Timing Systems - Redux
DaveSigaty: Note - This is still in progress, but I would welcome constructive comments at this time. I intend to take it to the KGS Wishlist in the near future. To comment please "Discuss page". Happy New Year!
Important Note!! - This page is not intended as a place to learn the details of the different timing systems. The individual pages on the different systems are much better places for learning the details (see time systems, byo-yomi, Canadian timing, Fischer timing, Bronstein timing, etc.). This page assumes that the reader is already reasonably familiar with the systems mentioned. The background material below is more to set the stage and mood for the analysis and discussion that follows.
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I would like to reopen the question of timing systems on KGS. I know from reading wms's comments on Sensei's that he is not enthusiastic about this. However, he also left a hole open for constructive discussion...
- "...Just thought I should add, I've been proven wrong before on things like this, so if somebody demonstrates to me that Fischer is indeed more fun than Byo-Yomi or Canadian, I may implement it later! But for now, it just doesn't look interesting enough." -- from wms's first comment on KGS Issue - Fischer Discussion
Rather than approach the issue of which is more fun (like taste, I think that fun "non est disputandum"), I think it is possible to demonstrate that both byo-yomi and Canadian timing have significant deficiencies as timing systems for Go. While they each had an important role to play in a world of analog clocks, there is every reason to look for better solutions in the digitial age and particularly for playing online Go. Indeed, the Go servers are the best place to seek such alternatives. They accumulate vast stores of games that can be used to analyze and test the real requirements to support playing Go. They also provide the easiest means to deliver alternative timing systems to players. (Before I am jumped on for not appreciating the work involved in adding and maintaining an additional timing system on a server, let me say that I do appreciate the task. However, everyone should stop for a moment and consider the effort required for the alternative of spreading new systems to the Go-playing public solely through the manufacture and sale of new generations of physical clocks!)
Fischer timing is one alternative solution, perhaps the most commonly known one outside the orient due its use in international chess and on chess servers. Due to its simplicity it does not suffer from the defects that byo-yomi and Canadian timing have. However, it is not necessarily the best timing system for Go. There may be better alternatives that have not yet been invented. In my opinion the most likely way to design any more successful system will be through analysis of the game time records on Go servers.
According to a recent feature (2006-11) on the Japanese Igo-Shogi television channel, the original introduction of time limits and clocks in Japanese professional Go was done at the insistence of the newspapers sponsoring games in the first half of the twentieth century. They wanted to be able to publish games according to schedules. The leisurely pace of play and multi-day adjournments common among pros at that time interfered with the publishing schedule. Thus clocks were introduced, with...
Purpose #1: Finish a game on time or within a mutually agreeable time period
The clearest and simplest system for achieving this purpose is absolute timing. A single block of time is delivered to the player and the complete game must be completed within that time or the player loses. Human nature being what it is, however, absolute timing leads (sooner rather than later) to time scrambles at the end of play and losses on time. Players, sponsors, and fans all have an interest in avoiding or limiting this problem since it hurts the quality of the game.
Purpose #2: Limit time scrambles and improve game play within purpose #1
All attempts to improve on absolute timing involve delaying the delivery of some portion of a player's time until later in the game. In Japan the most common system for this in professional games has been Japanese byo-yomi with time delivered per play after the main time (absolute timing) has been used. The strict time per play is further ameliorated by providing a number of additional periods (often called byo-yomi periods) that allow the player to think longer on particular plays a limited number of times. However, Japanese byo-yomi requires assistance for the players. While today digital clocks can provide this assistance directly, traditionally this requirement has been fulfilled by a third person acting as a timekeeper. This is not practical for large amateur events with tight schedules so other systems were developed.
In Japan most amateur tournaments still use absolute timing (and analog clocks). Common is 45 minutes with rounds set one hour and 45 minutes apart to fit up to five rounds into a day's schedule.
An interesting article on timing used in Korea from the American Go Association EJournal from 2006-11-13 (quoted with permission):
- THE PLAYING LIFE: Studying - Quickly -- in Korea
- By Jon Boley 6d
- For the last two months I've been in Seoul, Korea studying Baduk at Yang Jae Ho's dojang (dojo, or school), along with Matthew Burall. At the dojang, Matthew and I do life and death problems, play league games, and study new Jung-sok (joseki) and Po-sok (fuseki). The games we play are 30 minutes each with overtime of 3 periods of 30 seconds. Before arriving in Korea, I've been in overtime just a few times, but this has proved impossible here in Seoul. The good news is that my overtime game has improved quite a bit, but I still hate playing with time pressure: you really have to be calm and focus completely. Since we are playing kids that are studying to be professional, we understood that the games would be fast; they are kids after all and play fast, unlike most adults.
