The Minimum-Speed Game Timer Manual for the Simulation

(1)

Manual for the Simulation

Royal C. Jones, Jr.

US Patent 10540827 (January 21, 2020) January 25, 2022

1 A Little Theory

The Minimum-Speed Game Timer (MSGT) is a digital chess clock that calculates and displays playing speed. In conventional chess clocks, such as were first patented in the UK in the late 19th century, playing speed is calculated as a required number of moves over an allotted period of time:

S = M

T , (1)

Playing speed in this sense is a mathematical average. It is ordinarily thought of as varying from move to move, depending on the difficulties presented by a particular position. From the mathematical average comes the notion of minimum playing speed, its principle of en- forcement. If the required number of moves has not been completed within the allotted time, then playing speed is below minimum, whereupon the player on the move forfeits the game.

By default the MSGT expresses time in seconds, but larger units are more practical.

Playing speed then becomes

S = uM

T , (2)

where the constant u is either 3600 seconds (i.e., per hour) or 60 seconds (i.e., per minute).

Since the unit of time divides time in the denominator of Formula 2, it is moved to the numerator. The formula is thus derived from this bit of high school math.

Formula 2 in practice is misleadingly called a time control. It might better be called a speed control, but we will maintain the standard usage. More than one time control may be used in timing a game. The goal is to keep playing speed consistent, so that

S₁ = uM₁

T₁ = S₂= uM₂

T₂ = · · · (3)

Since the value of a time control may be repeated, there is theoretically no limit to the number of time controls. The sequence may be ended with a terminal time control, where the number of moves is not specified (see Sudden Death, Section 4.3). If the last time control in a specified sequence is non-terminal, as the sequence of three controls displayed on the MSGT, its value will repeat until the end of the game (e.g., by mate, resignation. or time forfeit). The entire sequence, however it ends, is called a time limit. Play over the board may not, of course, follow the abstract description of a time limit very far. There is always a chance that the outcome of a game will be decided in the first time control.

This is probably a good time to point out that, except for the unpredictable influence of a terminal time control, a time limit expresses average playing speed. In terms of the variables of Formula 3

S_a= u(M₁+ M₂+ · · · )

T₁+ T₂+ · · · , (4)

continuing indefinitely in the absence of a terminal time control.

The tradition of time controls in chess does not emphasize playing speed. It was hardly noticed, for example, that the once common “forty in two” (forty moves in two hours) implies an average playing speed of 20 moves per hour. Fischer’s 1988 invention of the bonus method for digital clocks, which adds an increment for each move completed, further obscured the question of playing speed. The same may be said of the more recent “simple” (or US) delay as well as the older Bronstein method. The MSGT enables calculation of the playing speed

(4)

resulting from any of these delay methods. It accomplishes this by substituting delay values into the speed formula:

S = uM

I + dM, (5)

where I is the initial time allotted to the time control, to which is added the delay incurred by each subsequent move. The entire denominator corresponds to the T variable of Formula 2 and similarly represents total elapsed time. Formula 5 assumes that each completed move is associated with a delay (d), but this is not always the case. Fischer and Bronstein delays normally come after a button is pressed to complete the move. There is consequently a lost delay at the end of a time control where the last delay is of no use in avoiding a pending forfeit.

The lost delay can be redeemed by inserting a delay before the first move of a time control.

A final version of the MSGT formula for playing speed includes a variable i representing the lost delay:

S = uM

I + d(M − i). (6)

When a delay is actually lost, i = 1. When a compensating initial delay is inserted, i = 0.

The effect on overall playing speed is usually quite small, but measurable nevertheless. Note that a simple (US) delay typically occurs before the execution of a move, zeroing out the lost delay. For the sake of consistency the unconventional omission of a simple delay at the start of a game on the MSGT produces the expected lost delay i = 1.

In short, the mathematics of the Minimum-Speed Game Timer is not especially challeng- ing, though it is hoped that its application in chess and other games may lead to better competition. We turn now, perhaps with a measure of relief, to examples. The author welcomes constructive comments at [email protected].

2 Getting Started

The MSGT of this manual is a simulation. It is lacking on/off switches, data storage, and other electronics of the real world. The user should nevertheless get a working knowledge of the hardware that may eventually come to market by perusing www.msgt.info. Having arrived at the site, the user simply clicks on the link A Simulation of the MSGT. The timer that comes up, front and back, is set for the official time limit of the International Chess Federation (FIDE): “There is a single time control [time limit] for all major FIDE events:

90 minutes for the first 40 moves followed by 30 minutes for the rest of the game with an addition of 30 seconds per move starting from move one” (FIDE Handbook, C.07). This time limit is a starting point that can be modified to suit one’s purpose. The FIDE time limit is ready to use at the outset, appearing much as it would to players about to begin an actual game. Modifications of the simulation are best postponed till the user has some idea of a usable time limit. A game begins when the user clicks one of the top buttons. The button on the opposing side then turns yellow, and the clock on that side begins to count down. The user may then complete his first move as White, presumably after appropriate consideration, by clicking the button. The game proceeds with alternating moves by the hypothetical Black and White pieces until one of the players exhausts the time remaining on his clock, or until the game otherwise ends. This procedure will be familiar to those who have used a standard chess clock.

