Reader feedback: the great draw debate continues

The subject is draws, the unfought, short kind. It is a debate that has kept our readers occupied like practically no other subject in the past years. "Babble", a chess blogger called it, or killing flies with a bazooka, as one reader suggested? We have seldom seen such a volume of creative energy expended on a chess subject, and this must not go to waste. Once again we ask you not to send in any new feedback until we have published a further comprehensive article (by Gene Milener) on the subject early next week. The following are messages we received after publishing the last two installments of the debate. The material is very extensive, but we publish it all as a potential source that officials and chess thinkers can mine for imaginative ideas pertaining to important technical aspects of the game.

Reader feedback on the drawing problem

Giulio Bertazzoli, Milan
I propose this solution, a draw proposal reduce your time at disposal to 30 minutes (if you have more) so you receive a great penalty at the beginning of the game decreasing to no penalty when you have only 30 minutes or less (at the end of the game).

Brian Theismann, Inver Grove Heights, Minnesota USA
I would like to weigh in on the draw issue. My analysis of the problem of draws is fundamentally different from any of the other analyses that you have posted. I believe that the problem is with the game, not with the players. I will borrow the structure of Kung-Ming Tiong's paper for the rest of this essay.

1. Definition. I define the problem as "the excessive number of draws in high-level chess." I choose not to define the problem as "short, pre-arranged draws" because I am not convinced that they are that big a problem and because the problem of collusion transcends the problem of draws.

2. Effects. I think the biggest problem with draws pertains to what I call the "ceiling effect." This refers to the tendency of strategy games to be subject to mastery by dedicated players. Examples are tic-tac-toe and video games that can be overcome by following a "pattern." Such games fail to capture the public's attention because they can only be lost by weak play; they cannot be won by innovative or exceptional play. While the high proportion of draws in professional chess may or may not actually be caused by the ceiling effect, it does appear to be causing many people in the media to perceive the game as lacking in the complexity necessary to view it as a serious spectator sport. After the draw-infested Kasparov vs. Deep Blue match of 1997 I remember a commentator in the press drawing the conclusion that the sport had been "solved." (By the way, does anyone really think that Kasparov and Deep Blue were colluding? How often do computers draw, anyway?)

3. Cause. I believe that the main cause of all the ties is that the strongest chess players have, indeed, reached the upper edges of the game's complexity. It is illogical to think that the efforts of players could be exactly equal in as many as 87 percent (2000 Kasparov-Kramnik match) of games without the stronger player running up against the limits of possibility. I believe that a secondary cause is the Swiss tournament system. The Swiss system acts to reward mediocre play by giving players weaker opponents when they draw or lose.

4. Solution. My strategy to solve the draw problem would be to make the game more challenging for the best players. Several different specific approaches could be used. First, I propose that games use faster time controls. Note that 62 percent of the Amber rapid games were won outright. That ratio is even higher if only the games of the stronger players are counted. My observation is that online blitz and bullet games have very low draw ratios- even among the strongest players. Another proposal of mine is for the strongest players to be forced to play against significantly weaker players more often. Such asymmetric games would ultimately be more challenging for the best players because they could not afford to play for draws. Maybe even have the super-grandmasters play simuls to test their strength. With regard to the weakness of the Swiss system, my proposal would be to use what I call a "reverse Swiss" system. Instead of having the strongest players face off, have the strongest players paired against the weakest players. Eliminate players from the tournament once they reached a certain number of losses and draws. The reverse Swiss system would encourage early wins and create more unbalanced games.

The Playchess.com server would be an excellent place to implement my ideas. I think the world is waiting for a "World Internet Chess Championship." I suspect that glacier chess only became popular because it reduces the frequency of the onerous task of setting up the pieces.

The Christmas Rule might be a good solution to the problem of collusion, but my worry is that imposing such a rule without addressing the ceiling effect would mostly just lead to longer- and thus more boring- draws. The Bilbao Rule might also lead to lower quality games. Granted, faster time controls would lead to weaker play. However, that consequence would be more than compensated for by a higher number of games and by making the games more understandable for spectators.

From my perspective, all of the other proposals have similar weaknesses, are illogical, or are unworkable.

FM Danilo Perus, Slovenia
On our correspondence chess server, which will be opened soon, we have decided to include the following system, based on practical and historical facts:

• scoring results with 0, 1 or 0.5 is
  • traditional,
  • simple to calculate,
  • chess players would probably dislike any change.
• players wants to make a quick draws because of:
  • fear of a loss of rating points,
  • placing in a tournament,
  • lack of motivation.
• A chess game is just a matter of two players
  • only those two players can decide about normal outcome of their game

We concluded that there is nothing wrong with chess results, which are a real practical and historical outcome of a chess game. The problem is human nature. Any new solution must not change simple and historical way of counting and summing chess results. So we need some additional criteria to “push” on players to fight more seriously.

