# The Case for mixed time controls in Quad Tournaments

At the Mukilteo Chess Club & Learning center

https://mukilteochess.wordpress.com/

I am planning on running quads that are designed to fit within a 4 hour time frame. The reason for this is because I am running free tournaments at local public libraries, which are open from 1 to 5pm on Sundays.

To get a good idea for the length of game I want for a quad, I simply counted backwards from the time we have to be out of there, 5pm - 5 minutes:

For G/35: Ends 4:55, R3 3:45, R2 2:35, R1 1:25 <-- works

For G/40: Ends 4:55, R3 3:35, R2 2:15, R1 12:55 <-- does not work

These estimations are done assuming the maximum amount of time a game can take is taken every round, with no space in-between rounds. I came to the conclusion that I want the maximum game time to last around the maximum length of a G/35 game (70 minutes), but absolutely no more than the maxLength of a G/40 game (80 minutes).

Of course, these estimations only work if you assume that only a small portion of games will last to their maximum duration for the time control. Most games will finish sooner, with one or both players having unused time on their clocks at the end of the game.

When you incorporate delay or increment into the time controls, the maximum length of time a game can last becomes dependent on the number of moves played in the game. Increment and delay have essentially the same effect on a game: They both add a certain number of seconds to the game's length for each additional move played. The only real difference betweeen increment and delay is that any unused delay time is wasted, whereas in increment the unused time is accumulated, meaning that it rolls over, and adds to the time a player has available to make the next move.

A practical example of this is that a G/35 +5 (5 second increment) game will last a maximum of 80 minutes at move 60.

5 seconds/move * 60 moves * (1 minute/60 seconds) = 5 minutes added

So therefore the maximum length of a G/35 +5 game at move 60 is the same as a G/40 game, which is 80 minutes. Note that the maximum duration of a G/40 game is not move-dependent, since there is no delay or increment.

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Now, I found some interesting chess statistics regarding the number of moves you can expect to have in a typical game of chess via the following web forum:

http://chess.stackexchange.com/questions/2506/what-is-the-average-length-of-a-game-of-chess

As it turns out, you can expect about half of chess games to last fewer than 40 moves, and maybe 3/4 of games to last fewer than 60 moves. (Yes, I realize that I'm pulling this 3/4 proportion out of my arse, but I will use it for the sake of argument. If anyone can give me the real proportion of games over 60 moves, please comment below. vvv)

In a quad tournament, the tournament director needs to only wait for 2 games to finish before starting the next round for a particular quad, not 20 games as is the case in an open tournament. Given the assumption that 1 in 2 games will finish before move 40, and that 3 in 4 games will finish before move 60, it is reasonable to limit the maximum duration for games still at move X. This will encourage games under X moves long to finish in under Y minutes, so that the next round in a quad can start sooner with a greater probability.

That is why I proposed 2 different time contol options to be used in the quad:

A: 40/20, 20/10, SD/5 +5

B: 40/20, SD/10 +10

Both of the above^ are relatively easy to remember (I will have the time control posted prominently at the event either way) because 40 halves to 20 which halves to 10 which halves to 5, and the increment is the same (in seconds) as the time added (in minutes) at the beginning of the final time control. As a control variable, I will add

C: G/30 +5

to compare to A and B. Note that for A and B, the increment is only in effect for the final time control. Observe the following table:

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Maximum Duration for Game, as a function of Number of Moves made in the game:

Time Controls: (time in minutes : seconds)

Move# | A | B | C |

40 | 40 | 40 | 66:40 |

41 | 60 | 60 | 66:50 |

50 | 60 | 63 | 68:20 |

60 | 60 | 66:20 | 70 |

61 | 70 | 66:40 | 70:10 |

62 | 70:10 | 67 | 70:20 |

63 | 70:20 | 67:20 | 70:30 |

64 | 70:30 | 67:40 | 70:40 |

65 | 70:40 | 68 | 70:50 |

71 | 71:40 | 70 | 71:50 |

77 | 72:40 | 72 | 72:50 |

81 | 73:20 | 73:20 | 73:30 |

85 | 74 | 74:40 | 74:10 |

90 | 74:50 | 76:20 | 75 |

95 | 75:40 | 78 | 75:50 |

100 | 76:30 | 79:40 | 76:40 |

105 | 77:20 | 81:20 | 77:30 |

110 | 78:10 | 83 | 78:20 |

Observations:

- When using time controls (TCs) A or B, 1/2 of all games (those lasting less than 40 moves) will fit within 40 minutes.
- For about 3/4 of all games played, which are games that last 60 moves or less, TC A keeps these games fitting within 1 hour.
- For the 1/4 of games that last between 40 and 60 moves, using TC B these games will last, at maximum, 3 minutes on average longer when compared with TC A. TC C will allow games 40 moves or less (accounting for 1/2 of all games) to last a whopping ~26 minutes longer, which will no doubt delay the start of the next round!
- For the outliers (that being games lasting more than 60 moves, accounting for 1/4 of games), TC A acts the same as TC C for total time allowed. TC B, because it has a 10 second increment instead of 5 like the other two, blows up. For extremely long games, TC B would not be ideal because it would allow these games to last a very long time, further delaying the start of the next round.

Conclusion:

I chose TC A to be the best time control for a quad to fit within 4 hours, with TC B coming in 2nd.