(5)

The “90 minutes for the first 40 moves” of the FIDE time limit presents no problem. It corresponds to the playing speed of Formula 2 above. “90 minutes” matches the starting time of 01:30:00 on the MSGT, and the 40 moves of the primary time control is prominently displayed under each clock. The resulting playing speed, adjusted for delays, is displayed on the back with the appropriate unit of measure, per hour in this case. To its right is a list of values under the heading “Moves in Time Control.” When players have used up the moves of the primary time control, the game moves on to the secondary time control, which here has a value of 0 moves. The zero value means that the second time control is effectively last in the sequence. It is a sudden death control providing “30 minutes for the rest of the game,”

as the FIDE specification has it. A value of 30 is accordingly assigned to the Sudden Death setting on the back of the MSGT. Finally, there is the question of move delays, which are set to a 30-second Fischer delay on the MSGT. The FIDE specification refers to “the addition of 30 seconds per move starting from move one.” It is not clear whether the delay is to be added before or after the first move, but Formula 6 above may shed some light. The insertion of an initial delay, as Fisher himself recommended in his 1988 patent, is accomplished in the MSGT by checking a box beneath the radio buttons for the three basic types of delay, giving six types in all. Since the FIDE specification does not mention an initial delay, the box is left unchecked. The resulting playing speed is 21.92 moves per hour as shown, compared with 21.82 moves per hour for the slightly slower version with an initial delay.

2.1 Notation

There is no standard notation for the setting of chess clocks. Notation used for the MSGT simply reflects the input entered on the front and back of the timer. The default FIDE time limit provides a convenient example:

Example 1. 01:30:00, 40d, 0d F30 SD30.

The notation for the FIDE time limit begins with an initial clock setting in hours, minutes, and seconds, as applied to both clocks. Then comes the sequence of time controls found on the back of the timer. The FIDE sequence uses only two of the three available time controls.

The primary control shows 40 moves. The small d next to this value, which corresponds to a check mark in the simulation, indicates a delay for each move in the time control. The delay is a 30-second Fischer delay, as indicated by the F30 notation. The second time control is the terminal control in the sequence. Its zero value indicates an indeterminate number of moves.

Its time value is 30 minutes, which appears on the timer in the Sudden Death box (SD in notation). A small d also follows the zero of the second time control. The move delay defined by input is available to all time controls, including terminal controls.

The FIDE time limit features a lost delay, the result of a Fischer delay with no initial delay.

A version of the time limit without a lost delay requires the addition of a single character to its representation by notation:

Example 2. 01:30:00, d 40d, 0d F30 SD30.

This differs from the previous example only by the addition of a small d preceding the first time control. This addition indicates the insertion of an initial delay. The effect is sometimes referred to as “Fischer-before,” producing a slight change in playing speed (see above). The secondary control in both examples shows a zero. The tertiary control does not come into play. It is automatically zeroed out and unchecked on the timer. Input on the back of the

(6)

timer has already been touched on. The time controls there proceed from top to bottom as listed until a zero value is encountered. This is the so-called “sudden death” or terminal time control, which signals the effective end of a sequence. If there is no sudden death control, the last time control is repeated indefinitely. An example would be the once popular “30 in 30”

time limit, represented on the MSGT by 30 moves in each of the three time control boxes:

Example 3. 00:00:30, 30, 30 30.

The initial time sets the pace for the entire time limit. After each time control 30 minutes is added to the respective clocks. There are no move delays.

It is possible to have only one time control in a time limit:

Example 4. 01:00:00, 0d F30,

usually called “Game/SD.” As in the FIDE time limit, there is a Fischer delay after every move. An initial delay would merely add 30 seconds to the allotted one hour.

2.2 Input

There is little to be done with the FIDE time limit for practical purposes. The user may move on to other time limits by clicking the Set button on the back of the timer in the lower right hand corner. This lights up six input buttons by changing their color from white to Light Goldenrod Yellow, indicating that these boxes are now receptive to changes in value.

Changes are effected by buttons to the left and right of each box, marked plus and minus for increasing or decreasing values. Holding down Control at the same time accelerates the action.

Alternatively the content of input boxes may be changed from the keyboard by selecting and overwriting values. There is only one active input box on the front of the timer. Any changes to its time value will be duplicated on the right clock when Set is clicked again to end input.

Input on the front is controlled by radio buttons below the clocks, which determine the units of time to be changed. Clock values roll over from one unit of time to the next in the course of a game, but not while values are being input. A one second increment at the start of play advances the hour setting in the following example:

Example 5. 01:59:59, 40d, 0d F30 SD30.

Move delays, as defined by input, are optional for all time controls, including sudden death, and are set by checking the accompanying boxes. Input is fixed by clicking again on the Set button. The Light Goldenrod Yellow of the input boxes changes back to white, except for the primary time control, which changes to green. With input fixed, values change only by the normal progression of the clocks.

2.3 Pause

The basic function of the Pause button is to do just what the name suggests, that is, to pause the operation of the timer. There are many occasions when this might be necessary.

“A player who wishes to make a claim of any sort or see a director for any legitimate reason may stop both sides of the clock before claiming and/or finding a director” (USCF’S Official Rules of Chess, 7th ed., p. 15). Pause on the MSGT allows adjustment of values on the front of the timer, similar to the adjustments made after Set is clicked. The background color of the input boxes is the same Goldenrod Yellow, but in the case of Pause it is a different set of

(7)

boxes, specifically the four inputs on the front of the timer. Normal operation of the timer resumes when Pause is clicked off, and the Set button is again enabled. If the user then clicks on Set, the original values are restored, and any changes made under Pause are lost. Changes to the default setting are made while the Set button is active. Changes in this case are more or less permanent when Set is turned off, and for this reason the Set button would be avoided if actual play were in progress.

