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Since AlphaGo's original training was to predict human moves, it should know how surprising a move is in addition to knowing how strong it is. My thought at the time was it could improve its game against humans by giving surprise value some weight -- when it can pick a slightly weaker but highly surprising move, pick the surprise.

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It definitely does know how surprising a move is - it generates 'surprisingness' numbers for both itself and its opponent based on how likely it is a human pro would have come up with the move.

I like your idea of maximising the 'alienness' of play though probably not to the exclusion of playing the strongest moves.

You're probably right, if they were optimizing for short-term win rate vs humans. The real goal is to advance the state of the art in AI though, in which case you wouldn't want to use 'cheats' like that to make the problem easier.

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