Rubilia/TimeGame

Time game - Introduction

I think, when we apply Combinatorial Game Theory to the time situation rather than to the board situation, with the minimum time needed for one move - say, one second^[1] - being represented as {0|} s, we obtain an interesting game of its own (which of course is affected by the time system). This time game is lost by the first player who runs out of seconds.

Examples:

• Absolute timing, White has 3 seconds and Black has 2 seconds left:

       g1 = {-2,-1,0|2,3} s = 1 s

• Bronstein timing with a delay of 2 seconds, White has 1 second and Black has 0 seconds main time left:

       g2 = g:{off,l:{off,l|l,on},g|g,r:{on,r|}} s = on & off s

• Japanese byoyomi, White has 2 periods and Black has 1 period left:

       g3 = g2

Combining time and board game

Each move in the board game simultaneously is a move in the time game, and vice versa.^[2] Time controlled Go then is a combination of both games. The nature of this "combination" can be intricate though. If time could be exchanged for moku (as possible under ING timing to a very limited extend), it would be a sum of interdependent games. Alas, not even that is usually the case.

Note: The best option in the combined game may entail a board or time move that is dominated in the separate board or time game, respectively.

Mutual effects on the "game qualities"

An optimally played time game usually involves race conditions where the physically faster player is at advantage. Any thinking beyond protected delays (as provided by Japanese timing or Bronstein timing) necessarily deteriorates that player's performance in the time game.

On the other hand, a sensible board game requires the time game to remain in the background. A more difficult to handle time system consumes more attention that the board game consequently is deprived of. If the time game is even predominant (i. e. under ultra blitz conditions), the actual board game easily becomes pretty pathetic.

[1] Instead of defining the grain evenly like this, we could also take the minimum time really needed by each player, which might be different.

[2] Since a longer thinking time does not necessarily lead to another move on the board, and also, a particular length of thinking time can occur on different occasions in a game, there is no one-to-one correspondence between board moves and time moves.