Moreover, the "double-flag" system would let us abandon the 50-move rule and the rule of threefold repetition. Apart from opening the possibility of playing out certain winning lines, this would allow players in long endgames to focus on the position on the board without counting moves and repetitions.
Game clocks
Many abstract strategy games are played in organized tournaments and international championships: Chess, Go, Backgammon, Scrabble, Draughts, Othello, Magic the Gathering and so on.
Competitions in such games require some method of restricting the amount of time that the players can spend on their moves. For this purpose, chess clocks were introduced in the late nineteenth century as the first international chess tournaments were arranged.
A chess clock has one clock and one button for each player. After making your move, you press your button, thereby stopping your own clock and starting your opponent's. A traditional analog clock has a flag (hinged at a couple of minutes before 12 o'clock) for each player that shows indisputably whether or not they have run out of time.
A chess clock is also convenient for casual play. It allows the players to agree in advance on how long the game should take, and to allocate their own time as they wish. You don't have to be annoyed when your opponent spends a lot of time on a move, and you don't have to apologize when you do the same.
And the clock can be used for a variety of games, look for instance at Chess Clock Jenga!
Games with reversible moves
Some games, by the nature of their rules, progress inevitably towards their conclusion. In Othello a new disc is placed on the board at every move, and the discs are never removed. Not counting pass moves, there can therefore be at most 60 moves in a game.
For such games, the simplest form of time limit makes sense: A fixed amount of time, for instance 30 minutes per player, for the whole game.
In other games like chess and draughts, pieces can move back and forth and there is no practical upper limit on the number of moves in a game. In such games, a fixed time limit for the whole game doesn't necessarily work well: The clock provides a new way of winning, and this can be abused.
Suppose for instance that in a game of chess, a position is reached where each player has only a king and a rook:
In such a position it's impossible to make any kind of progress unless the opponent makes a very unlikely blunder. But neither can anyone force the game to end. It ought to be a draw, but a player determined to try to win can keep moving indefinitely. If the game is played with a fixed time limit, a player with better manual dexterity can keep moving until the opponent runs out of time.
One might have thought that something as silly as this couldn't take place in serious tournament play, but it can actually occur at the highest level. The infamous game between Monika Soćko and Sabina-Francesca Foisor from the women's world championship in 2008 (which can be seen around 1.30 to 2.30 into this video) led to the even more ridiculous king and knight versus king and knight endgame, which White eventually won by playing on until Black ran out of time.
This is not in the spirit of the game, and hardly compatible with ideas of everyone, young, old or physically disabled, competing on the same premises.
Even with many pieces on the board, a game can pass a point of no return after which it becomes obvious that none of the players has enough time to finish the game. The 2008 US women's championship was decided by a tie-break game between Irina Krush and Anna Zatonskih where, after a number of nonsense moves on the side of the board closest to the clock, Zatonskih won on time in a lost position with one second left on her clock.
As was pointed out in an excellent article by Tom Braunlich written shortly after the Soćko - Foisor game, this sort of thing is a consequence of the rules, not something nefarious that the players are doing to cheat.
These games were played more than ten years ago, but so-called armageddon games are still used as tie-break in international championships. Something equally absurd could have decided last year's world championship match between Magnus Carlsen and Fabiano Caruana, and no amount of sportsmanship on the part of the players would have resolved the issue.
Bonus time and rules for claiming a draw
In order to avoid meaningless "time scrambles", practice since the early days of tournament chess is to allow more time as the game progresses. A system like 2 hours for the first 40 moves and then another hour for every 20 moves (plus time remaining) is easily implemented with a mechanical clock: Every time a flag falls, the player must have made at least the prescribed number of moves.
Nowadays games are required to finish quicker, but digital clocks allow for systems of bonus time (also called increment or add-on) per move, where for instance 30 seconds are added to a player's time at every move.
But this still doesn't solve the problem of how to claim a draw. Special rules (50-move rule, threefold repetition) are required in order to make it possible to claim a draw in a position where an opponent keeps playing without making progress.
The 50-move rule is a compromise which is somewhat flawed at both ends: On one hand it means that some endgames become drawn even though they could otherwise be won. These endgames famously include some positions with king, rook and bishop against king and rook. And something like K+B+B+N vs K+R would even be an easy win for a moderately skilled player, were it not for the 50-move rule. There are also examples with many pieces on the board where the 50-move rule has been highlighted. In the beginning of this video, Magnus Carlsen explains that (in this game against Veselin Topalov, London 2015) he had to allow the exchange of a pair of knights, thereby severely diminishing his winning prospects, because the 50-move limit was approaching.
On the other hand, the 50-move rule is often insufficient and difficult to implement, especially at fast time controls but also in endgames with mobile pawns.
Even though the old article 10.2 has now been removed, the official FIDE rules (Guidelines III) still include situations where an arbiter may have to assess whether a player makes "sufficient attempts to win by normal means".
There have been, over the years, extensive discussions and several changes in regulation of time controls and situations in which a player can claim a draw (see for instance this discussion of the history of the 50-move rule by Edward Winter).