- Or so we thought. During our stay in Korea, the Korean Amateur Baduk Association (KABA) had its First World Amateur Prime Ministers Cup (Lui & Kim Make Top 10 In Korean Tourneys 11/6 EJ). They brought players from all over the world to compete in a week of competition consisting of three major tournaments, the Prime Minister's Cup, I Chun Ho Cup, and the KABA Cup. Here are the time limits for these games: Prime Minister's Cup: 1 hour and 3 periods of 30 seconds. Not bad, but nothing like the 1.5 to 2 hours per player in the US Open. I Chun Ho Cup: Day 1 : 20 minutes with 3 periods of 30 seconds; Day 2: 30 Minutes, 3 periods of 30 seconds. KABA Cup: 10 (yes, ten!) minutes, 3 periods of 30 seconds.
- So the games we are playing with the kids at the Dojang are actually long, thoughtful games by standard Korean tournament play. I was shocked.
- In addition to these three tournaments, KABA also hosted a lightning tournament during the week but it was for foreign players only. Eight minutes each and no OT, just sudden death. Everything is so fast here!
- One thing is for sure, Matthew and I hate to lose so we are learning to use every bit of time that we get to read and read some more. Hopefully, when playing the longer games at the US Open we will continue this practice and see some marked improvement in our play.
- Boley manages the Seattle Go Center in Seattle, WA
Presumably this is all done with digital clocks that support byo-yomi. Considering the recent and overwhelming popularity of Baduk in Korea, they probably do not face the problem of large supplies of old clocks.
The dominant timing system for amateur tournaments outside of the orient seems to be Canadian overtime. A block of time is delivered and a certain number of plays must be made within that block of time. This was a practical solution for playing tournaments using analog clocks for timing. The clocks could be set for a clear period (for example 10 minutes) and the required number of stones could be physically segregated on the table by the board (for example 30 stones). It was then easy to keep track of both the remaining time on the clock and the remaining stones to be played within the remaining time.
With the advent of digital clocks alternative timing systems have become possible. Digital clocks can reliably add and subtract precise amounts of time from a player's clock. They make it possible to contemplate timing systems that can not be reasonably implemented with analog clocks. This is even more true for online Go servers since they also automate the interface between player, board, and clock.
An interesting report on the use of Fischer timing in New York from the American Go Association EJournal from 2006-11-06 (quoted with permission):
- LIU & LOCKHART RULE IN NYC IWAMOTO TOURNEY: Xiliang Liu 7d and Will Lockhart 2d took top honors on Sunday at the New York Go Center's Iwamoto Memorial Tournament... Directed by Paul Matthews,... Matthews employed the "bonus overtime" system (also known as Fischer overtime), which was new to many participants. Each player began with only ten minutes, but earned twenty seconds for each move, so that players who finish quickly often wind up with twice as much time on their clock as when they began...
- - reported by Roy Laird 3k
edgy: The NY Go Center changed the time limit for their tournament this weekend (2007-01-06) to 18 minutes main time and a 15 second increment (it had been 10 minutes/20 seconds). This both allowed a little more time for reflection in the opening and sped up the games somewhat (I think all the games in each round finished in well under 2 hours).
I talked with Roy Laird (NYGC Vice-President) about the timing; he says they've been experimenting with various settings at the Princeton Go Club (if I remember correctly), and that increments under about 15 seconds seem to cause trouble when the players run short of time.
For me, the new time limit was fine (though unfortunately I did win one game on time, in a very complicated middlegame fight when we were both got very short on time). Possibly they could add a few minutes to the main time (at 15 seconds of delay) and still keep the round schedule brisk.
I'd like to set down some basic concepts about timing systems to allow the discussion to focus on different issues separately. Elsewhere in the pages on timing systems concepts like "lives" and "restoring" time are used. While these may be excellent ways to characterize what happens under a particular timing system, they are not universally applicable to all systems. Therefore I would like to avoid them in order to facilitate comparison of different systems. To that end the following can be said about all systems (with the exception of the choice "none" available on KGS):
- All timing systems "deliver" time to each player. The amount of time delivered may be "fixed" for a game (absolute or sudden death timing) or it may be "variable", depending on such things as the number of turns played (Canadian, Fischer, Japanese byo-yomi, etc.), your opponent's play (hour glass), purchase for points (Ing), etc.