A unique feature of the MSGT is the ability to change the player on the move (White or Black), which requires the Pause button to be active. Consider the situation where a player has made an illegal move. If his opponent noticed the slip, he could stop the timer immediately by clicking Pause. Adjustments of the timer would then be needed to specify which player is on the move, which requires nothing more than clicking a top button. Absent other adjustments the clock that is running simply changes sides. A practical application of Pause by the Association of Chess Professionals is seen in Section 6. There Pause is used to append an extra minute of time to the side with the white pieces in compensation for the handicap of having to win.

Control boxes change color when a time control is completed. The control that has been completed returns to its normal state, and the control that has started turns green. Note that time controls are completed on different moves for the two players. When White completes a time control, Black has yet to complete that control. (Sides are determined by the first top button to be clicked, which is the side with the black pieces, i.e., Black. White in chess has the first move.) By convention a control box turns green when White completes the first move of a new control. There is no color change when Black replies. This seems to be the less confusing of the alternatives.

3 Time Controls

The default FIDE time limit was used in Example 1 to give the basics of time controls.

Clicking on the top buttons alternately to simulate a game played under this time limit is a useful exercise. The user can observe the countdown on each clock. When a button is clicked to end a hypothetical move on the board, the time on the corresponding clock increases by the Fischer delay of thirty seconds, and the number of moves displayed under the clock decreases by one. To avoid having to click through the entire time control, one can take the following example to represent its last few moves:

Example 6. 01:30:00, 2d, 0d F30 SD30.

Starting the time from here causes the usual routine on each side, with the number of moves falling to 1. A second move brings the number of moves to 0, and time increases by 30 minutes. Why 30 minutes? That is the time in minutes allotted to sudden death in the secondary time control. There is no 30-second increase after the move because it is the last move of the time control, which does not provide for a delay (the 30-minute delay would be augmented with a 30-second delay if the box for Initial Delay had been checked). The moves thereafter revert to the delay after the move, which is indicated by the check mark next to the secondary control, as well as the radio button for the Fischer delay.

Another time limit that is useful for testing time controls consists of an endless sequence of single-move controls, which is written as:

Example 7. 00:06:00, 1d, 1d, 1d B360

(8)

or

Example 8. 00:00:00, d 1d, 1d, 1d B360.

This time limit emulates an old time limit from Standard American Checkers, which gives a player six minutes to complete a move, whereupon the original six minutes is restored for the next move. The intent is to exploit the properties of a Bronstein delay, but as written the time limit behaves as if there were no delay at all. This may be verified by setting it up on the MSGT and simulating a number of moves. The reason for the failure of the time limit is that a single move in a time control with either a Fischer or Bronstein delay must be regarded as the last move of the control. Completing the move by pressing a top button precludes its extension with a delay.

Fortunately, misbehavior of the time limit from American Checkers was corrected with a Game/SD interpretation (see Section 4.3):

Example 9. 00:06:00, 0d B360 or

Example 10. 00:00:00, d 0d B360.

This SD version would be handy for informal chess contests, or perhaps for checkers itself.

With six minutes allowed for every move in the game, time pressure would become a rarity.

For an estimated 60 moves, playing speed would be 10 moves per hour, though unused time would likely raise this figure considerably.

4 Playing Speed

The formulas of Section 1 provide a definition of playing speed. In formal contexts it is best referred to as minimum average playing speed. The “minimum” aspect comes from the fact that a time control requires a certain number of moves M to be completed in a given time period T (Fromula 1). It is also true that a player may complete many more moves than are required. There is no maximum playing speed. The “average” aspect of playing speed applies to a sequence of time controls, as pointed out in the discussion of Formula 4 above. It is possible to play at a slower rate than the minimum over a time control without forfeiting, provided that sufficient time has been accumulated from previous controls.

Once playing speed has been defined for the primary time control, the MSGT maintains that playing speed over subsequent controls. This is accomplished by defining the initial time I⁰ of each subsequent control in terms of the original playing speed:

I⁰ = uM⁰

S − d(M⁰− i), (7)

which is a transformation of Formula 6.

A bug in this method is known to produce a negative value for initial time I⁰, which may occur when the primary control has no delay (the box to its right is not checked) while a subsequent control does have a delay (the box to its right is checked).

Example 11. 00:08:00, 40, 20d, 10d F20.

(9)

Playing speed in this time limit is established by the primary time control as five moves per minute. The second control, with M⁰ = 20 in Formula 7, gives I⁰= −140. The third control, with M⁰= 10, gives I⁰ = −60. A simple way to deal with this problem is to set the delay to zero:

Example 12. 00:08:00, 40, 20, 10,

which gives the non-negative results I⁰ = 240 and I⁰ = 120.

Another approach is to adjust the delay to avoid negative I⁰. If I⁰ in Formula 7 is non- negative,

0 ≤ uM⁰

S − d(M⁰− i). (8)

By addition

d(M⁰− i) ≤ uM⁰

S , (9)

and by division

d ≤ uM⁰

S(M⁰− i). (10)

If Equation 10 holds true, we know that I⁰ is non-negative, which provides a test for each measured time control after the first. The right side of Equation 10 then evaluates to 12.63 for the second time control of Example 11, and to 13.33 for the third time control. The Fischer delay in Example 11 is larger in each case, making Equation 10 false. The time limit of Example 11, as we have seen, gives two instances of a negative value for I⁰.

