Life In 19x19

A disadvantage of Bronstein is certainly the possibly more varying duration of games during a tournament round, resulting in somewhat more time required to finish a round.

One recurring statement was that a player might be upset to have to "lose" spilled time in Bronstein.
About this however, I think that if you have for example a 20s Bronstein period, the following might rather apply:
-such moves (squeeze, ko threat, standard sequences) should actually affect both players nearly equally, since they are "sequences" after all, so both will in the same boat, therefore no loss in comparison between the players.
-finishing thinking about one situation and then -still within the same 20s delay- switching to think about a completely different situation while keeping the first one in mind might not be practical.
Therefore rather than forcing anyone to think about more stuff in order to make use of his time, Bronstein can instead allow the players to relax for a moment, since the mental effort might be of little payoff compared to calming down instead. This is somewhat leading to next point:

Some things that I perceive as disadvantageous about Fisher:
-if bonus time is quite low, eg < +15s, the faster you move your arm the more time you can get out of it. Better start doing pushups so you can save 1s on each move in the next tournament. Ok I'm not completely serious here, but it's annoying that you have to go for the clock button at max speed on every move you make.
-Fisher forces a much larger scale active time management by each player.
It is annoying to have to consider and estimate on each move if it might not be worth spending ten, five or even one more second so you may save it up. This might shift the game of Go too much towards raising mental effort for active time management:
In Fisher, you cannot simply think "if I keep these 15 minutes time reserve I have left I should be able to think through situation X that might come up later" but instead you'll need to be more like "I used up 20 minutes so far, and probably the game will last about 100 more moves where probably 20 will be end-game, then that means I shouldnt take more than 8 seconds per move for this sequence so i will have anough time to handle situation X which will probably come up over there later.".

Further, it was mentioned that absolute time is pretty bad in tournament as it allows to play nonsense moves to make the opponent suffer a time loss. However, this may also (although on a much lesser scale) surface with Fisher time, IF we assume that in fisher time the bonus time on each move is [considerably] small, THEN Fisher time allows your opponent to play nonsense moves to drive you into a corner if he picks his timing to do so right when you're in a Fisher 'time valley' ie have spent most of your time reserve for handling a critical situation that had just been finished on the board and are planning to accumulate it again since usually only basic moves would follow for a while now. Of course by far not as bad as Hour Glass time or Absolute time though, but still different from Bronstein where this isn't an issue.

Overall: Large bonus fisher time settings, like +20 seconds for example, seem to me to avoid disadvantages to Bronstein listed above quite effectively, and at the same time give us the full spectrum of tournament time management advantages Fisher time offers, so i'd vote for Fisher if bonus time is, say, at least +15s, otherwise for Bronstein - just my personal taste.

About most of 'our classical' time modi: Both Bronstein and Fisher are certainly superior by far to absolute time, canadian byoyomi and japanese byoyomi. Personally, im especially taken back by both byo-yomi variants about emphasizing the opening as the place to spend thinking time at, since base time will run out anyway, even if a move is made without much thinking. not that i dont like to think during the opening, but still i'd like more control there.

Also, if you want to play a really relaxed game of Go in a pub, without the emphasis on tournament or competition for prizes, Bronstein time will nicely keep away the need to keep spending mental ressources on time management and to frantically grab for the clock.

C. Blue wrote:Both Bronstein and Fisher are certainly superior by far to absolute time, canadian byoyomi and japanese byoyomi.

Yes, thanks for putting this into perspective.

However, I should like to answer some of your points:

Some things that I perceive as disadvantegous about Fisher:
-if bonus time is quite low, eg < +15s, the faster you move your arm the more time you can get out of it. Better start doing pushups so you can save 1s on each move in the next tournament.

That is the case in any non-spilling time system. The only reason that spilling time systems do not always have this characteristic is that they spill anyway; you lose the same time in two ways, but the effect does not double.

-Fisher forces a much larger scale active time management by each player.

You gave some fictitious report on how someone might think himself into a needless panic with regard to this. I do not see any merit to this claim, however, especially since you did not work out how this could be avoided, not even with Bronstein timing, which you seem to prefer. I can tell you from personal experience that I do not need to think about the time at all while playing with reasonable Fischer settings.

Further, it was mentioned that absolute time is pretty bad in tournament as it allows to play nonsense moves to make the opponent suffer a time loss. However, this may also (although on a much lesser scale) surface with Fisher time, IF we assume that in fisher time the bonus time on each move is [considerably] small, THEN Fisher time allows your opponent to play nonsense moves to drive you into a corner if he picks his timing to do so right [...]

