"Isidor Gunsberg" wrote:
.... Well, the problem is the allocation of blocks of thinking time.
The longer the game, the more thinking time you need. ....

You included a lot of detail, and several specific time control schemes, in
your post.

What it all boils down to, though, is that in most increment schemes, the
increment is faster than the average time per move in the fixed controls.

With 40/120, then 20/60, then 20/60 indefinitely, with no sudden death and
no increment, the average time per move is 3 minutes.

If, instead, the time control is 1/3 (one move in 3 minutes), then 1/3, then
1/3 indefinitely, with no sudden death and no increment, again the average
time per move is 3 minutes.

Furthermore, these two schemes have the same structure -- N1 moves in M1
minutes, then N2 moves in M2 minutes, indefinitely.

Yet, the latter is precisely an increment, in its purest form -- no main
time, but 3 minutes per move throughout. It's just that the "blocks" you
speak of are 1 move each.

Any time the increment is shorter than the average time per move, you will
eventually reach a point where the players have to move more quickly than
they did at the start of the game. Sudden death, with no increment, is the
extreme example.

So it gets back to the age-old argument of fixed-move-number controls vs
sudden death. Do we want the former, for quality chess, or the latter, to
avoid adjournments and late-starting rounds? Increment schemes are simply
an attempt to compromise between these two goals. Different increments are
appropriate in different tournaments (championship vs amateur, 1 round a day
vs 2 or 3, etc). But a 30- or 60-second increment (in an otherwise slow
time control) will never eliminate the need for the players to eventually
move more quickly than they did in the initial stages.

Bill Smythe