Round Down Timing

Definition

Round Down Timing is the time system where

• one gets several time periods of same size,
• after each N-th move time used for the last N moves only deducts as many periods as fit into this time (possibly none),
• and counting seconds is done when one's number of periods is equal or less than a certain number.

Diagram

|---|---|---|---|  periods before

|---------|        time for N moves

        |---|---|  periods after

Remarks

This system generalizes

• Japanese Timing (only has one stone per period)
• Canadian Timing (only has a single period, and no byoyomi)

With only a plain clock, Round Down has to be emulated -- see below.

Emulation

The player gets

• one period,
• N stones,
• and P - 1 coins (P periods in all).

If the player runs out of time and has no coin:

• the player loses on time.

If the player runs out of time with at least one coin:

• the opponent stops both clocks,
• the player pays one coin,
• the opponent puts one period on the player's clock,
• they check,
• and the opponent starts the player's clock again.

If the player runs out of stones:

• the player stops both clocks,
• the opponent puts one period on the player's clock,
• the player counts out N stones,
• they check,
• and the player starts the opponent's clock.

Example

3 moves ("stones") in 3 minutes, 2 periods ("lifes").

  #   Lifes  Time  Stones  Used
  -----------------------------
  1     1    3:00    3     0:20
  2     1    2:40    2     0:50
  3     1    1:50    1     0:50
  4     1    3:00    3     1:10
  5a    1    1:50    2     1:50
  5b    0    3:00    2     1:40
  6     0    1:20    1     0:30
  7     0    3:00    3     3:00
  8     0    0:00          lost

(The second life was on the clock.)