If you use bad settings, you get bad outcome. This has nothing to do with the time system.

One recurring statement was that a player might be upset to have to "lose" spilled time in Bronstein.
About this however, I think that if you have for example a 20s Bronstein period, the following might rather apply:
-such moves (squeeze, ko threat, standard sequences) should actually affect both players nearly equally, since they are "sequences" after all, so both will in the same boat, therefore no loss in comparison between the players.

All (serious) time systems affect both players equally. The problem is not the spill itself, but the incentives it gives for time management, namely that it can be advantageous not to play directly even though the move has been adequately thought about.

Therefore rather than forcing anyone to think about more stuff in order to make use of his time, Bronstein can instead allow the players to relax for a moment, since the mental effort might be of little payoff compared to calming down instead.

This is pure speculation about what might benefit a player. Why not let him decide for himself what to do with his time?

C.Blue wrote:However, this may also (although on a much lesser scale) surface with Fisher time, IF we assume that in fisher time the bonus time on each move is [considerably] small, THEN Fisher time allows your opponent to play nonsense moves to drive you into a corner if he picks his timing to do so right when you're in a Fisher 'time valley' ie have spent most of your time reserve for handling a critical situation that had just been finished on the board and are planning to accumulate it again since usually only basic moves would follow for a while now. Of course by far not as bad as Hour Glass time or Absolute time though, but still different from Bronstein where this isn't an issue.

IANRG, but how does this work? If the basic moves are A, the nonsense moves are B, and then whatever difficult moves are coming are C, then we can suppose two scenarios:

standard
AC the person in the time crunch gains time during A, then spends it during C. At the end, he has little time remaining, but has never been severely pressed.

timesuji
BAC the person in the time crunch struggles during B, and gains time in A before spending it in C (assuming there is not a loss on time during B).

Now, this only applies if B consists of moves such that answering them correctly makes you lose time. On the assumption that these are nonsense moves, that will not be so common to begin with?

But how does Bronstein fix the problem? The moves are no easier to answer, so why won't you end up in a bind?

Harleqin wrote:

C. Blue wrote:Some things that I perceive as disadvantegous about Fisher:
-if bonus time is quite low, eg < +15s, the faster you move your arm the more time you can get out of it. Better start doing pushups so you can save 1s on each move in the next tournament.

That is the case in any non-spilling time system. The only reason that spilling time systems do not always have this characteristic is that they spill anyway; you lose the same time in two ways, but the effect does not double.

Indeed it is the case. However, for that claim of 'losing time' which is a term you seem to strongly emphasize in talk about spilling time-systems, I suggest you keep the quote closer together with its preceding context. If you found the suggested scenario unlikely, that'd be a different matter to talk about I guess.

-Fisher forces a much larger scale active time management by each player.

You gave some fictitious report on how someone might think himself into a needless panic with regard to this. I do not see any merit to this claim, however, especially since you did not work out how this could be avoided, not even with Bronstein timing, which you seem to prefer. I can tell you from personal experience that I do not need to think about the time at all while playing with reasonable Fischer settings.

I guess it comes down to playing style too, which time management scenarios apply or not apply to a player. The "report" as you describe it in a certain way obviously need to be viewed in a situation where the scope for the total duration of a game is the same for both time systems. Of course you're free to ignore aspects of time management, no matter the system. The difference between Bronstein and Fisher however can be extrapolated from the fact that Bronstein periods are usually longer compared to corresponding Fisher periods given a fixed scope for approximate total duration of the game. There you are of course right, that it isn't avoided in Bronstein, but the effect is usually lessened quite a bit.

Further, it was mentioned that absolute time is pretty bad in tournament as it allows to play nonsense moves to make the opponent suffer a time loss. However, this may also (although on a much lesser scale) surface with Fisher time, IF we assume that in fisher time the bonus time on each move is [considerably] small, THEN Fisher time allows your opponent to play nonsense moves to drive you into a corner if he picks his timing to do so right [...]

If you use bad settings, you get bad outcome. This has nothing to do with the time system.

That statement seems pretty correct in general, but here maybe you could actually explain what the correct settings would be to make up for what was put down by me as the weakness of a certain aspect of described time system, or alternatively argue how it being a flaw is actually not the case and the scenario described is either inconsistent or cannot happen at all. I'd actually welcome a refutation since I do not at all dislike Fisher time intrinsically.