- All timing systems "consume" the time delivered to each player. The consumption includes:
- Time "used" by the players for thinking and playing stones. This is the time that runs off your clock after your opponent makes a play (pushes the clock button or clicks the mouse) and you respond (pushing your clock button or clicking your mouse). As far as I am aware, all timing systems handle this "used" time in the same manner. Therefore, this part of time consumption can generally be ignored when we compare different timing systems.
- In addition, some systems systematically consume time that has not been used by the players. This is called spilling on SL. Absolute timing, Fischer timing, and hour glass timing are examples of systems that have no spilling. Canadian and Japanese byo-yomi are examples of systems that have spilling. Players on KGS see spilling in action during byo-yomi. For example you are playing in 30 second byo-yomi. The system provides you with 30 seconds for the current play. You think for 10 seconds then click the mouse. For this analysis we conceptualize what happens next as: first, the system "spills" (consumes, erases, whatever!) the remaining, unused 20 seconds from the time allowance for the current play, then 2. the system delivers the fixed allowance of 30 seconds for the next play. What you actually see is the clock changing from 20 seconds to 30 seconds.
All readers should realize that just these simple basics can already lead to disagreement on timing systems. Particularly the use of the concept of "spilling". The fact that this is defined above as the consumption by the system of unused time may make us automatically expect that spilling is a "bad thing". We could alternatively think of spilling as being part of the delivery process. For example, we could say that byo-yomi delivers an amount of time for each play that is equal to the amount used by the player on the previous play. This is actually quite a natural description of what happens in byo-yomi and it takes away some of the possible negative connotation involved in "spilling". I prefer the approach of dealing with spilling as part of the consumption process for a couple of reasons:
- First, formalizing spilling as part of the consumption process makes it easier to compare the total time delivered by different timing systems. I think that the total time delivered is important because that is where we started theoretically with Purpose #1 above and, in more practical terms, it is what we have to deal with in planning tournament schedules, etc.
- Second, I think it makes it easier to think about the effects that different timing systems have on the way people play, when we compare systems. In particular, it becomes easier to understand that under spilling systems time is delivered on a conditional basis. Spilling is the mechanism for effecting a "use it or lose it" condition on the delivery of time. In spilling systems if you do not use the time delivered within the limits set by the system, that unused time is consumed by the system and you never get it back.
In practice, different timing systems are often combined to control the time allowed for a single game. For example, what we often call Canadian timing is typically a combination of absolute timing to start (referred to as "main time") followed by Canadian overtime. Such combinations tend to make the overall delivery of time in a game uncertain. In the example here, it is not clear at what point in the game the transition from absolute to Canadian overtime will occur, therefore it is not possible to say in advance how much time will be delivered for either the game as a whole or for a game of any particular length.
I downloaded and examined ten game files from the KGS archives. The SGF files report the time remaining after each play. It is possible in principle to subtract the time remaining after play X from that remaining after play X-1 to find the time consumed for play X. However, the time remaining shown in the case of byo-yomi is always the full time allowance (e.g. 30 seconds), so the files for byo-yomi games can not be used to analyze the use of time in this way. In the case of Canadian timing, there is a problem on the last play of each block of plays. The time remaining always shows the full Canadian time allotment for the next block (e.g. 300 seconds under 5-minute Canadian). Therefore it is impossible to tell how much time was used for the final play and how much spilled. Nevertheless, since this is an issue only every 25 plays or so, it was possible to analyze the games played under Canadian timing. I used five absolute timing games and five Canadian timing. All the absolute timing games were played with 60 minutes main time followed by byo-yomi, however, all the games were finished without the players entering byo-yomi. I selected the long periods hoping to see what "natural" play looked like. The Canadian timing games ranged from 3 minutes/25 stones to 10 minutes/25 stones. The players ranged from 2d to 7d.
The ten games provided interesting examples of actual time usage by Go players. I believe that the patterns observed are important when we attempt to evaluate and compare the fitness of different timing systems. They contradict certain assumptions about the use of time that appeared in previous discussions on this subject here on SL.
