Thinking time charts for AlphaGo vs Lee Sedol

[yoyoma]

Credit https://www.reddit.com/user/junkwhinger

Reddit thread for Game 1
Reddit thread for Game 2

Inline images below, click the links for better resolution versions. On those you can see the move numbers but they are full-ply, multiply by 2 to get the traditional move numbers. y-axis is in seconds.

Game 1

The biggest spike for Lee at move 52 was answering AlphaGo's invasion of the right side. You can also see that after that long think, AlphaGo answered very quickly. We know AlphaGo uses the opponent's time to continue thinking, and even though Lee though for a very long time his move was to be expected. So AlphaGo had enough time to decide that move already.

Game 2

The spike for Lee's 19th move is him thinking how to respond to AlphaGo's unusual 5th line shoulder hit.

Game 3

AlphaGo spent the most time on White 61 aka White 122 -- connecting 4 white stones in a squeeze on the right. Not sure why it would think so much at that point... AlphaGo's quickest move was 71 aka 142 -- blocking a push by Black. Makes sense that it could answer quickly there.

Game 4


ETA: We don't have detailed information on AlphaGo's assessment of it' winning chances, but I wonder if you can tell something about the tailing off of time near the end. In Game 1 you can see a clear downward trend in time usage after White 71 aka White 142, which secured the life of white's corner in the lower right. This is also consistent with an article I saw that said the Google folks saw the evaluation of the game go up around 30 minutes before the end of the game. In Game 2 you see something similar with Black 80 aka Black 160, where Black initiates a sequence to seal off a good chunk of center territory.

[mika]

Has there been any information or educated guesses as to how AlphaGo manages it's time? The commentators seemed to think it sometimes takes a lot of time to think about 'obvious' moves. I'm wondering if it has some set minimum limit per move (what has been the shortest time AlphaGo has used for a move in all it's games?) and how does it decide to stop searching for a better move.

[Kirby]

Obvious moves aren't good enough for AlphaGo :-p

[Cassandra]

Obvious moves aren't good enough for AlphaGo :-p

Probably AlphaGo has to consider, whether locally "obvious" moves will be the best choice globally ?

[lightvector]

Has there been any information or educated guesses as to how AlphaGo manages it's time? The commentators seemed to think it sometimes takes a lot of time to think about 'obvious' moves. I'm wondering if it has some set minimum limit per move (what has been the shortest time AlphaGo has used for a move in all it's games?) and how does it decide to stop searching for a better move.

I don't know what the time usage policy is, but I have experience writing bots for games, and my experience is that "good" time usage policy is fairly hard and unfruitful for how much gain it gives you over something simple. Particularly with AlphaGo only having only 1.5 years of development and on the heels of a breakthrough in other techniques that are likely producing all sorts of low hanging fruit, it's reasonably likely that the AlphaGo team did something not too complicated (at best, a mix of some heuristics about distance to game end, time available including pondering, and maybe entropy of its desire to play different moves) and instead devoted their effort to more valuable things.

I would be extremely surprised if the time usage policy ever became anywhere close to as nonuniform as Lee Sedol's. Doing so is very very dangerous for the playing strength of your bot - from an algorithmic perspective it's not easy to tell when a move is "obvious", so the risk of blundering due to moving way too fast is not worth it.

[yoyoma]

Added chart for Game 4 to the OP.