That is not really a variant. Blitz Chess rules used to be that way, where I live. And announcing check is considered an insult in the first place, amongst serious players, like they would be to dumb to see it themselves...
Chess with no checks - is there such a variant
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I'm trying to figure out whether there is an actual known variant like this.
The only difference from regular chess is that there are no checks. You do not announce anything when you make a move that puts the opponent's king in threat. If you blunder your king by not noticing that it's under threat, or if you blunder it by making a move that puts your own king under threat, and your opponent notices that, then they can just capture your king and the game is over.