Instead of 20, let us assign the Fischer delay a value of 12, which renders Equation 10 true for both instances of M⁰. The adjustment of d thus gives non-negative results for the time controls of Example 11.

4.1 Calculating Playing Speed

Playing speed is calculated by a straightforward implementation of Formula 6. It appears on the back of the MSGT with a Light Salmon background at the completion of input. The background color becomes Powder Blue for estimated playing speed, used for a sudden death time limit comprising a single control. An example may be input as the very simple time limit:

Example 13. 01:00:00, 0

which gives one hour to each player at a playing speed of one move per minute without delays.

The number of moves required of each side is estimated to be 60 (see subsection 4.3, although the notation shows a single zero in the primary time control for an indeterminate number of moves.

The main complication of playing speed is an initial move delay that compensates for the loss of a delay at the end of a time control. It is input by checking an Initial Move box that appears just below the radio buttons for delay type. The initial delay augments the first move in a measured time control and leads immediately to a countdown. In the current version of the MSGT the Initial Delay may be any of three types. The presence or absence of an initial delay usually has little effect on playing speed. If the default FIDE time limit is modified to include an initial delay, as

(10)

Example 14. 01:30:30, d 40d, 0d F30 SD30,

its playing speed becomes 21.82, a decrease of .1 move per hour. Initial time, designated I in equations, is simply the time input by the user in hours, minutes, and seconds. In notation it is indicated by a d before and separate from the first time control, as “d 40d.” A time control featuring a simple delay typically includes a delay before each move, including the first. The initial delay must nevertheless be indicated in notation, as

Example 15. 02:00:00 d 40d, 0d S5 SD60,

which is the second example in the list of USCF time limits, Table 1. Playing speed is 19.46 moves per hour. However, the initial delay may be omitted, which is written

Example 16. 02:00:00 40d, 0d S5 SD60.

The simple delay with this omission is counted as an additional type, though it does not change the start of play appreciably. Playing speed here is 19.47 moves per hour.

4.2 Range of Playing Speed

The range of conceivable playing speeds extends from extremely fast to extremely slow, both impractical for ordinary games. In previous designs the MSGT would adjust input values automatically with the aim of producing a reasonable playing speed, but this strategy left the user at odds with the timer. Now it is left to the user to decide whether or not a playing speed is reasonable, and playing speeds in terms of moves per second or moves per day are possible. A rule of thumb based on Formula 2 yields an acceptable range of playing speeds for a given unit of time as

1 ≤ uM

T . (11)

The idea is to keep the integer portion of the resulting mixed decimal as small as possible without yielding a simple decimal fraction. With speed measured in moves per second, for example, u = 1. For this unit of speed it is clear that M must not be less than T ; otherwise, the speed becomes a simple decimal. Thus, with 30 moves over an initial time of 40 seconds, speed becomes .75 moves per second, which is revised to 45.00 moves per minute on the MSGT.

Example 17. 00:00:40, 30, 0.

On the other hand, with 40 moves over an initial time of 30 seconds, playing speed is 1.33 moves per second.

Example 18. 00:00:30, 40, 0.

On the slow end of the range, there is Example 19. 10:00:00, d 10d 0d, S5.

Playing speed in terms of moves per hour here is slightly below 1 because of the 5-second simple delay. The MSGT opts for a larger unit of time, yielding 23.97 moves per day, although a rounded figure for moves per hour is somewhat more comprehensible at .9986 move per hour.

With no delay at all, the playing speed is exactly 1 move per hour.

The limits of playing speed on the MSGT are interesting as curiosities. The maximum without overcrowding the registers is 99 moves per second.

(11)

Example 20. 00:00:01, 99, 0.

The minimum exceeds the limitations of the above rule of thumb but can be calculated at 0.24 move per day. Delays cannot be added to the initial time without error.

Example 21. 99:59:59, 1, 0 4.3 Sudden Death

A zero move time control on the MSGT has an indeterminate number of moves. It is some- times called a terminal time control because it cannot logically precede any measured time control. Popularly it is known as sudden death. If the primary time control is terminal, it applies to the entire game (Game/SD), for example:

Example 22. 00:10:00, 0,

where neither contestant may exceed 10 minutes on his side.

Following a measured time control, either the primary or secondary, the value of the Sudden Death input is added to any time remaining:

Example 23. 00:00:24, 4, 0 SD10.

Here, when a player successfully completes his fourth move, 10 minutes is added to whatever is left of his 24 seconds, and the number of moves remaining on that side is displayed as zero for the rest of the game. Playing speed is determined from the primary time control as 10 moves per minute. For a game lasting exactly 60 moves, playing speed would be 5.77 moves per minute.

The popularity of sudden death is attested to by the many entries in Table 1. Its advantage seems to be that it determines the maximum time required for a game, which would clearly be of benefit in tournament scheduling. Any resulting time pressure on players is mitigated by move delays. If the primary time control takes the form of sudden death, then it is the only time control, called “Game/SD.” Its playing speed is estimated from Equation 2, assigning to M a plausible number of moves for the entire game, 60 in the MSGT (see Example 13). This estimate represents the minimum average speed for a full 60 moves under the assumption that all the allotted time is used. The actual playing speed will depend of course on the number of moves made on the board as well as the portion of available time that is used, neither of which can be known in advance.

