Northwestern economics professor Jeff Ely has a fun post on his blog about the economics of pinball:
In 1986, Williams High Speed changed the economics of pinball forever. Pinball developers began to see how they could take advantage of programmable software to monitor, incentivize, and ultimately exploit the players. They had two instruments at their disposal: the score required for a free game, and the match probability. All pinball machines offer a replay to a player who beats some specified score. Pre-1986, the replay score was hard wired into the game unless the operator manually re-programmed the software. High Speed changed all that. It was pre-loaded with an algorithm that adjusted the replay score according to the distribution of scores on the specified machine over a specific time interval. ...
The other tool is the match probability: you win a free game if the last two digits of your score match an apparently random draw. While adjustments to the high-score threshold is textbook price theory, the adjustments to the match probability is pure behavioral economics. Let’s clear this up right away. No, the match probability is not uniform and yes, it is strategically manipulated depending on who is playing and when. For example, if the machine has been idle for more than three minutes, the match probability is boosted upward. You will never match if you won a free game by high score. And it gets more complicated than that. Any time there are two or more players and they finish a game with no credits left, one player (but only one) is very likely to match. Empirically, the other players will more often than not put in another quarter to play again.
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