The two main points that are important for this topic are:
- A typical game consists of a majority of plays made using very little time and a minority of plays made after thinking for longer periods of time. This probably surprises no one familiar with the game. However, the extent to which the distribution of plays is skewed toward the short end probably will surprise many. Typically players use about 10% of their time for the shortest half of their plays and 90% for the longest half. Typically players use 40% to 60% of their time for their longest 10 plays.
- The plays that use more time are randomly scattered throughout the game. This contradicts the "common knowledge" that Go players think longest early in the game and require less time later.
These findings were very consistent across all the absolute timing games and the Canadian games of 5 minutes or more. The specific percentage relationships were less clear with Canadian 3 minutes.
Here are some of the examples:
Game 1 was played with 60 minutes main time followed by 5-period / 30-second byo-yomi. Neither player entered byo-yomi although Black finished the game with only 1 minute left on the clock. The game lasted 296 plays with Black using 59 minutes and White using 40.
- For Black 38% of total time was used on the longest 10 plays, an additional 54% was used for the next 64 plays ranked by thinking time, and only 8% was used for the shortest 74 plays.
- For White 58% of total time was used on the longest 10 plays, an additional 35% was used for the next 64 plays ranked by thinking time, and only 7% was used for the shortest 74 plays.
The first two graphs are histograms grouping and counting the plays by the length of time taken for them. Note the clustering in the very short periods (the tallest bar on both charts is for plays that used 2 to 4 seconds).
Note: All the histograms shown on this page were made with 50 bins, 2 seconds wide from 0 to 100 seconds. The remaining, longer plays are shown in the ">100" bin on the far right.
The next two charts graph the use of time for each play chronologically throughout the game.
While Black's play might fit general expectations with the longest thinking in the earlier part of the game, White's play is a mirror image with very quick play throughout the beginning and the longer thinking in the latter part of the game.
Game 2 was also played with 60 minutes main time followed by byo-yomi. Again neither player entered byo-yomi. Both Black and White used right around 48 minutes in this game. This game went 264 plays.
- For Black 43% of total time was used on the longest 10 plays, an additional 48% was used for the next 57 plays ranked by thinking time, and only 9% was used for the shortest 67 plays.
- For White 32% of total time was used on the longest 10 plays, an additional 58% was used for the next 57 plays ranked by thinking time, and only 10% was used for the shortest 67 plays.
Here are the histograms for Black and for White:
And here are the charts of the time used per play:
In contrast to Game 1, both players in Game 2 scattered their longer plays pretty evenly throughout the game.
Canadian Game 1 was played with 5 minutes main time followed by 10 minutes/25 stones Canadian. White used significantly more time than Black in the game, but we can not tell exactly how much since we can not calculate how much spilling occurred on the last play in each time control. This game went 213 plays.
- For Black 40% of total time was used on the longest 10 plays, an additional 46% was used for the next 43 plays ranked by thinking time, and only 14% was used for the shortest 53 plays. (Note that these figures are after adjusting the time for the three longest plays, which appear to contain obvious spilling.)
- For White 37% of total time was used on the longest 10 plays, an additional 49% was used for the next 43 plays ranked by thinking time, and 14% was used for the shortest 54 plays. (Note that these figures are after adjusting the time for the longest play, which appears to contain obvious spilling.)
Here are the histograms for Black and for White:
And here are the charts of the time used per play:
The patterns are very similar to those for the absolute timing examples.
More examples could be added here. However, the number is limited in any case and it was a lot of work for me to produce all the pretty graphs manually so do not hold your breath :-). Much more interesting would be if someone with a statistics background (which I do not have) could be given access to a large chunk of data from server games. It would be very interesting to see a large-scale study that could be much more definitive about how people use their time under all the current timing systems. Do people at different ranks use their time differently? How much measurable impact does the choice of timing system have on time usage? How prevalent are losses on time under different systems and different settings?
(Disclaimer - some of the finer details of the different systems such as time delivery before versus after play are glossed over below; please ignore it and consider the major differences and their impact on play :-)
- Begin with only an initial main time with no additional time delivered after the beginning of the game and we have Absolute timing...
- Take the initial time and add a non-spilling increment per play to give us Fischer timing...
- Take the Fischer per-play increment and make it spilling to give us Bronstein timing...
- Divide the Bronstein initial time into sub-periods that each have spilling and we have byo-yomi...
- Alternatively, drop the initial time and expand the Bronstein increment per play into an increment per X plays (still spilling) and we have Canadian timing.