One recurring statement was that a player might be upset to have to "lose" spilled time in Bronstein.
About this however, I think that if you have for example a 20s Bronstein period, the following might rather apply:
-such moves (squeeze, ko threat, standard sequences) should actually affect both players nearly equally, since they are "sequences" after all, so both will in the same boat, therefore no loss in comparison between the players.

All (serious) time systems affect both players equally. The problem is not the spill itself, but the incentives it gives for time management, namely that it can be advantageous not to play directly even though the move has been adequately thought about.

I agree with you there. I don't perceive it as problem though, maybe a minor quirk, but not a distracting one. Maybe someone else even sees it in a positive light.

Therefore rather than forcing anyone to think about more stuff in order to make use of his time, Bronstein can instead allow the players to relax for a moment, since the mental effort might be of little payoff compared to calming down instead.

This is pure speculation about what might benefit a player. Why not let him decide for himself what to do with his time?

As was hopefully visible from the context you left out, this was actually a reply to the assumption made that it forces a player to spend time thinking (an interesting 'drawback') and also upsets a player, so I was actually just giving an opposing scenario.

From your somewhat magisterial way of writing however I take it that you are not ever going to tolerate anything other than Fisher time, going as far as dismissing probable scenarios about what aspects of one time system or the other could cause as pure speculation or even describing it pretty unrelated as patronization of the players, so I guess we won't really get much further here.

hyperpape wrote:But how does Bronstein fix the problem? The moves are no easier to answer, so why won't you end up in a bind?

Simply because you have a greater amount of time per period than you'd have per Fisher period, because if we assume a fixed duration of the game, the delay-system periods will system-immanently be longer than the non-delay ones. That's why I mentiond that the periods need to be sufficiently small to make a difference. For example, 30s Bronstein vs 20s Fisher wouldn't matter. 15s Bronstein vs 7s Fisher could matter more, depending on the player's lightning play abilities.

Hm, if Mr William 'wms' Shubert reads this thread maybe he'll consider adding the systems to KGS, finally. *hope hope*

I think for serious games Fischer is better because it's fairer due to its non spilling nature.
I prefer Bronstein for casual games(in particular online(WMS: Give me Bronstein instead of byo-yomi)) because the opponent can't accumulate a big time depot wasting my time towards the end of the game.
It's relatively easy to see at which point a game is serious enough to switch to Fischer: Once the players start waiting until the last second of their delay-time before moving to avoid spilling Bronstein degenerates.
I've read that strong players in serious games typically thing until the end of their byo-yomi period to prevent spilling. Which I regard as undesirable. And Bronstein suffers from the same problem.

But of course Fischer vs Bronstein isn't an either or decision, but one can interpolate between them in a number of ways. But I'm not sure if the added complexity is worth it.
One possible way of mixing them is adding only a fraction(for example half) of the bonus time remaining after the move to the players time depot.

Arimaa timing rules are a good inspiration of a timing system with flexible parametrization.

C. Blue: I try to write concisely and quote sparingly, because I do not like the pages-long passages of quote-counterquote-countercounterquote that often emerge in a forum discussion like this. Please do not think that I dismiss your arguments summarily based on their outcome; I will not make such a claim about your writing either.

In a comparison between Bronstein and Fischer timing, I have yet to see a compelling argument, from the view of Fischer timing, for:

• letting the unused part of the last bonus spill and
• making the bonus a bit larger to compensate

or conversely, from the view of Bronstein timing, against:

• not letting the unused part of a delay spill and
• making the delay a bit smaller to compensate.

Under Bronstein timing, you add a bit more time each move and then throw away some random part of it, also each move. The only net effect I can see is that it makes the variance of the overall game time bigger.

What goals should a timing system achieve?
1 Fairness, both players get the same amount of time
2 Limiting the maximum duration of a game
3 Should feel natural and the player shouldn't have to think about time every move.
4 Ensuring a fluent game

In tournament games 1 and 2 are the most important points. And Fisher does both of them better.
Point 3 can be a problem with Bronstein, as the players try to avoid spilling and thus use the remaining time after deciding on the current move to read something else, count,... And that feels unnatural for me. But they only do that if winning is very important to them, and not in a casual online game.

Bronstein is better than Fischer for 4). For example the game is played quickly until one player makes a significant mistake on move 200. He has accumulated quite some time he now spends, either desperately trying to find a comeback, or just to annoy his opponent.
Or another example is a player spending all of his remaining time on the endgame, just because he has left the time and doesn't want to waste it. This is fair to do in a tournament, but annoying in a casual game.

