bounces, and the number of ways to get each total follows the binomial distribution: there is only one path to the far left bin, twelve paths to the next one, and 924 paths to the middle. Drop enough balls and the counts settle into that shape.
Why it is not perfectly symmetric. This board is a real physics simulation rather than a coin-flip model, so a ball can skid along a peg, ricochet off a neighbour, or land on top of another ball still rolling into a bin. That is exactly what happens on a physical board, and it is why the outer bins get slightly more traffic than the pure binomial predicts. Turning the bounciness down makes the balls behave more like the idealised model; turning it up makes the board livelier and the spread wider.
The sliders. Rows sets how many rows of pegs there are and therefore how many bins. Changing it rebuilds the board and clears the counts. Ball size relative to the peg spacing changes how often a ball falls straight through a gap rather than deflecting, which also narrows or widens the curve. The Pause button freezes everything mid-fall, Save PNG grabs the current frame, and Reset returns the sliders to their defaults.
Reading the numbers. Landed counts the balls that have come to rest in a bin. Most common bin is the mode, which is almost always the middle bin or one beside it. Centre bins is the share of balls in the middle two or three bins, which for a twelve-row board sits around 45 percent once a few hundred balls have dropped. Everything runs in your browser; no data is sent anywhere.
FAQ
Why do most balls land in the middle bins?
Each peg is roughly a coin flip, so a ball's bin is the number of rightward bounces it made. There is only one path to the far-left bin but hundreds to the middle ones, which is the binomial distribution and the reason a bell curve appears after enough drops.
Why are the counts not perfectly symmetric?
The board is a physics simulation, not a coin-flip model. Balls skid along pegs, ricochet off each other and land on balls still rolling into a bin, so the outer bins get slightly more traffic than pure probability predicts. Lower bounciness brings it closer to the ideal.
What does changing the ball size do?
Ball size is relative to the peg spacing. A small ball often falls straight through a gap rather than deflecting, which narrows the curve; a large ball hits nearly every peg and spreads wider.
Why do the counts reset when I change the rows?
Changing the number of rows rebuilds the board with a different number of bins, so the old counts no longer map onto the new layout. Ball size and bounciness change without a rebuild.
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