But a more subtle problem underlies sudden death, especially when it is combined with move delays. Let us suppose that a player completes the primary time control of the FIDE time limit with 30 seconds remaining. He is then allotted 30 minutes to complete the game with a Fischer delay of 30 seconds added to his clock for each move he makes. An obvious strategy suggests itself: namely, to complete each of his remaining moves in no more than 30 seconds. He would then have an infinite number of moves to complete the game. A refinement on this strategy would be to make some moves in less than 30 seconds, which would allow him to accumulate time on his clock in order to relax his time limit somewhat. A tournament director might have reason to worry about scheduling problems.

The problem is laid out less graphically in Section 7.

(12)

5 Delays

The slowing of play by periodically stopping or reversing the forward motion of a timer is termed a delay. Since delays are usually added to individual moves, the term is often expanded to move delay. Delays redistribute allotted time forward, toward the end of a time control, making them invaluable for avoiding time pressure. There are three common types of delay:

simple, Fischer, and Bronstein, represented on the back of the timer by three radio buttons.

The MSGT doubles the number of types with the option of an initial delay for each type.

Its effect on the simple type is especially worth noting because the simple delay is usually thought of as preceding a move.

5.1 The Simple Delay

Example 24. 01:30:00, 40d, 0d S10 SD30.

A 10 second simple delay here replaces “F30” of the FIDE time limit for the sake of an example. With the lost delay, playing speed is 24.87 moves per hour. As in Example 26 there is no initial delay. White’s clock starts to count down as soon as Black starts the timer. On subsequent moves, if White does not complete his move within the 10 seconds of the simple delay, his clock resumes the countdown. A novel feature of the MSGT is that the simple delay, rather than simply stopping action, has its own countdown.

A more typical example includes the initial delay Example 25. 01:30:00, d 40d, 0d S10 SD30,

where the 10 second delay begins at the very outset. The delay is arguably wasted here if players are ready to begin, but it establishes the standard simple delay, coming before the move. Playing speed is 24.83 moves per hour.

5.2 The Fischer Delay

Fisher’s 1988 invention was a useful complement to sudden death, which became popular in the eighties. The FIDE time limit incorporates both. The following example revisits Example 26 with its Fischer delay reduced to 10 seconds:

Example 26. 01:30:00, 40d, 0d F10 SD30.

The example begins with a measured time control giving a minimum average playing speed of 24.87 moves per hour. Moves are not counted in the sudden death control. The game continues until the 30 minutes allotted for sudden death (plus any time remaining from the previous control, plus the bonus for each completed move) is used up. The beauty of this scheme is that the Fischer 10-second bonus for each move completed may continue indefinitely to replenish the time reserve.

5.3 The Bronstein Delay

The Bronstein delay is the earliest of the popular delay schemes, introduced by Soviet grand- master David Bronstein in 1973 (Wikipedia). It has affinities with both the Fischer and the simple delays. Like the Fischer delay it usually issues after a move, but like the simple delay it does not increase a player’s reserve of time. By Rule 5F in the sixth edition of the USCF

(13)

rule book, “TD TIP: Delay mode and Bronstein mode are equivalent.” The seventh edition is more circumspect, stating in Rule 5F1, “An increment capable clock is the standard timer for use with an increment time control.”

The issue of whether the simple delay and the Bronstein are equivalent hinges on the optional initial delay of the MSGT. (I was once of the opinion that the Bronstein delay would misfire when time left in a time control neared zero, but a little thought reveals that it continually pushes back by the amount of the delay.) Substituting the Bronstein type into Example 25,

Example 27. 01:30:00, d 40d, 0d B10 SD30,

with the same minimum average speed of 24.83 moves per hour. However, the initial delay of this example is not typical of the Bronstein delay on other timers. Typically the Bronstein delay comes at the end of the first move, as described in the following example:

Example 28. 01:30:00, 40d, 0d B10 SD30.

If thinking time on the first move has lasted for at least as long as the delay, here 10 seconds, the end of the move causes the clock to retreat by that amount. If thinking time has been shorter than the delay, the clock retreats to starting time. Minimum average speed for the entire time control is calculated with the decremented value M − 1, giving 24.87 moves per hour, slightly faster than the minimum average speed of Example 27. In comparing minimum average playing speeds, remember that it is common practice to use only a portion of the posted delay. Players on the first move in Example 27, for example, will probably not need the intial delay for thinking time, which immediately increases the actual average of playing speed.

5.4 Lost Delay

The theory of the lost delay was discussed around Equation 6, but its relation to time controls needs filling out. In time limits consisting of multiple time controls, the initial time of a measured time control after the first control is taken from Equation 7. If the variable i = 1 in this equation, the final delay is said to be lost. This is a matter of mathematical reasoning, not a policy decision. Whether an initial delay is needed for terminal time controls not so clear. Example 6 under Section 3 examines the transition from the measured control to the terminal control in the FIDE time limit. It is assumed that an initial delay should be omitted from the terminal control because the Initial Delay box is unchecked. It could be argued, however, that all terminal controls should have an initial delay. The playing speed of the terminal control provides no guide because it is indeterminate.

As a practical matter, the presence or absence of an initial delay in the terminal control is not likely to make much difference in the overall average playing speed. The operation of the timer will depend, however, on the rule that is built into it.

