What it was
A videotape format created by Sony that enabled people to record their favourite programmes and rent pre-recorded ones, which was launched shortly before VHS.
Why it lost
Betamax never had the support of enough hardware companies to flourish, keeping the price of the hardware high and allowing VHS to undercut it. It was also harder to rent movies on Beta -- video stores had walls of VHS, but a much smaller selection on Betamax.
The lack of pre-recorded material meant the decks were most useful for home recording, but initially Betamax could only record for 60 minutes. This was rectified eventually, but it was a serious limitation. Ludicrous tape-changing mechanisms were launched to swap tapes when one became full, but this was hardly an ideal solution -- especially in light of Matsushita and RCA's four-hour Long Play system.
Why it should have won
Betamax was better than VHS in a number of ways. The tapes were smaller and the recorders were able to reproduce colour better than their rivals. They were also not unthreaded from the heads during fast-forward and rewind, which meant the Betamax decks responded better, returning to play or fast-forward quicker than VHS (although it couldn't spin the tape as fast).
Betamax also had a nifty trick that enabled 'bookmarking' at certain parts of the tape. Called APS, or Auto Programme Search, it was possible because the tape was always in contact with the play head. Essentially, the recorder put an electronic marker on the tape. When APS mode was engaged during fast-forward, the player would stop the tape at the start of each recording, negating the need to keep stopping the tape, pressing play to see where you were and then forwarding some more.
One of the last Betamax recorders released, the SL-HF2100, was one of the most sophisticated video recorders when it was released in 1991. It had features that put it far ahead of its time, including not having a single button anywhere on it. Everything was controlled with touch-sensitive displays and a funky LCD remote control with virtual buttons.
Our fantasy outcome
To win the format war for Betamax, Captain Tech would need to disco back to the 70s, win the support of the adult-entertainment industry and persuade them to release movies on Betamax instead of VHS.