When we set down the relationships between systems this way, we can use the list above to examine each transformation in turn and ask whether or not the change favors the players. In other words does each change improve the experience of playing Go or not?
1. We will take the first step, the introduction of a time limit, as a given. See the Background section for some information on the history involved.
2. When we move from absolute timing to Fischer by adding a non-spilling increment per play, what happens? The delivery of a portion of the time allowance is spread out across the game in a linear fashion using an algorithm of so many seconds per play. This prevents the player from using all the time allowance before the end of the game. How much time in absolute terms is spread depends on the size of the increment. How much time as a portion of the total game allowance is spread depends on the relative sizes of the initial time and the increment. Fischer timing is the simplest of all the systems for delaying the delivery of time that we will look at here. It is the only system that allows us to calculate the exact time available to the player based solely on the length of the game. This is because the time is delivered to the player "no strings attached".
In the previous discussion of Fischer timing for KGS several people stated that the Fischer delivery of time does not match the needs of Go players well. However, because Fischer includes an initial time as well as a time per play, it is very flexible in how it delivers time even without resorting to using a separate main time element.
Consider the graph above. This shows the time delivered for three different Fischer settings. They all deliver exactly 30 minutes total time in 125 plays (a 250 play game). The three settings are:
- Initial time 312 seconds (5 minutes and 12 seconds), time per play 12 seconds. This is "Fischer12" in the graph. In this case 17% of the total time is in the initial time.
- Initial time 684 seconds (11 minutes and 24 seconds). time per play 9 seconds. This is "Fischer09" in the graph. In this case 38% of the total time is in the initial time.
- Initial time 1,056 seconds (17 minutes and 36 seconds), time per play 6 seconds. This is "Fischer06" in the graph. In this case 59% of the total time is in the initial time.
Trading off time per play for a larger initial time allows more thinking time in the earlier stages of the game while retaining the same expected total game time. The downside is that if a player uses up the total accumulated time midway through the game, the time per play available in the late going is smaller.
3. When we convert the increment from non-spilling to spilling (moving from Fischer timing to Bronstein timing) what happens? The delivery of the incremental time becomes conditional. The condition is use it or lose it. In Fischer timing the increment is added to the initial time unconditionally. When to use that time is completely at the player's discretion. When we change to the Bronstein increment we make the incremental time available only on the next play. For example, assume the increment is 15 seconds. In Fischer timing the full 15 seconds is added to the clock each time the the button is pressed. It remains on the clock until used. In Bronstein timing the full 15 seconds is added but if the player does not use it on the following play, the time spills and is gone for good. "Well that seems fair, that's the whole idea behind this system", you say. But wait! We know from our examination of the way players use time in games that the typical game of Go consists of many plays made with very little time used and a smaller but still significant number of plays made after longer periods of thought.
So how do we choose time limits that will provide the time necessary to play a game naturally? Consider a "20/20" game (20 minutes initial time and 20 seconds per play increment) in Fischer timing versus Bronstein. In Fischer timing these settings yield a total time allowance of exactly 60 minutes for a 240-play game. What do they imply under Bronstein timing? Let's look at a hypothetical match between two players "Nature Boy" and "Gamester".
- As we saw in our examination of game files, even when the time allowance is 60 minutes the largest group of plays in a typical game are made in the 0 to 6 second range and the shortest 50% of all plays use only about 10% of total time. In game 1 of our match that means Nature Boy makes 60 plays using about 6 minutes. But the increment on those 60 plays is 20 minutes (60 times 20 seconds or 1,200 seconds). Thus spilling eliminates 14 minutes out of the total expected game time of 60 minutes. In other words Nature Boy loses just under 25% of the expected time allowance by playing in his usual natural rhythm. Nature Boy is very upset that he ends up losing game 1 when he is unable to think through a complicated fight late in the game.
- OK we'll fix that by increasing the initial time from 20 minutes to 34 minutes for game 2. But now along comes Gamester. She understands the implications of timing systems a little better than Nature Boy (one of the reasons she plays White in our match!). She realizes there is a big time advantage from altering her pattern of thinking. She takes a very disciplined approach and carefully uses at least 20 seconds for each play. When faced with simple situations she uses her time to recount the board or ponder the aji in other parts of the board. As a result, while Nature Boy gets 60 minutes under the new settings, Gamester gets 74. Nature Boy loses his second game in a row and runs howling from the Go club swearing never to touch a clock again!