Distractions in long endgames
We have mentioned some rather spectacular situations, but the rules for time control and claiming draws are influencing many games. Let's look at a fairly common situation: We are far into an endgame and one player has an advantage, say queen versus rook. There is nothing special about this, the same remarks would apply to many other endgames.
Although K+Q vs K+R is a well-known theoretical win for the stronger side, it's quite challenging against good defence. But under current rules there will always be distractions from trying to play the endgame well. Suppose first that the game is played under a fixed time limit, so-called "sudden death". Since this sort of position only occurs near the end of an unusually long game, the rule rather than the exception is that both players are short of time.
If White has better time, they might try to win by moving aimlessly but quickly. When it succeeds, the result will appear to be fair since after all White had a theoretical win. Again notice that White may have had the best intentions, but they too were in time trouble and could have lost if they had spent the time trying to play with precision.
Assuming that White tries to win on the board, another problem presents itself: How long does White dare to play for a win? If White is down to only a few seconds, there is suddenly a risk of losing. This means that White might have to keep an "emergency exit" by playing in such a way that they can force an exchange of the last pieces or a perpetual check if needed.
If on the other hand the game is played with a classical time limit and a 30 second bonus, there are other distractions. White can now start by rattling off a number of aimless checks, this time in order to accumulate time of their own rather than to make their opponent spend theirs. In the position of the diagram, White could for instance (depending on where the black king moves) give checks on g5, g6, h5, h6 and then g5 again, collecting a couple of minutes of extra time.
But all of a sudden the players have to try to keep track both of the number of moves played since the last pawn move or capture, and of the positions that have occurred before (and those that have occurred twice). And White has to manage a trade-off between gaining time on the clock and staying within the 50-move limit.
The double-flag chess clock
The purpose of this post is to describe a simple system for time control that solves all the problems we have mentioned at once. I'd like to call it the double-flag chess clock. The idea is to have a system of bonus time, but to allow the bonus to be used only in order to obtain a draw.
Let's first look at how this might work in a simple example setting of rapid chess. First the players are given a fixed amount of time, say 15 minutes, that we call the main time. In order to win the game, you have to checkmate your opponent without using more time than this (unless they resign or overstep both their main and their extra time).
If a player uses up their 15 minutes before the end of the game, their first flag falls. They can now no longer win the game (even if they checkmate their opponent!) but are allowed to play on for a draw. At this point they are given a batch of extra time, let's say 1 minute. In this new phase of the game, they (but not their opponent!) will be given a bonus per move that guarantees they always have at least a certain minimum, say 10 seconds, for every move. But the bonus system will be designed so that they can never accumulate more extra time on the clock than 60 seconds (the initial amount).
There are a couple of different ways of implementing this idea (as discussed below). What I will suggest is that when a player using extra time presses the clock, the full bonus of 10 seconds will be added if they have up to 40 seconds left, while if they have between 40 and 60 seconds, the bonus is half of what remains up to 60. For instance, if they have 44 seconds before pressing the clock, 8 seconds will be added and the display will read 52 seconds once they have pressed the clock.
Let's say that Black runs out of their 15 minutes of main time while White still has some of their main time left. Now White can, whenever they wish, stop the game and claim a draw. If White chooses to play on, there are a couple of possibilities. If the game ends on the board with a white win or a draw, then that is the result of the game. But if Black wins on the board while playing on their extra time, the game counts as a draw.
If Black oversteps time again, by failing to move within the stipulated extra time, then they have actually lost the game on time. The final possibility is that White too oversteps their main 15 minutes. If this happens, the game is drawn regardless of the position on the board.
Features of the double-flag system
Let's see how the double-flag system solves the problems we have mentioned. Suppose first that we arrive at a "meaningless" endgame like king and one piece against king and the same sort of piece. Since a player using their extra time can never be forced to overstep it, the outcome if their opponent insists on playing is that eventually they too will run out of their main time and the game will be drawn.
If in a complicated position both players are about to run out of their main time, there will not be a nonsense time scramble for a full point. Instead the logical conclusion is again a draw. If both players are down to only a few seconds of main time, it doesn't matter who runs out of it first, and there is no point in making quick nonsense moves. You might try to bamboozle your opponent with a surprising king's attack though!
Since the game cannot go on indefinitely anyway, the 50-move rule is no longer needed. And neither is the rule of threefold repetition, which too is a hassle in cases other than direct repetition. This means for instance that if a player reaches K+B+N against a bare king with 5 minutes of main time remaining, they will have 5 minutes to try to figure out how to checkmate, regardless of whether it takes them 30 or 60 moves. On the other hand they can't hope to win on time and there is no point in even trying.
In a normal but long endgame, players will be able to focus on the board without being unnecessarily distracted by having to look at the clock or the protocol. There is no need to count moves or repetitions.
Long-winded play and repetition of positions can never increase winning chances, but favours a player trying to draw. This gives the players the correct incentives: In a position like K+Q vs K+R discussed earlier, White is the one who has to try to make progress in order to win, while Black will be happy to give repeated checks or retain status quo. And if White runs out of time, they can, for all practical purposes, claim a draw just like they could if Black didn't have checkmating material.
