Wikipedia:Reference desk/Archives/Mathematics/2016 March 11

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March 11

Over the breakfast table (possible numbers of chess moves versus go)

The following sentence in the Daily Telegraph caught my eye this morning:

Go is a lot more complex than chess - there are 10⁷⁶¹ possible moves, compared with 10¹²⁰ possible in chess.

How are those figures calculated? Two chess players could keep moving their knights backwards and forwards and the game could go on forever. 81.147.143.221 (talk) 11:22, 11 March 2016 (UTC)

See section Chess#Mathematics and computers and Go (game) the third paragraph.

Related: Go and mathematics.

Also Game complexity#Complexities of some well-known games. --CiaPan (talk) 12:47, 11 March 2016 (UTC)

In Chess, 10¹²⁰ (= 32⁸⁰) is the number of games of a typical length. The corresponding number for Go would be 10³⁶⁰ (= 250¹⁵⁰), so 10⁷⁶¹ seems to also count games that are unusually long (but still not maximally long). I would say that Wikipedia is technically wrong to call those figures "number of possible games" in paragraph 3 of Go (game), and the meaning of what is actually being counted got further mangled when the Daily Telegraph used the word "moves" instead of "games". Egnau (talk) 16:24, 11 March 2016 (UTC)

I removed that paragraph from the article (and added a talk page thread about it). -- BenRG (talk) 21:53, 11 March 2016 (UTC)

You can't just keep moving two pieces back and forth in chess, as that leads to a repeated board position draw. Also, comparing such huge numbers seems entirely meaningless to me. In neither case will a brute force approach work, where you calculate every possible move until the end, and take the best one (except when you are almost at the end). So, a more sophisticated approach is needed in both cases, and the number of possible games hardly seems relevant. StuRat (talk) 23:17, 11 March 2016 (UTC)

Technically, the draw by repetition can be claimed on the third repetition, but if neither player claims it, it does not come into automatic effect until the fifth repetition. (In the past it would never come into automatic effect, but that changed in July 2014. The July 2014 amendments are mostly there to prevent infinite games, even if the players both want them.) Double sharp (talk) 06:29, 15 March 2016 (UTC)

This video [1] seems relevant here. --RDBury (talk) 01:20, 14 March 2016 (UTC)

He starts out by saying that Shannon's number is the number of games of chess (it isn't) and then that it's an estimate of the number of games (it isn't). I didn't watch the rest of the video. -- BenRG (talk) 19:56, 14 March 2016 (UTC)

The video is only half bad. At 7m14s he considers all games up to 11800 plies. Later he mentions Hardy's estimate of 10¹⁰⁵⁰, but he fails to point out that Hardy's number is way too large to be of the form (branching_factor)¹¹⁸⁰⁰. For a serious take on the number of possible chess games I would recommend this article instead [2]. Egnau (talk) 21:41, 14 March 2016 (UTC)

I added to the title to give some clue as the what the Q is about. StuRat (talk) 21:56, 14 March 2016 (UTC)