This is the problem with the change to spilling time periods. The "use it of lose it" conditionality of spilling does not fit the way people naturally play go. The players either play naturally and are penalized by the time system or they change the way they play because that is the behavior that the timing system rewards.
4. When we divide the initial time into sub-periods and make the sub-periods spilling (moving from Bronstein timing to byo-yomi) what happens? We have extended the "use it or lose it" conditionality to the initial time as well as the per-play increment. This has two important negative effects on the gaming experience:
- First, this change penalizes natural playing rhythms just as the spilling of the increment does, this time at the long end. As we know from viewing the histograms of game file timings, the times when players think longer on their plays do not fall into neat categories that will fit a limited set of fixed-size blocks of time. The players will be forced to fit their thinking into the size of the sub-periods.
- Second and even more important, the change imposes a strict limit on the number of times that the players can think for longer than the incremental time. This is a tremendously negative change. The game files clearly show that players think throughout the game. The normal settings for byo-yomi periods are completely inadequate to support the number of times that people think longer during a game.
The following graph illustrates the transitions discussed above from Fischer to Bronstein to byo-yomi, with a set of "natural" timings. It is based on the actual times used by Black in Game 2 above. The graph shows the time remaining in the game as reported in the SGF file. In addition, it shows simulations of 25/22 Fischer (25 minutes, actually 25:08, initial time plus 22 seconds per play increment), 25/22 Bronstein, and byo-yomi with 22 seconds per play plus 86 (!) extra periods of 22 seconds each (equal to 31 minutes and 32 seconds). I chose the 22 second increment for this simulation because that is the average (mean) time used per play by Black in the actual game. I chose the initial time and byo-yomi extra periods here such that the Bronstein and byo-yomi simulations would run out of initial/extra time on the last play of the game.
The divergence between the Fischer and Bronstein lines represents the impact of the spilling in the Bronstein increment. At the time that the Bronstein simulation runs out of main time, 52% (nearly 25 minutes) of the time delivered via the per play increment has spilled. There would thus be a significant benefit in additional time to Black from abandoning the natural pace played in the game in favor of using at least 22 seconds per play.
The convergence of the Bronstein and byo-yomi lines from starting points 6 and a half minutes apart represents the additional spilling of the byo-yomi periods. Here again there is a significant benefit from adapting the actual thinking time to fit the byo-yomi period. Although it is not shown here, the use of 60-second extra periods, like in the NHK Cup on Japanese television, would require an additional 12 and a half minutes (total of 44 extra periods) in order to match the result shown, due to the much lower efficiency of the larger period.
5. If we alternatively drop the Bronstein initial time and expand the Bronstein increment per play into an increment per X plays (moving from Bronstein to Canadian timing) what happens? We take the "use it or lose it" condition and spread it out over a block of X (typically 25) plays. The effect of this is to give the players more flexibility. The Canadian pattern supports a more natural mix of plays within its block of X plays than byo-yomi. However, it is important to note that the flexibility applies only within each block. Canadian's comparison to Bronstein timing is less clear due to Bronstein's initial time. While the initial time lasts, Bronstein may be preferable. However, if/when the initial time runs out, Bronstein reverts to Canadian where X = 1. This is far less flexible than X = 25. From this we see that the position of Canadian within our list of timing systems is somewhat ambiguous. So how does it compare to Fischer if we jump back up our original list of timing system transformation?
It is interesting to compare the delivery of time under Canadian to that under Fischer. A little playing with the figures reveals that for any set of Canadian parameters the Fischer set up with initial Fischer time equal to half the Canadian block time plus half the average time per play (Canadian block time / stones per block) and time per play equal to the average time per play in Canadian will yield a result where:
- The two systems have delivered exactly the same amount of time at the midpoint of the Canadian period (e.g. for 25-stone Canadian on the 13th, 38th, 63rd play, etc.),
- The maximum excess of time delivered by the Canadian system over the Fischer is on the first play after the Canadian delivers a block and is equal to half the block time minus half the average time per play,
- The maximum excess of time delivered by the Fischer system over the Canadian is on the last play before the Canadian delivers a block of time and is also equal to half the block time minus half the average time per play.
Take a Canadian set up of 25 stones in 5 minutes (300 seconds). The average time per stone is 300/25 or 12 seconds per stone. If we use an initial Fischer time of 300/2+12/2 = 156 seconds and 12 seconds per play then:
- On the first play Fischer delivers 156 seconds and Canadian delivers 300. The difference is 144 seconds.