Harlequin, I'm sorry if I misperceived your statements; so let's carry on with the time system discussion.

If we ask in what part of the game (fuseki, chuban, yose) a player can spend the largest block of thinking time on his next move, Fischer time emphasizes the later game stages more than the opening (by the way I believe that this is why wms dislikes Fischer time, based on reading the KGS wish list), basically because it doesn't "spill":
For example if you start with 20 minutes base time and get +20s on each move, that means if you play very fast during the opening, you might have about 40 minutes to spend somewhere around the middle game fighting. If however you are a player whose strengths are in the opening, you'll only be able to spend about those 20 minutes.
As you mentioned, a time system's usability depends on the actual settings. In this case, the game could probably be made fairer by setting the fischer bonus to the actual period of time a "fast" move takes, for example 4 seconds, and optionally also increase the base time to keep the total game duration somewhat similar to the example above, say, 45 minutes. Now a player could use 45 minutes right in the fuseki if he's a "fuseki person" and play quickly afterwards, or he could play quickly in the fuseki, about keeping his 45 minutes, to spend them later on when fighting arises if he excels at it.
The dilemma is that the smaller the bonus, the fairer the players are treated in terms of when exactly they would like to invest most of their time, while on the other hand a smaller bonus will move the time system closer towards the problem faced in absolute time where unreasonable moves can be played to attempt and make the opponent lose on time (or make a really big mistake).
A spilling time system has the flaw already pointed out of asking a player to continue thinking even if he already solved the 'local problem at hand', just to make sure he won't "waste" or "lose" time. On the other hand, in this system the base time pool could grant the same continuous block of time to be available in any phase of the game, not favouring either opening or later stages.
It becomes a fair guess that there just isn't THE perfect time system really.

I'd like to make two suggestions:

a) a mix of Bronstein and Fischer time, let me call it "Bronstein Carry" maybe.
Carry, because a percentage (for example 50%) of the usually spilled time will be added to your time pool, ie carries over. (So a 100% setting would result in this actually being same as Fischer time.)
The reason why I think this isn't just an arbitrary compromise but could actually improve the overall situation is as follows:
In my opinion, after the player finished thinking about the main local issue at hand, and in order to avoid spilling any time starts thinking about secondary issues, the quality of this thinking time is inferior because he cannot completely focus on it (he has to keep his primary conclusion in mind and mustn't forget it). Further, time spent _after_ your move (or after you have already decided on your move and just not yet placed it, as in this scenario of avoiding to spill time) but _before_ your opponent's move is less "valuable" than the time available to you _after_ the opponent has also made his move. Why? Because you have to consider less variations when trying to read out a sequence, since your opponent's play has probably just reduced the amount of branches to consider.
From these thoughts I deduce that gaining 50% or even just 30% of your spilled time added to your base time might actually be a pretty decent compensation that could strongly reduce the annoyance that you might feel in a spilling system.
At the same time, the bonus added on each move can be kept significantly below a comparable Fischer bonus, thereby reducing the time system's bias towards later stages of the game (if we look at the 'biggest continous usable time block' issue stated further above).

b) A "Fischer Byo-Yomi" time system.
Basically you'd have a main time same as with any other byo-yomi such as japanese and canadian, and after that you'd have a Fischer-style extended time.
Example: 45 minutes base time, 3 minutes Fischer byoyomi at +10 sec each move.
This way, you could emphasize fuseki a bit more, or rather prevent de-emphasizing it, by avoiding piling up more time later than you started with (without having to do artificial limitations that are sometimes suggested such as capping the total time you may get from Fischer bonus).


On a side note, I found a somewhat related quote in article http://senseis.xmp.net/?TimingSystemsRedux which might be nice to know:

"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."

C. Blue wrote: If we ask in what part of the game (fuseki, chuban, yose) a player can spend the largest block of thinking time on his next move, Fischer time emphasizes the later game stages more than the opening.

No, it does not. You are just presenting a scenario where the bonus has been chosen too long in comparison to the basic time. Your proposed setting 20/20 is just a bad choice; it would be better to use something like 32/15. Since you mention it, yes, wms has expressed the same misconception.

You afterwards went to the other extreme, setting an extremely short bonus in 45/4. That is also a bad choice, in my view, because 4 seconds per move is an inadequate pressure in comparison to the overall game length.

Then, you chose these words:

The dilemma is that the smaller the bonus, the fairer the players are treated in terms of when exactly they would like to invest most of their time, while on the other hand a smaller bonus will move the time system closer towards the problem faced in absolute time where unreasonable moves can be played to attempt and make the opponent lose on time (or make a really big mistake).

