5

A games of chess with perfect play from both sides may be a draw. And while we don't have any perfect chess players it does seem that a match between two equally strong grandmasters is more likely to be drawn that a game between two equally strong amateurs (though I have no statistics on this).

I believe the closest thing we have to perfect play is world-class correspondence play. Are top quality correspondence games yet more likely to be drawn that OTB grandmaster games?

EDIT in response to @Rauan's question: I'm not sure whether world-class correspondence play allows for use of computer, but I would be interested in statistics either way.

EDIT: in response to @Spork's point engine vs. engine games, I looked around online. The CCRL list shows the strongest AIs drawing 45%-60% of the time at relatively brisk 40-moves-in-40-minutes time controls. I found a post on chess.org that says that human grandmasters "have a draw rate approaching 60% or more in their games with other GMs," but these would be at longer time controls than the 40/40. So I don't think there's a clear signal.

A site called KCEC has a regression analysis showing that stronger engines to tend to draw more than weaker engines even when correcting for the difference in rating between opponents.

  • Would the correspondence games allow engines? – Rauan Sagit Mar 31 '14 at 12:25
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    There are several organizations for correspondence chess, but the ICCF (the FIDE-affilitated correspondence chess organization) does allow engines. – RemcoGerlich Mar 31 '14 at 17:19
  • I'm pretty sure the best thing we have is world class engine vs engine, and they still don't always draw.. But they do draw a lot more than humans. A 5m game otb is less likely to be drawn than a 4h game otb, and a correspondence game is more likely to be drawn than an otb game because the time limitation is even less present. – Spork Apr 1 '14 at 23:59
  • @Spork, this answer claims that humans can beat engines at correspondence chess. Presumably humans assisted by computers (as RemcoGerlich tells us are legal under ICCF rules) are even stronger. – kuzzooroo Apr 2 '14 at 1:37
1

Are top quality correspondence games yet more likely to be drawn that OTB grandmaster games?

Yes, for the same reason that classical games between grandmasters are more likely to be drawn than blitz games. When you have more time to think, you can double check every move and avoid mistakes. In chess, if your opponent doesn't make a mistake, you cannot win. This hasn't been proved, but it is a general observation in chess. You will not find a game where a side has won and there is nothing the opposing side could do to prevent that victory.

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    Thanks. In fact the question of whether chess is theoretically drawn is exactly what I was trying to get a window into with this question. Do you know of a source of statistics that can confirm this? – kuzzooroo Apr 2 '14 at 1:38
  • @kuzzooroo, unfortunately, I don't. If I find any, I'll update my post. – Wes Apr 2 '14 at 1:39
  • I haven't got around to getting to data together to make a proper answer, but as far as I know, top correspondence games have a higher draw rate than top over the board chess, but the drawing rate at top computer chess is lower. – RemcoGerlich Apr 2 '14 at 16:43
6

We can compile some "statistics" from the FICS games database. It doesn't have correspondence games, but it has a range of time controls and a range of ratings, so we can extrapolate a little bit. I'm putting "statistics" in quotes because this is low quality data (nothing against FICS, but online ratings aren't always the most reliable) and very sketchy analysis.

I've taken the rated blitz and standard games from January 2014 (just picked a month at random), restricted to "close" games (meaning that the ratings of the two players differ by less than 100 points), and grouped them into bands with ratings 900-1000, 1000-1100, etc. (Each game belongs to the band for the average rating, e.g. if it's 1480 vs 1510, then the average is 1495 so it goes into the 1400-1500 band.) Below you can see graphs of the drawing percentages for each band.

Overall, the draw rate is slightly higher for standard games (4.9%) than for blitz (4.1%). Generally speaking, higher rated players seem more likely to draw, but there are some odd blips. The very strongest players are mostly computers.

Graph of drawing rates for FICS blitz games, January 2014

Graph of drawing rates for FICS standard games, January 2014

Draw rates for blitz games:

   rating band    draw rate         number of games
         650      0.14285714               7
         750      0.06250000             128
         850      0.02761001            1159
         950      0.02683616            6372
        1050      0.02766602           18145
        1150      0.02921338           42994
        1250      0.03549412           68941
        1350      0.03599521           93568
        1450      0.03968357          108080
        1550      0.04040593           96075
        1650      0.04451169           73037
        1750      0.04832920           50425
        1850      0.05731055           32542
        1950      0.06335272           17884
        2050      0.07692308            6058
        2150      0.07191781            1168
        2250      0.04819277              83
        2350      0.22137405             131
        2450      0.32692308             312
        2550      0.30275229             109
        2650      0.42307692              26
        2750      0.52356021             191
        2850      0.63428571             175

Draw rates for standard games:

   rating band    draw rate         number of games
         950      0.00000000               1
        1050      0.00000000              23
        1150      0.02554745             274
        1250      0.01761364            1760
        1350      0.02784332            6357
        1450      0.03215792           12563
        1550      0.03699803           15190
        1650      0.04336597           16649
        1750      0.05255485           14404
        1850      0.06633868            6301
        1950      0.09838646            2541
        2050      0.11631664            1238
        2150      0.16666667             210
        2250      0.30069930             143
        2350      0.26229508             183
        2450      0.39890710             183
        2550      0.47738693             199
        2650      0.56578947              76
        2750      0.44642857             112
        2850      0.25000000               4
  • In the table "draw rates for blitz games", the second column is labeled "percentage". But the numers are all small between 0 and 1, is there a factor of 100 missing? Maybe the column should be relabeled as "draw rate", as in the other table. – Diedrsch Sep 27 '18 at 15:22
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    Wow, three and a half years after the original post, and you're the first one to point out the typo! Thanks @Diedrsch, you're correct. I've edited the column heading. – Alexander Hanysz Oct 3 '18 at 10:18
1

The general heuristic is that good play from two sides results in a higher likelyhood of a draw. This, as Wes notes in his answer, is based on the fact that the moves of the losing side could've been retraced to a certain point in time when there was another, superior move to make. As this holds for both sides, in general no side should ever lose.

One other point is that the stronger a player is, the stronger he can calculate for his opponent. A chess player always has to assume his opponent will choose the strongest line he has calculated for his opponent. The strongest possible chess thinker will therefore never make the mistakes described in paragraph 1 for him nor for the moves he expects of his opponent. The deeper / better the moves are calculated, the more likely a draw is.

That is, of course, until chess is fully solved, and we can answer if it's a draw (likely), a win for white (who knows), or a win for black (zugzwang on move 1!)

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