A 'Time-Control' Higher Math Question{?}

.. An acquaintence recently asked me, if a '5/5' game.. {ie. 5 min. game with 5 sec. per move increments}.. was 'faster' or 'slower' paced, than a '10 minute' game.

My response, was a 'cleaned up' version of - 'hellif-Iknow'!?

Any mini-'Einstein' math-o-phobes, are welcome to contribute! - Including, the 'math' formula, for determining that. {!?}

I'm not sure what you're asking since you already know what the second "5" means in "5|5" (not "5/5"). The added 5 seconds per move is mostly negligible, and obviously division is not involved since the correct symbol is "|", not "/". Obviously a 5-minute game is faster paced than a 10-minute game.

I don't think it is obvious.

If you assume a 40 move game, 5x40=200 seconds are added for each player, so they get a total of 81/3 minutes each.

For a sixty move game, each player will get exactly 10 minutes at 5 / 5.  Longer games will give the players more time at 5 / 5.

As 60 moves is a longer than average game, the 10 minute game will go longer on average, but not by much.

If your interpretation is what the OP is asking, then you're right: it's somewhat more complicated, but it can still be described with simple algebra. I'm still not sure if that was what the OP was asking, however.

I can see your point Sqod.

But my interpretation is the one that can give you clear answers, via fairly simple algaebra as you say.  I don't think it is properly called higher math, despite that making me sound very clever which is to be encouraged.  :P

Which game is faster paced meaning more moves being made in the early minutes... depends on how players allocate their time.

And I think you are right, typiocally the 5/5 game will be faster early on average.  But its not true of every game and can only be proved by surveying lots of games.

In a 10 minute game you have 10 minutes.

In a 5|5 game you have 5 minutes + 5 seconds per move.

The difference in initial time is 5 minutes.

So compute 5 minutes / 5 seconds to find out how many moves are needed to make up the 5 minute initial difference: 300/5 = 60.

In a 60 move game the allotted time is equal.

I suppose to check you could ask yourself:  "how many seconds will I have gained after 60 moves?"

BungaBunga gave an algebraic expression.

I suppose this is the first kind of math beyond basic arithmetic. Higher math is completely different though.

Hmph. A *real* mathematician would have called him Bunga Squared.

I'm not a mathematician, so I'm ok here 

A 5|5 game is faster, however if you have more time visibly on your clock, the time goes by quicker. Now, if you know anything about the speed of time, then I suspect that you should understand that the actual time you get to calculate, make decisions is less in 10 minutes, as you can't increase it later in the game, and would lose on time, as you have more likely taken your time rather than hurrying in a seemingly 5 minute game, but which you are safed with 5 secounds extra per move in time scramble.

Conclusion: Technically 5|5 minute games are faster as games end usually before 40 moves, however practically the time spent in a 10 minute game is longer per move, making the efficienty of the time spent also less.

Here is another way to answer:

If you pace your play in expectation of less than 60 moves, then 10|0 will be played at a slower pace.

If you pace your play in expectation of more than 60 moves, then 5|5 will be played at a slower pace.