# Average number of moves until checkmate for two players of unequal strenth

Suppose a game is played, until checkmate, between players of unequal strength, say 1800 vs 2800. What would be the average number of moves be for, say, 1000 games? I also ponder 2000 vs 2800 and 2200 vs 2800? for any time control.

I was thinking to pitch two computer engines, but I could not find any computer vs computer online. Then I tried myself (1750) vs Stockfish level 20. On the 5th attempt, I lasted 40 moves, much longer than Iexpected.

Edit: Edward: Good point, likely knowing I can't win vs machine I was just exchanging all the way, don't remember any more. DM: I was thinking checkmate, as different players will resign at different times. There is question on this site, "Can you resign if your opponent has only king?". Apparently - yes?! Mike Jones: This would be good test likely, though I'm not sure with such discrepancy in rating how many games are there. And I'm not in possession of any. Thank you all.

• Interesting question; to my knowledge length was never researched since length is irrelevant for the outcome. Also, I expect a computer with +500 ELO advantage to win much faster than a human with the same. Jan 1 at 16:29
• I suppose it would depend on if the weaker player is playing to win, as if the opponent was equal strength, or playing to lose as slowly as possible. Jan 1 at 17:31
• "moves until checkmate" supposes that there is, in fact, a checkmate. But even with players of unequal strength, a few games will be drawn, and it's likely that many games would end with resignation. Do you want "checkmate" strictly, or is total game length good enough?
– D M
Jan 1 at 17:35
• Below master level, most games are decisive by the 19th move. As the rating increases, the longer it takes for a mistake to appear. Another test is to get databases with your criteria and, since most games end with a forced mate, just have a compute the checkmate move and find the average. Jan 1 at 20:51

Tried to run it with engines from CCRL blitz rating list using common 16 opening positions without adjudications. Each opening is played twice such that each engine handles both white and black side from the start of the game.

The games are played at TC 1min + 1sec inc.

The result is as expected, as the rating of the opposition increases the number of plycount also increases - showing resistance.

The plycount in a game is the total number of moves played by each player. The movecount is approximately equal to plycount/2.

We can also infer that as we increase the TC the resistance also increases.

#### Results

mean_plycount  games
cat
2800_1800             85     32
2800_2000            100     32
2800_2200            118     32

#### Engines

engine  ccrl_blitz_rating
0  Rhetoric 1.4.3               2806
1     CDrill 1800               1806
2   Requiem v0.53               2009
3     CT800 V1.31               2205

#### Openings

0             King's Indian
1         Caro-Kann defence
2        Alekhine's defence
3                      Reti
4   Nimzovich-Larsen attack
5                  Sicilian
6            Benoni defence
7                  QGD Slav
8              Pirc defence
9         Gruenfeld defence
10   Queen's Indian defence
11                  English
12                      QGD
13                Ruy Lopez
14             Giuoco Piano
15           French defence
• this answer would be more interesting is you had 3000 vs 2000 and 3200 vs 2200 so we could see what happens as both programs get stronger, but maintain the same elo gap. Jan 7 at 7:52