Designing the bonus system
There are systems of time control already in use that limit the accumulation of bonus time. With Bronstein delay, a player can get back the time they spent on the last move, but not more than that. In Go, a system called byo-yomi has a similar effect: A certain minimum time per move is guaranteed, but bonus time cannot be accumulated.
The bonus system for the double-flag clock can be regarded as a hybrid between delay and add-on: Bonus time can be accumulated, but only up to a certain threshold.
The reason it shouldn't be possible to accumulate bonus time beyond the initial amount is that a player whose first flag is about to fall should never be able to gain anything by letting their main time run out in order to get more quickly to the bonus per move. With the initial amount as an upper limit on the accumulation of extra time, it will always be better to run out of main time at a later stage: You obtain the initial batch of extra time when your main time runs out, and you could not have had more at that point in the game if your first flag had fallen earlier.
Let's look at some possible implementations, assuming again (as an example) that the minimum time per move is 10 seconds and the maximum accumulated bonus is 60 seconds.
1. Truncated bonus: The simplest implementation of a bonus system satisfying the requirements is just truncating the extra time at 60 seconds. When you make a move playing on extra time, the full 10 second bonus will be added, except if you already have more than 50 seconds, in case the extra time will be set to 60 seconds. The addition of the bonus follows the formula
\[ t \mapsto \min(t+10, 60).\]
A slight flaw of the truncated system is that a player with more than 50 seconds of extra time has no incentive of moving immediately, even if they have decided what to play.
2. Linear bonus: We might therefore prefer the added bonus to decrease gradually as the accumulated time approaches the 60 second limit. An alternative to a truncated system is a linear one, where the added bonus decreases linearly from 10 seconds when the time remaining is essentially zero, to nothing if you already have 60 seconds. This is the same thing as saying that the time added always takes you one sixth of what remains up to 60 seconds. Mathematically:
\[ t \mapsto t + 10 - \frac{10}{60}\cdot t.\]
But with a purely linear system, it might be annoying that the bonus decreases too quickly even at moderate levels of accumulated extra time.
3. Hybrid linear: What I suggest, again to minimize distraction of the players, is a hybrid system where the full 10 seconds are added as long as the player has at most 40 seconds (the initial amount minus two times the minimum per move) when pressing the clock. Above that, the bonus decreases linearly, which means that the time on the clock is taken half-way up to 60 seconds. With mathematical notation,
\[ t \mapsto \min\left(t+10, \frac{t+60}{2}\right).\]
For example, if a player presses the clock with 42 seconds of extra time, the new time is 51 seconds, while if they press it with 58 seconds remaining, the time is adjusted to 59 seconds.
Classical time limit
The double-flag system can be implemented on all time-scales. For a classical game we normally want to encourage good endgame play by adding extra time at move 40. One possibility would be to let the main time consist of an initial 1h 30 min, or perhaps 1h 45 min to better suit players accustomed to the "90+30"-tempo, and a secondary 15 or 30 minutes added after 40 moves.
With such a system, no mercy needs to be given a player who oversteps the time for the first 40 moves. Only after the final period of main time should there be extra time available for holding a draw. For the extra time we might have a bonus of the usual 30 seconds per move, and a maximum accumulated bonus of 5 or perhaps 10 minutes.
New possibilities
Apart from the advantages already mentioned, the double-flag clock offers new possibilities at both ends of the spectrum from bullet to classical games.
Abandoning the 50-move rule will allow players to treat certain endgames correctly, but there are other consequences: In a game where one player has run out of their main time, the other player might try a dangerous line in order to stir up winning chances in a position where they would normally have played safely to secure a draw. This could lead to interesting play that would otherwise not have occurred on the board.
At the faster end of the spectrum, the double-flag system offers possibilities of playing interesting games even at "bullet" or "lightning" time controls (1-2 minutes). Under traditional rules, the game deteriorates to a parody of chess as the time is decreased. With the double-flag system, sensible (but aggressive) play is rewarded, and the game remains a miniature version of chess. At extremely fast time controls it just becomes drawish.
Since the double-flag system would allow serious competition at very fast time controls, we can even imagine bullet chess becoming recognized as an e-sport!
Related ideas
The idea that one doesn't necessarily lose the game when time runs out seems historically to have preceded the more modern notion that the game is immediately lost when the flag falls.
The primitive chess clocks of the late 19:th century weren't very exact, and the first consequence of overstepping time seems to have been that a tournament director requested you to play faster. According to this article, you could also be fined.
A principle that has been applied in Othello (IV 6. Time Defaults) is that if your flag falls, you are given two minutes of extra time that can only be used in order to minimize the margin of loss. If the player who lost on time later wins or draws on the board, the score will be 33-31 (the smallest possible win) in favour of their opponent. My guess is that the reason for this rule is that rewarding a player with a 64-0 victory for their opponent's bad time management might be considered unfair to a third party.
Advantages of the double-flag system, in short
Games are finished in time.
No nonsense time scrambles.
Long-winded play never increases winning chances.
Allows us to abandon the 50-move rule and the rule of threefold repetition.
Promotes good play and focus on the board.
Allows sensible blitz and bullet games.