6 Handicaps and Reprieves

Adjustments on the front of the MSGT using the Pause button can be used to handicap a time limit in offhand speed games. In a 2012 survey of 30 ACP players, the following “widely-used”

time limit was offered for consideration (Table 4, line 4e):

(14)

(5⁰/60 − 4⁰/60) + (0⁰/SD + 3⁰⁰),

which is to say,“white has 5 minutes, black has 4 minutes, an increment of 3 seconds is added starting from move 61; white has to win.” A translation to MSGT notation might be

Example 29. 00:04:00, 60, d 0d F3 SD0, W +60,

where the solitary lowercase d confers an initial delay to the terminal time control. Without this initial delay there is the possibility of a player having virtually no time left on his clock when he completes the primary time control. It is true, of course, that such a nicety is not likely to be noticed at a playing speed of 12 or 15 moves per minute. Although White has the handicap of having to win, his playing speed is slower than Black’s. The primary task facing Black is to complete 60 moves in four minutes. The added clause gives White an additional minute to complete the primary time control. The sudden death time control is reminiscent of the FIDE time limit (Example 26) except that here there is no time allotted to balance the move delays. “SD0” reminds the user to zero out the Sudden Death box.

To test the MSGT version of this time limit, we can set up a stripped down example:

Example 30. 00:01:00, 2 d 0d F3 SD0, W +60,

which avoids having to wait for the hypothetical players to complete the actual time limit.

We add White’s extra time, 60 seconds as in the original, using the Pause function after the time limit has been set up. The top buttons should remain off while this adjustment is made.

Remember to check Initial Delay, which comes into effect as soon as the primary control is completed. Also, uncheck the the box next to the number of moves in the primary time control, as that control does not use the three-second Fischer delay.

Here is a step-by-step description of a test using Example 30:

1. Start White’s clock by clicking the right top button as Black. The left clock begins to count down from two minutes. Note that the orientation of the timer follows that of the ACP notation.

2. Click the left top button. The number of moves remaining for White drops to 1. There is no delay, either before or after the move. The countdown switches to the right clock starting from one minute.

3. Click the right top button. The countdown switches to the left clock.

4. Click the left top button. White’s move count drops to 0, and 3 seconds is added to his clock as the initial delay for the terminal control. Countdown switches to the right.

5. Click the right top button. Black’s move count and initial delay mimics the White side. Countdown switches to the left.

6. Click the left top button. White’s move count remains at 0 and 3 seconds is added to his clock as the delay after a move in the terminal control.

7. The above pattern repeats itself on both sides indefinitely to the end of the game by mate, draw, resignation, or time forfeit..

The MSGT allows a time forfeit to be overridden, either to correct irregularities or in friendly contests. To test this feature, simply allow time to expire in the foregoing test. The bright red on the face of the expired clock is erased by clicking on Pause. Its zero value may then be adjusted to any value deemed suitable. Clicking on Pause once again resumes action immediately.

(15)

7 Indeterminate Playing Speeds

We turn now to an aspect of playing speeds that I discovered quite late in this project. Given its importance, the discovery may be considered a retraction of sorts. It begins with the standard FIDE time limit of Section 2, repeated here for the sake of emphasis: “90 minutes for the first 40 moves followed by 30 minutes for the rest of the game with an addition of 30 seconds per move starting from move one.” Its press release on December 26, 2000 brought considerable controversy (“Time Controls–One Side Fits All?”chessnews.org/fidetl.html), but the focus here will be on its interpretation for playing speed.

The theory of Section 1 defines minimum average playing speed for the primary time control. The second FIDE time control seeks to limit overall time by means of sudden death, allowing 30 minutes for the rest of the game. It was argued in Subsection 4.3 that this configuration determines the maximum time required for a game: in this case, the 109.5 minutes taken by the primary time control, plus the 30 minutes allotted to sudden death, for a total of 2 hours, 19 minutes, 30 seconds. But this argument fails to take into account the pervasive 30-second increment per move. Unfortunately, the number of moves required for the second time control cannot be known in advance of an actual game, leaving an indeterminate value for maximum total time. There are, of course, practical limits to the number of moves required, but this is not likely to satisfy the scheduling requirements of every tournament.

Mathematically, an ideal number of moves for the second time control can be found by a transformation of Formula 6, similar to the transformation used to find I⁰, the initial value of a subsequent time control. The new transformation is

M⁰ = S(I − di)

u − Sd , (12)

where S is the playing speed of the primary time control, giving 13.41 moves. As a check of the result, one may substitute this value for M in Formula 6, giving the standard FIDE playing speed of 21.92 moves per hour. The ideal number of moves is reasonable enough, although there is no way of assuring that anything like it would arise in actual games.

8 Equivalents to Conventional Time Limits

The four appended tables present lists of time limits as described by their sources, and for each time limit a translation into MSGT notation. Playing speeds may be verified by the equations above. Differences in notation are largely a matter of taste except for initial delays, which are made explicit in MSGT notation. The absence of an initial delay indicator makes for a degree of ambiguity in other notations. The delay in that case is most likely implicit, though not necessarily implemented correctly.

Table 1 shows a list of recommended USCF time limits in order of playing speed. The FIDE time limit at the head of the list is conspicuously out of place. For the other time limits, with the exceptions of 17 and 18 (which have no delays), an explicit initial delay is indicated in the MSGT versions.

Table 2 shows a collection of fifteen time limits, listed in order of popularity, from a survey submitted to members of the Association of Chess Professionals (ACP) in 2004, with equivalent MSGT time limits.

Table 3 uses the same data processed with an explicit initial delay. The preponderance of integer playing speeds suggests that the initial delay was intended.

