# Pinball Algorithms

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 early versions of this algorithm were crude, essentially targeting a weighted moving average. But later implementations were more sophisticated. The goal was to ensure that a fixed percentage, say the top 5% of all scores would win a free game. The score level that would implement this varies with the machine, location, and time. The algorithm would compute a histogram of scores and set the replay threshold at the empirical cutoff of 5%. Later designs would allow the threshold to rise quickly to combat the wizard-goes-to-the-cinema problem. The WGTTC problem is where a machine has adjusted down to a low replay score because it is mostly played by novices. Then anytime an above average player gets on the machine, he’s getting free games all day long.

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.

(The tilt tolerance, by contrast has always been controlled by a physical device which is adjusted manually and rarely in response to user habits.)

Pinball attracted a different crowd than video games like Defender (my new pal designed Defender and Stargate too,) and this is the fundamental theorem of pinball economics. Pinball skill is transferrable. If you can pass, stall, nudge, and aim on one machine you can do it on any machine. This is both a blessing and a curse for pinball developers. The blessing is that pinball players were a captive market. The curse was that to keep the pinball players interested the games had to get more and more intricate and challenging.

Pinball developers struggled with this problem as pinball was slowly losing to video games. Video games competed by adding levels of play with increasing difficulty. Any new player could quickly get chops on a new game because the low levels were easy. This ensured that new players were drawn in easily, but still they were continually challenged because the higher levels got harder and harder. By contrast, the physical nature of pinball, its main attraction to hardcore players, meant that there was no way to have it both ways.

Eventually, to keep the pinballers playing, the games became so advanced that entry-level players faced an impossible barrier. High-schoolers in 1986 were either dropouts or professionals in 1992 and without inflow of new players that year essentially marked the end of pinball. In 1992 The Addams Family was the last machine to sell big. By this time, pinball machines used a free-game system called replay boost. After any replay, the score required was increased by some increment. Apparently, only hardcore pinballers were left and this was the only way to prevent them playing indefinitely for free.

## Notes:

Folksonomies: computer science history

Taxonomies:
/technology and computing/hardware/computer components (0.780293)
/technology and computing/hardware/computer (0.765602)

Concepts:
Game (0.957090): dbpedia_resource
Economics (0.750774): dbpedia_resource
Play (0.716425): dbpedia_resource
Players (0.685242): dbpedia_resource
Electronic game (0.676697): dbpedia_resource
Player (0.653817): dbpedia_resource
Moving average (0.613542): dbpedia_resource