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How I spotted problems by first hamnd experience, and used it.
In the old days, before the NES, Most people were trying to accommodate both left and right handers on their own default sticks. Intellivision had 3 buttons, with one button mirrored on left and right. Colecovision had 2 buttons. Colecovision Super Action Controllers had a 4 button + roller ambidextrous style. It's vertical style is brilliant because it always made your main trigger on your index finger. But its downfall are games where you have to actively manual repeat fire, your fingers could get tired. But if you held down the buttton, it was good. Atari 5200 had 4 buttons, 2 tops were mirrored, and 2 bottoms were mirrored, which is one of the brilliant ideas behind the stick, because your index finger is the main trigger and that same hand's thumb is the auxiliary trigger on either hand hands.
Even the Atari 2600 and 400/800 had solutions. They fall in 3 categories. One is a "gender bender" that went between the Atari stick and console which rotated your stick 90 degrees and put the fire button by your right thumb. The second, used by third parties, made 2-button controllers. one for the left thumb, one for the right thumb. And a third solution used in the Atari computers was a software-based left hand mode where pressing L (Shift L for player 2) shifted that player into letting you rotate the stick 90 degrees.
Nintendo made a good catch all-device in their control pad, which was cheap, durable, and a good base controller. When they made their Advantage, they made it so it copied their d-pad. They didn't think of making a left and right hand version or an ambidextrous version. One third party, Beeshu, decided to improve the stick by making it right handed. For some reason, Nintendo never licensed it. They licensed other stuff. At first I thought they were actively squelching right-handed designs. I don't know the real reason why it's not licensed.
The Sega Master System had an official right handed joystick, but a left handed pad. You have 2 choices for buttons, for Tutankham where the is a left fire and right fire, the setup Sega used made sense, but for pretty much every other game that absolute design was awful because your main fire button is still on the left, and rapid firing with your middle finger sucks. For most of their games, a relative design would have worked better too. Unauthroized Beeshu to the rescue. Turbo Grafx 16 had enough sense to license a Beeshu joystick for their system. And they had the relative to the index finger model, where 1 and 2 were swapped absolutely, but relative to the index finger, it makes sense for most games. The only game I know of it does not work well with right handed is Side Arms, where the left fire button shoots right and vice versa, and Pac-Land. where the buttons on the left are reversed. (right to run left)
Since the Genesis and SNES, it became impractical to make fight sticks ambidextrous. With 6+ buttons, button contour became important. You had to either make buttons on both sides, or a joystick on both sides, but the buttons had to be contoured right. And Street Fighter had on some arcade machines a left-vs-right setup. So if there was a time to release an ambidextrous joystick, THAT would have been the time. But most people couldn't think of a design that worked well enough with both hands.
I believe that if it were fairly easy to make an ambidextrous design, it would attract more people for the following reasons. 1) Newcomers haven't picked a side yet, so they don't have that much dedicated muscle memory towards the game. 2) people over 40 years of age have muscle memory with a right handed stick for certain games and left handed for other games, so an ambidextrous stick could save having to buy 2 separate sticks, I admit I have Left-hand Muscle memory from Simpsons Arcade, and I'm the Simpsons Arcade one credit world record holder on actual hardware, so for THAT game, I don't want to learn it right handed. This is to show I can do left handed well, despite my obstacles. But for most games I haven't developed joystick memory for, I'd prefer right-handed. and 3) If there were an easy, cheap, and reasonably contoured way to accommodate left and right hands, then it would be a no brainer where you can advertise "play both left and right handed", "Guaranteed better scores with a right handed setup or you get a good left handed one included free." especially if all you have to add is 1 button to make the contour correct both ways. And that would make a good select button for games using select as taunt and Mega Man using it as weapon select menu.