According to https://arcadeblogger.com/2021/01/31/anatomy-of-arcade-high-score-tables/ who is quoting Atari’s Steve Calfee, the **main** reason for the 3-character-limit was to prevent profanity.
English has a lot of colorful 4-letter-words.
Memory is a factor, but it is an arbitrary factor. There is no hardware reason why allowing 3 would save you an incredible amount of memory over allowing 4. *Usually* a high score entry (that is Initials + Score) will keep it under 12 bytes; but that kind of limitation would also quickly have become legacy. If an arcade machine maker would have wanted to allow 4 characters, they would have been able to. The ‘profanity prevention’ explanation makes a whole lot more sense.
There’s also the issue of legibility and competetiveness. Fewer characters means more easily readable high score tables with more space for entries and more space for larger score values, making players more competetive, making more money.
Memory.
Imagine computer memory like a whiteboard. You can play a game – but only if ALL of the rules of the game, and anything that needs to be remembered, and anything else for the game can all be written on the whiteboard.
Modern computers have MASSIVE whiteboards. Some of them can have more written on them than an entire library worth of books. But older computers had less space; and when you’re limited in space, you’ve got to limit how much space you use for anything – and so they squeezed the high score section in a little corner of the whiteboard and limited how much you could write there.
In addition to memory constraints, arcade games were generally popular and often had lineups of people waiting to play, so the faster you got players off of the cabinet, the more money the game could make.
Limiting the time it took for players to enter their name on the high score board with a joystick made the game more profitable.
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