- Play by play thereafter Fischer delivers 12 additional seconds while Canadian does not. On the 13th play (the midpoint in the Canadian period of 25 plays) Fischer has grown by 12x12 or 144 seconds and now has delivered the same 300 seconds as Canadian.
- On the 25th play (the last before Canadian delivers its second block of time) Fischer has grown by another 144 seconds from 300 to 444. It now exceeds Canadian (still at 300) by the same 144 seconds that Canadian exceeded Fischer on the first play.
- On the 26th play Fischer grows an additional 12 seconds to 456. Meanwhile Canadian delivers its second block of 300 seconds. Total time delivered for Canadian jumps to 600 seconds. It once again stands 144 seconds ahead of Fischer and the cycle begins again.
The time delivery by these two systems is illustrated in the graph below.
From this I believe it is difficult to claim that there is any rationale for Canadian overtime being employed with digital clocks or on Go servers even before considering the negative impact of spilling. The block-style delivery of time is unnecessary and the periodic time crunches that can occur at the end of each block of plays is related only to the number of plays and bears no relationship to the development of the game. For Canadian to make sense in the digital world there would have to be some game-related reason for the player to be relatively time constrained at plays 25, 50, 75, etc. but relatively awash in time on plays 26, 51, 76, etc.
Here are some equivalent Fischer set ups for common Canadian time limits:
Canadian: 3 minutes (180 seconds), 25 stones Fischer: 7.2 seconds per play, initial time 93.6 seconds
(Whoa, wait a minute! What's this fractional second stuff?? Two things actually: 1. The formula above yields non-integer results, using them makes the total figures come out exact - so the graphs look nice, 2. In examining SGF files I realized that KGS stores the time to at least 1/1000th second precision since that is what it writes to the files - so why not!? :-)
Canadian: 5 minutes (300 seconds), 25 stones Fischer: 12 seconds per play, initial time 156 seconds
Canadian: 8 minutes (480 seconds), 25 stones Fischer: 19.2 seconds per play, initial time 249.6 seconds
Canadian: 10 minutes (600 seconds), 25 stones Fischer: 24 seconds per play, initial time 312 seconds
If we look at both the delivery and consumption of time under Fischer compared to Canadian, what do we see? I took Canadian Game 1 (5 minute main time plus 10 minute/25 stone Canadian) shown above and simulated the accumulation of time under Fischer timing using the usage figures derived from the SGF file. The Fischer timing is 18/18 (18 minutes initial timing plus 18 seconds per play increment). Why these settings? The game settings could be expected to deliver about 55 minutes (5 Canadian periods of 10 minutes in addition to the 5 minutes main time) over the course of a typical game. Fischer 18/18 will deliver about 54 minutes (18 minutes initial plus 18 seconds x 120) over a typical game. Consider the following graphs...
The first graph ("Unadjusted") simulates the Fischer timing with the raw numbers from the SGF file. The second graph ("Adjusted") reduces the times for three Black and one White play at the Canadian time controls that appear to contain obvious, significant spilling. Note that the adjustment has no impact on the Canadian lines, B Actual and W Actual, because Canadian timing spills ("use it or lose it"). I believe that the jagged up and down movement of available time from Canadian timing is undesirable in a game of Go and that the smoother availability of time under Fischer timing would provide a better gaming experience.
Based on the comparisons above I would like to assert that once we have the ability to handle time with digital clocks, Fischer is the simplest, most natural, and least restrictive timing system among those currently available. Simply start with as much time as one would like initially on the clocks and add a set increment on each play throughout the game. Whatever time is on the clocks is available unconditionally to be used or saved for later at the players' discretion. There are no internal changes from one timing system to another, no special internal time limits (a la Canadian), no collapse to single period byo-yomi (like Bronstein and byo-yomi), and no opportunities to use more time by timing your plays in specific patterns.
Despite the analysis above, are there additional factors that could push us to choose timing systems for particular situations despite apparent defects in those systems? In particular, are the situations of over the board play and online play sufficiently different that different timing systems may be preferable for each?
