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In turn based games like chess, the player playing the first move has an advantage the whole game. One way to "remedy" this is to let the player starting the game make one move (and have the advantage) but after that, let the players make two moves in a row. The first move to "catch up" the other player's advantage and then the second move to her-/himself get an advantage. Rinse and repeat.

Is chess ever played like this? If yes, how does it differ from regular chess? Is it fairer (=black wins as much as white)? Any other interesting observations about a game like that?

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    There are a couple of well known chess variants that are played that way. In one, check may only be given on the second of your two moves, and the king must get out of check on the first move and may not move through check. In the other variant, the concept of check is abolished, the the game is won by capturing the king.
    – bof
    Dec 5, 2020 at 1:19
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    en.wikipedia.org/wiki/Marseillais_chess
    – bof
    Dec 5, 2020 at 1:21
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    chessvariants.com/multimove.dir/doublemove.html
    – bof
    Dec 5, 2020 at 1:23
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    You may also be interested in the pie rule, another suggested way of dealing with the initial White advantage. This gives Black the option after White has played his first move of requiring that the two players swap sides. Another way is to give Black draw odds: to consider as wins for Black all results that are currently scored as draws. This forces White to play for the win, whereas Black can play for any outcome that according to the normal rules counts as a draw, because they all yield 0-1 exactly as if he checkmates White's king.
    – user18768
    Dec 5, 2020 at 1:53
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    Note that these double-move variants are not just minor adjustments to the game of chess, the play is quite different from standard chess. In view of the common complaint that too many chess games end in draws, the fact that White has a bit of an advantage is probably considered a feature rather than a bug. By the way, there is another variant called progressive chess (or Scottish chess) where White makes 1 move, Black 2 moves, White 3, Black 4, White 5, and so on. The games don't last very many turns, and they rarely end in draws.
    – bof
    Dec 5, 2020 at 2:45

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