This is not a dilemma, it is a simple optimization. Make the maximum forced pace (determined by the bonus time) adequate in comparison to the overall thinking time. In my experience, 20/10, 30/15, 40/20 are good ratios.

I do not see a need to make this system more complicated.

Harleqin wrote:

C. Blue wrote: If we ask in what part of the game (fuseki, chuban, yose) a player can spend the largest block of thinking time on his next move, Fischer time emphasizes the later game stages more than the opening.

No, it does not. You are just presenting a scenario where the bonus has been chosen too long in comparison to the basic time. Your proposed setting 20/20 is just a bad choice; it would be better to use something like 32/15. Since you mention it, yes, wms has expressed the same misconception.

Well, the way I see it is that the misconception is actually on your side, because all the time settings you suggested and dubbed optimization do not really seem to work around system-immanent issues by providing a sufficient general improvement over all aspects. (On a side note, in this regard I'd also like to point again to the quote about Fischer time experimenting given in the Redux text.) Of course if you are fine with a certain bias in either direction, because it fits your playing style, the settings will certainly work well for you.
Although complicating systems is certainly a disadvantage, a Fischer-byoyomi does actually seem easier and not more complicated in comparison to currently established time systems aka japanese and especially canadian byoyomi.

You afterwards went to the other extreme, setting an extremely short bonus in 45/4. That is also a bad choice, in my view, because 4 seconds per move is an inadequate pressure in comparison to the overall game length.

This value was picked for a very specific reason, as was explained in the text.

I'd actually discard "Bronstein Carry" in favour of Fischer byoyomi if it's just for the sake of an easy system. Maybe at least this one could be added to KGS, since it should widely follow wms' demands to a time system.

C.Blue wrote:[...]because all the time settings you suggested and dubbed optimization do not really seem to work around system-immanent issues by providing a sufficient general improvement over all aspects.

Can you give an argument for this claim? Can you show why the balance between time management flexibility and maximum forced pace might not be achievable by simply balancing out basic and bonus time? Somewhere on the line (60/3 - 55/5 - 50/7 - 45/9 - 40/11 - 35/13 - 30/15 - 25/17 - 20/19 - 15/21 - 10/23 - 5/25) is an optimum. Why is it not good enough?

Can you show how your proposals could improve on that balance? Start with Fischer time 30/15, for example. How do you switch to Bronstein time and still keep the same overall game length?

(The report from the New York Go Centre is certainly an interesting anecdote, but you may note that they chose a rather large bonus again, compared to the game length. I do not see what kind of conclusion you want to draw from that.)

"Fischer-byoyomi" would certainly be an improvement over Canadian byoyomi (low hanging fruit), but it would still suffer from the same problem as all the other "main-time plus byoyomi" systems: you never know how many stones the players play during main time (they do not need to play a single stone), so the overall game length is very hard to guarantee. Such uncertainties always mean that a tournament director has to err preferably on the short side of time settings. In other words: the more uncertain the maximum game length is, the shorter the average game length must be to keep the tournament schedule. You may note that spilling also introduces such an uncertainty.

Harleqin wrote:

C.Blue wrote:[...]because all the time settings you suggested and dubbed optimization do not really seem to work around system-immanent issues by providing a sufficient general improvement over all aspects.

Can you give an argument for this claim? Can you show why the balance between time management flexibility and maximum forced pace might not be achievable by simply balancing out basic and bonus time? Somewhere on the line (60/3 - 55/5 - 50/7 - 45/9 - 40/11 - 35/13 - 30/15 - 25/17 - 20/19 - 15/21 - 10/23 - 5/25) is an optimum. Why is it not good enough?

Can you show how your proposals could improve on that balance? Start with Fischer time 30/15, for example. How do you switch to Bronstein time and still keep the same overall game length?

The supposed imbalances of Fischer time system have already been laid out in detail and it'd actually been nice if you could back up the claim of how to "optimize" it with some concrete examples, in which is visible how either drawback of the time system does not surface very much. Anyway, some more concrete stuff here:
-It is pretty clear that Fischer time is actually by far the system that most easily allows game total duration (and thereby tournament round duration) planning.
-If you have at any stage of the game less than about 15 to 20 seconds for your next move, you might be very hardpressed to respond to nonsense invasions.
-If you gain more than about 10 seconds on each move, it becomes possible that you amass time rather quickly (ie surpassing your starting time pool) in a way that might deemphasize the opening a lot.