When I think about playing over the board in a club versus online on a server, it is clear that the gaming experience is very different. It is more than just the "feel of the stones". The club offers much more feedback to the players. We can see our opponent across the board, see and hear other games going on around us, see the shaking heads and hear the muttered dire predictions of the arrogant kibitzers that think they know better than we do where our last play should have been :-) On the servers there is much less feedback from the environment. In the "real world" we are either alone or, in a family setting, surrounded by people involved in quite different activities. On the server, we effectively lock ourselves in a little room in order to play a game. While hundreds of other games go on around us we are completely cut off from the rest of the action while concentrating on our own - the board window is designed that way. We even have a screen between ourselves and our opponent. Only the occasional click of a stone tells us that we are still in a game. In one of the 60-minute games that I downloaded above, one of the players thinks for 19 minutes at one point. I could not help wondering what the opponent felt as that time got longer and longer. With the current state of net technology, we inevitably start to worry about lost connections when there is any long pause in play. Are we still connected to the server, is our opponent? Does this lead us to prefer short(er) time limits and timing systems that require us to play more frequently? (BTW - I was interested to run across this thread on GoDiscussions.com about playing Go in Second Life; is this what the future holds for Go servers?)
If there is a preference for lively, more frequent play in online Go, what is the best way to achieve it? Is Fischer too flexible and natural for online play? Do we have to avoid Fischer and stick to systems like byo-yomi or Canadian that force us into artificial patterns of play in order to guarantee a lively pace? There are potential modifications to the timing systems that could support a more flexible, enjoyable game while maintaining the desired lively pace:
- One idea would be to add an additional setting to the timing system - maximum thinking time (MTT). Suppose that we could set a max time of 3 minutes (or 5 minutes) for any one play? People might say that both byo-yomi and Canadian already do this. However, in both those cases the limit on maximum thinking time is bound up in the process of delivering time and depends on the use of spilling to create a limit. As we have seen above, these are undesirable "features" that we would be better off without. As a separate setting, the MTT would be cleaner and leave more flexibility overall. It would not greatly change the ability of people to use their time. Just as in the existing systems today, people would be able to "buy" another 5 or 3 minutes at the cost of a ko threat. In doing so, however, they would have to act and give feedback to their playing partner. If I look at the 5 different 60-minute main time games that I analyzed above, a total of 15 plays in the 5 games would have been truncated by a 3-minute MTT and only 4 would have been truncated by a 5-minute MTT. It is not obvious to me how this would be programmed and handled in the current user interface. It seems like it would necessarily be rather complicated.
- Another alternative under Fischer timing would be to cap the accumulation of time. The chronos game clock has such a mode, created by accident I believe. It is the clock's blitz Fischer mode (CH-P4). Like other blitz modes on the chronos only 3 digits are displayed (out of a maximum 6) under the assumption that only short time limits will be used. As a result, the display tops out at 9 minutes and 59 seconds (9:59). After that the clock continues to run normally but no further time accumulates. If you run your time down thinking, the Fischer increment will push it back up to but never beyond 9:59. Imagine this as an option in Fischer timing on a server. Set the cap at 10, 5, or 3 minutes. If run down, time can be replenished but it can never get out of hand. The replenishment capability keeps the key difference between Fischer and Bronstein or byo-yomi. It is somewhat like Canadian but the increment process is preserved so we are never caught in time scrambles at an internal time control. Unlike the MTT idea above, this seems like it would not be so difficult to add (when adding Fischer in the first place :-). See the discussion topic "modifying Fischer timing?" for additional material on this idea.
What can we do to test our theories and opinions about the impact of the observed differences between timing systems? Several opportunities come to mind:
- First, the existing KGS data could give us the oppotunity to compare absolute timing, Canadian, and byo-yomi. How frequent are losses on time under the different systems at different settings? This comparison would not be perfect however. It is not uncommon for players simply let their time run out rather than resign. I would assume this is more common under byo-yomi than Canadian or absolute timing because on average you do not have to wait as long :-)
- An alternative test is suggested by wms's earlier work on very short time limits ( http://www.igoweb.org/~wms/minTime.html). Within this finding is there a diffence between timing systems in the point at which the ratings become unreliable? In other words are some timing systems better (produce more reliable results) than others at the same very short time limits? In theory I would expect Canadian to do better than byo-yomi because it is more flexible. The alternative hypothesis would be that it is easier to fall behind by Canadian and be unable to make one of the block-end time controls. In any case, I would expect Fischer to to provide more reliable results than any of the other systems due to its controlled delivery of time (versus absolute) and superior flexibility in usage (versus Canadian or byo-yomi).