(16)

Table 4 gives the results of a more recent ACP survey. Time limit 4e is analyzed in Section 6.

The USCF has made an effort toward standardization of its time limits: “Although these are not all of the possible time controls, organizers are encouraged to select one of the above (or very similar) so that all participants are clear as what to expect and under which system the event will be rated” (Rulebook Changes, 2003-2014). The first three time limits of Table 1 vary in playing speed around 20 moves per hour, which suggests a further standardization based on that playing speed. However, a fifth table proposing standard time limits for the USCF has been withdrawn in view of objections raised in Section 7. The total time that could possibly be required by the FIDE time limit, which is the first listed in Table 1, could be clarified by confining delays to the first time control, perhaps increasing the 30 minutes assigned to the sudden death time control in compensation. A fixed value for total possible time is useful in scheduling tournaments.

9 The MSGT in Perspective

The main purpose of a chess clock is to enforce a certain playing speed or, to be exact, a minimum average playing speed. Accordingly, the MSGT makes minimum average playing speed central to its design. Playing speed is consistent over any number time controls, ex- cluding sudden death, and is estimated when sudden death is the only time control in a time limit. The MSGT is the only chess clock based on a comprehensive theory of playing speed, making possible a standardization notably lacking in the diversity of modern time limits. In conventional chess clocks playing speed is inferred from the ratio of number of moves to time allotted in a time control. Delays or increments are taken as free time without regard for their precise effect on playing speed. Nor is there any guarantee that playing speed will be consistent from one time control to the next without deliberate calculations.

Focusing on playing speed, the MSGT is systematically organized. Other chess clocks require as many as 90 preset time limits, essentially templates for possible modes of operation.

With the MSGT virtually any time limit can be set with the input controls on the front and back of the timer. Its versatility allows it to emulate other timers and, most importantly, to display precise minimum playing speed to players, spectators, and officials.

(17)

Table 1: Examples of Standard USCF Time Limits

(United States Chess Federation’s Official Rules of Chess, 2019, p. 11) USCF Notation MSGT Notation ^Playing ^Initial

Speed Time

1. 40/90 SD/30 inc/30 01:30:00, 40d, 0d F30 SD30 21.92/hr 01:30:00 2. 40/120 SD/60 d/5 02:00:00, d 40d, 0d S5 SD60 19.46/hr 02:00:00 3. 40/115 SD/60 d/5 01:55:00, d 40d, 0d S5 SD60 20.28/hr 01:55:00

4. G/120 inc/30 02:00:00, d 0d F30 24/hr* 02:00:00

5. G/120 d/5 02:00:00, d 0d S5 28.8/hr* 02:00:00

6. G/115 d/5 01:55:00, d 0d S5 30/hr* 01:55:00

7. G/90 inc/30 01:30:00, d 0d F30 30/hr* 01:30:00

8. G/90 d/5 01:30:00, d 0d S5 37.89/hr* 01:30:00

9. G/60 inc/30 01:00:00, d 0d F30 40/hr* 00:60:00

10. G/60 d/5 01:00:00, d 0d S5 55.38/hr* 01:00:00

11. 30/30 SD30 d/5 00:30:00, d 30d, 0d S5 SD30 55.38/hr 00:30:00

12. G/30 d/5 00:30:00, d 0d S5 1.71/min* 00:30:00

13. G/25 d/5 00:25:00, d 0d S5 2/min* 00:25:00

14. G/25 d/3 00:25:00, d 0d S3 2.14/min* 00:25:00

15. G/15 d/3 00:15:00, d 0d S3 3.33/min* 00:15:00

16. G/10 d/3 00:10:00, d 0d S3 4.62/min* 00:10:00

17. G/10 d/0 00:10:00 6/min 00:10:00

18. G/5 d/0 00:05:00 12/min 00:05:00

19. G/3 inc/2 00:03:00, d 0d F2 12/min* 00:03:00

*Estimated playing speed for Game/SD

(18)

Table 2: Time Limits from a Survey by the Association of Chess Professionals http://www.chess-players.org (September 17, 2004)

ACP Time Limit MSGT Equivalent Playing

Speed 1. (100⁰/40 + 50⁰/20 + 10⁰SD) + 30⁰⁰ 01:40:00, 40d, 20d, 0d F30 SD10 20.08/hr 2. 120⁰/40 + 60⁰/20 + 30⁰SD 02:00:00, 40, 20, 0 SD30 20/hr

3. (90⁰/SD) + 30⁰⁰ 01:30:00, 0d F30 30.13/hr*

4. 120⁰/40 + 60⁰/SD 02:00:00, 40, 0 SD60 20/hr

5. (120⁰/SD) + 30⁰⁰ 02:00:00, 0d F30 24.08/hr*

6. (100⁰/40 + 50⁰/SD) + 30⁰⁰ 01:40:00, 40d, 0d F30 SD50 20.08/hr 7. (100⁰/40 + 30/SD) + 30⁰⁰ 01:40:00, 40, 0d F30 SD30 20.08/hr 8. (100⁰/40 + 50⁰/20 + 15⁰/SD) + 30⁰⁰ 01:40:00, 40d, 20d, 0d F30 SD15 20.08/hr 9. (75⁰/40 + 15⁰/SD) + 30⁰⁰ 01:15:00, 40d, 0d F30 SD15 25.40/hr 10. 120⁰/40 + 60⁰/20 + [(0⁰/SD) + 30⁰⁰] 02:00:00, 40, 20, 0d F30 SD0 20/hr 11. 120⁰/40 + 60⁰/20 + [(15⁰/SD) + 30⁰⁰] 02:00:00, 40, 20, 0d F30 SD15 20/hr 12. (90⁰/40 + 15⁰/SD) + 30⁰⁰ 01:30:00, 40d, 0d F30 SD15 21.92/hr 13. (90⁰/40 + 30⁰/SD) + 30⁰⁰ 01:30:00, 40d, 0d F30 SD30 21.92/hr 14. 120⁰/40 + [(60⁰/SD) + 30⁰⁰] 02:00:00, 40, 0d F30 SD60 20/hr 15. 120⁰/40 + 60⁰/20 + 60⁰/SD 02:00:00, 40, 20, 0 SD60 20/hr

