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Chess variant that allows humans to be competitive vs computers

It seems that computers can beat the majority of chess players out there, and at the current rate in which distributed computing is going, it seems like the #1 chess player out there will be computers these days.

However, this is different with Go, as the best AI available out there cannot beat a decent player.

Are there any chess variants, which while still maintaining some sort of similarity with chess, cannot be effectively played by a computer, while still playable by humans at a level better than AIs?

I was thinking a bigger board with more pieces would help, but rules changes might be needed as well to change the gameplay a bit. But I suppose the further you drift from the original chess game, the less interest people might have on it.