![]() ![]() The first thing that should be apparent is the normal-like nature of the first graph, and the increasingly skewed nature of the following graphs as the puck starts out closer and closer to the sidewall. The graphs for the left side would be symmetric but skewed in the other direction. Keep note that the y-axis does change on these graphs, and that the graphs also only reflect the right side of the board. With this information it's pretty easy to calculate the cascading odds of the puck being in any given position on the board based on the gate in which it starts, and the probability that it will fall in any of the prize gates given that same starting gate. I think this is also the spirit of what a pegboard is meant to do. For any single collision that is certainly at least a little off, but over the course of the path through the board I suspect those random differences should more or less cancel out. ![]() The big assumption that I'm going to make here is that when the puck hits a peg it has a 50/50 chance of falling to either the left or the right. We'd need to know the coefficient of friction between the puck and board, the slope of the board, the elasticity of the collision between the puck and pegs, the relative size of the puck and the pegs, and the starting velocity of the puck (the idea is to drop it from stationary, but a contestant could easily impart some force when letting it go). Now, if we knew a lot more about the board we could get a lot more accurate. The idea of the pegboard is pretty simple, and we can make some assumptions about the way the puck travels down it that should help approximate what's happening. I've numbered them starting at the center, and if we assume that the board doesn't have any problems the gates should produce symmetric results about the center. The green areas up top are the the different gates that contestants can drop the puck through at the beginning of the game. If you're not familiar, Plinko is a game where contestants can earn a number of little round disks (think hockey pucks but a little larger diameter, maybe a touch thinner) which they then drop down a pegboard with different valued gates at the bottom. In thinking of where to start with something like this I couldn't help but pass up perhaps the most well known game on The Price is Right, Plinko. In short, The Price is Right is full of examples of and opportunities for the use of practical statistics. I've been watching The Price is Right since very early in my childhood, so it's always very painful to see people on it who aren't familiar with the strategies of different games, or even just of some of the basic probabilities underlying those games. Through this, I suspect that The Price is Right is many children's first exposure to some fairly deep probability and statistics. It's certainly among the most well known game shows of all time, and its placement during daytime TV makes it a wonderful time sink for children. Just yesterday, The Price is Right celebrated its 40th anniversary. ![]()
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