*Estimated playing speed

(19)

Table 3: Time Limits of Table 2 Revised with Initial Delay http://www.chess-players.org (September 17, 2004)

Speed 1. (100⁰/40 + 50⁰/20 + 10⁰SD) + 30⁰⁰ 01:40:00, d 40d, 20d, 0d F30 SD10 20/hr 2. 120⁰/40 + 60⁰/20 + 30⁰SD 02:00:00, 40, 20, 0 SD30 20/hr†

3. (90⁰/SD) + 30⁰⁰ 01:30:00, d 0d F30 30/hr*

4. 120⁰/40 + 60⁰/SD 02:00:00, 40, 0 SD60 20/hr†

5. (120⁰/SD) + 30⁰⁰ 02:00:00, d 0d F30 24/hr*

6. (100⁰/40 + 50⁰/SD) + 30⁰⁰ 01:40:00, d 40d, 0d F30 SD50 20/hr 7. (100⁰/40 + 30/SD) + 30⁰⁰ 01:40:00, d 40, 0d F30 SD30 20/hr 8. (100⁰/40 + 50⁰/20 + 15⁰/SD) + 30⁰⁰ 01:40:00, d 40d, 20d, 0d F30 SD15 20/hr 9. (75⁰/40 + 15⁰/SD) + 30⁰⁰ 01:15:00, d 40d, 0d F30 SD15 25.26/hr 10. 120⁰/40 + 60⁰/20 + [(0⁰/SD) + 30⁰⁰] 02:00:00, 40, 20, 0d F30 SD0 20/hr†

11. 120⁰/40 + 60⁰/20 + [(15⁰/SD) + 30⁰⁰] 02:00:00, 40, 20, 0d F30 SD15 20/hr†

12. (90⁰/40 + 15⁰/SD) + 30⁰⁰ 01:30:00, d 40d, 0d F30 SD15 21.82/hr 13. (90⁰/40 + 30⁰/SD) + 30⁰⁰ 01:30:00, d 40d, 0d F30 SD30 21.82/hr 14. 120⁰/40 + [(60⁰/SD) + 30⁰⁰] 02:00:00, 40, 0d F30 SD60 20/hr†

15. 120⁰/40 + 60⁰/20 + 60⁰/SD 02:00:00, 40, 20, 0 SD60 20/hr†

†Same as Table 2

(20)

Table 4: Survey of Top 30 Players on Time Limits

Association of Chess Professionals (ACP), News date: 2012-09-19

http://www.chessprofessionals.org/content/survey-among-top-30-players-about-time-control

Speed 1. Which of the following 2 time controls should be used

in final stages of World Championship Cycles?

a) 120⁰/40 + 60⁰/20 + (15⁰/SD + 30⁰) 02:00:00, 40, 20, 0d F30 SD15 20/hr b) (100⁰/40 + 50⁰/20 + 15⁰/SD) + 30⁰⁰** 01:40:00, 40d, 20d, 0d F30 SD15 20.08/hr

2. The following 2 rapid time controls are widely used.

Which of them should be used in World Rapid Championships?

a) 15⁰+ 10⁰⁰ 00:15:00, 0d F10 2.42/min*

b) 25⁰+ 10⁰⁰** 00:25:00, 0d F10 1.72/min*

3. The following 3 blitz time controls are widely used.

Which of them should be used in World Blitz Championships?

Please sort the possibilities from best to worst.

a) 5⁰ 00:05:00, 0 12/min*

b) 3⁰+ 2⁰⁰** 00:03:00, 0d F2 12.08/min*

c) 4⁰+ 2⁰⁰ 00:04:00, 0d F2 10.06/min*

4. The following 5 time controls are widely used for sudden death games.

Please sort them from best to worst.

(Starting times and playing speeds in MSGT notation are for Black.)

a) 5⁰− 4⁰** 00:04:00, 0, W +60 15/min*

b) 6⁰− 5⁰ 00:05:00, 0, W +60 12/min*

c) (4⁰− 3⁰) + 1⁰⁰ 00:03:00, 0d F1, W +60 15.06/min*

d) (5⁰− 4⁰) + 1⁰⁰ 00:04:00, 0d F1, W +60 12.04/min*

e) (5⁰/60 − 4⁰/60) + (0⁰/SD + 3⁰⁰) 00:04:00, 61, 0d F3 SD0, W +60 15.25/min

**Voted favorite

The Minimum-Speed Game Timer Manual for the Simulation

Manual for the Simulation

Contents

1 A Little Theory

2 Getting Started

3 Time Controls

4 Playing Speed

5 Delays

6 Handicaps and Reprieves

7 Indeterminate Playing Speeds

8 Equivalents to Conventional Time Limits

9 The MSGT in Perspective