Now, if we want to go for perfect tournament round planning and make everything else low priority, then of course we need Fischer time.

With the other points in mind, being asked about what other time settings I could imagine, for example I wouldn't mind 30min/20s/40% "Bronstein Carry". I'd expect to take at least 3 seconds per move, so assumed the opening is really played very quickly, the time bonus per move would be around 7 seconds. Still, if I find myself in a situation where the opponent start playing odd invasion moves, I have at a guaranteed decent minimum of 20s to think about my move. If I play a move very quickly, I won't have to be too concerned about finding and thinking about another issue on the board, since I know I could at least get 40% of my remaining time added to my pool, and spend it after the opponent made his move and it's my turn again.
I will certainly admit of course, that this system will not allow for as smooth tournament planning as Fischer, which is and will be system-immanently the leader in this department. For the above example, each move would take 10s..20s. The median would probably be around 13-15s, but I don't have data to back this up. That we have a reduced interval of 10s..20s per move is however already a nice improvement over the usual 0s..20 when going for a maximum round duration without presenting the players too "edgy" a time system such as raw Bronstein.
An advantage of "Bronstein Carry" might be that the base time size and time period setting are rather independant, whereas compared for Fischer time, depending on the kind of optimization as was mentioned, those might need more attuning to each other.

About Fischer Byo-yomi, mainly I just wanted to emphasize that it should be fitting into KGS design (lots of main time to spend during fuseki etc.), since it'd be pretty neat to at least have one smooth type of overtime available.

(The report from the New York Go Centre is certainly an interesting anecdote, but you may note that they chose a rather large bonus again, compared to the game length. I do not see what kind of conclusion you want to draw from that.)

Well, if the text appears to you to not provide relevant information, I don't really want to stretch it, since I already said that it is just a side note anway.

C. Blue wrote:

Harleqin wrote:

C.Blue wrote:[...]because all the time settings you suggested and dubbed optimization do not really seem to work around system-immanent issues by providing a sufficient general improvement over all aspects.

Can you give an argument for this claim? Can you show why the balance between time management flexibility and maximum forced pace might not be achievable by simply balancing out basic and bonus time? Somewhere on the line (60/3 - 55/5 - 50/7 - 45/9 - 40/11 - 35/13 - 30/15 - 25/17 - 20/19 - 15/21 - 10/23 - 5/25) is an optimum. Why is it not good enough?

Can you show how your proposals could improve on that balance? Start with Fischer time 30/15, for example. How do you switch to Bronstein time and still keep the same overall game length?

The supposed imbalances of Fischer time system have already been laid out in detail and it'd actually been nice if you could back up the claim of how to "optimize" it with some concrete examples, in which is visible how either drawback of the time system does not surface very much. Anyway, some more concrete stuff here:
-It is pretty clear that Fischer time is actually by far the system that most easily allows game total duration (and thereby tournament round duration) planning.
-If you have at any stage of the game less than about 15 to 20 seconds for your next move, you might be very hardpressed to respond to nonsense invasions.
-If you gain more than about 10 seconds on each move, it becomes possible that you amass time rather quickly (ie surpassing your starting time pool) in a way that might deemphasize the opening a lot.

First of all, you should not work with absolute numbers in the criteria, because the adequacy of a specific pressure is dependent on the overall game length. For example, in a blitz game that is meant to last for about half an hour, it is not sensible to call a maximum pace of 15 seconds per move "too fast", because that pace would imply an overall game length of at least an hour. On the other hand, in a five hour game, 20 seconds is quite fast, and one might find 30 seconds more adequate. You always have to compare to the average pace of the game.

So, let us take a 30/15 game of 240 moves. The average time per move is 30 seconds. The maximum pace, i.e. the miniumum forced time per move, is 15 seconds. That seems sensible to me: you cannot be forced to play more than twice as fast at any point as required on average. I think that this shows that inadequate time pressure is not possible.

Another way to see it is to divide the overall time into two parts: one that you have from the start, and one that will be unblocked bit by bit as you move. Of the same game, each player gets 30 minutes from the beginning, and another 30 minutes are unblocked at 15 seconds per move. That also seems sensible to me: half the time is free, half is rationed. In other words, you can spend at least half of your overall time on the first few moves. I think that this shows that the opening is not "deemphasized".

You claim that keeping a specific schedule is not the most important part of having a clock. However, in order to compare two timing systems at a respective setting, you need them to keep the same schedule. Otherwise, it is no question that the longer one likely has less potential pressure and more time for the opening.