So we took the following steps on our correspondence chess portal:

a) no changes in counting results

b) rating system (as proposed in ChessBase articles by Jeff Sonas):

• We(white) = 0.541767 + 0.001164 * (WhiteRating - BlackRating) or
• We(black) = 0.458233 + 0.001164 * (BlackRating - WhiteRating)
• Rating Points (RP) = K * (GameResult (W) - We)
• Rating difference between all players on the same tournament can be maximum 300 points
• Attenuation factor (K-Factor) is 24 and it is permanent
• Ratings are calculated promptly.

First practical example: we have two players – white has rating 2445 and black has rating 2463. We(white) = 0.52 We(black) = 0.48. As we can easily see even here when White is playing against a stronger player with a higher rating, he will loose rating with a draw.

Second practical example: here white has rating 2445 and black 2381. We(white) = 0.62 We(black) = 0.38. Here White will lose even more with a draw. Please don’t forget also on high and permanent K = 24.

c) What to do on tying places? I believe this is the most important thing, which can help to produce more fight and which helps not to complicate other stuff. Why? I will illustrate this with practical example, but first I will write down the tying criteria:

Let’s see just the top of the bigger round robin table (columns: wins with black, wins with white, draws, losses, total of chess points, total “tying” points)

Conclusion:

I believe – even though this is just an illustrative example – that this system will force more aggressive players higher on tournament table as others. It is highly selective – we have no single tying in table!!

On the other hand I have to say that there is no ideal system and none will ever exist. Every method has pros and cons. We followed our principles to solve this problem; others might not find it useful. I just wanted to share our try to break through the problem. Time will show if we are right. While our rating system is based on Jeff Sonas proposal, we claim the copyright on tying solution!

On the end I would like to invite all serious correspondence chess players to visit our CCS server in May 2008. Serious means a great will to play chess, not a high rating. We will be glad to see you on the server – and we will see together, if we succeeded with the new system. – FM Danilo Perus, creator of the CCS server and ChessBase distributor for Slovenia. Feedback contact: danilo.perus (at) volja (dot) net.

Mark Galeck, Mountain View, USA
This is Mark Galeck, whose proposal was criticised in the article by Mr Tiong. I take it on the chin, my proposal isn't perfect and has it's flaws too. My proposal is not original, it is used in some Go tournaments, but perhaps it is more psychologically suited to Go than to Chess.

Anyhow, I want to notice one thing, about Mr Tiong's scoring system, which can be described as: For win/draw/loss, B gets 1.1, 0.6, 0 : W gets 1, 0.4, -0.1 ... It turns out, that this system is equivalent to a simpler system, that only changes the scores for draws compared to the traditional system. So the adjustment to win and loss scores, is unnecessary. By "equivalent", we mean that with both systems, the tournament tables at the end of a tournament, would have the same order of players.

Here is the proof: we start from Mr Tiong's system and step by step make equivalent scoring systems. Let us assume first that every player plays the same number of games with white (odd number of total players). So we can modify Mr Tiong's system, increasing all white values by 0.1, and obtain an equivalent system - for W/D/L black scores 1.1, 0.6, 0, and white scores 1.1, 0.5, 0. (This system is equivalent to the previous one because we just added to each player, the value of 0.1 x number of white games).

Now, a digression: if a tournament has an even number of players, then half of them will have played one more game with white (than the others). If we modify Mr Tiong's system as above, we would have to subtract 0.1 point for every one of those players to get to a system that is equivalent to Mr Tiong's. Regardless of their results, half of all players would all just get penalized. I think we agree that this is not a change for the better. So, in case of an even number of players, the system with 1.1, 0.6, 0 for black, and 1.1, 0.5, 0 for white, is even slightly better than Mr Tiong's (but really it does not make much of a difference, and is not important - this is just an inherent flaw with tournaments with even number of players).

Now we divide all values by 1.1 and again obtain an equivalent system: black: 1, 6/11, 0, white: 1, 5/11, 0. As you can see we can get rid of most of the modifications of Mr Tiong's proposal, and just use the suitable modification for the draw results, black 1/2 + some constant c, white: 1/2 - c, and obtain an equivalent system (or, in the case of even number of players, a slightly better system). End-of-proof

So I think both me and Mr Tiong, and reasonable people would have to agree, the only question is: how to determine "c". This is exactly the question I posed in my first proposal quoted on Chessbase. I proposed an auction system. I agree this is a bit complicated and unwieldy.

On the other hand, remember, what the goal is: to get rid of "grandmaster draws" (short unfought draws). I submit to you that if we just go for the kill (Topalov style), and set c = 1/2, that is for the draw, black gets 1, white gets 0, there would be NO grandmaster draws. Period. We would immediately solve the problem.

Of course, that would have it's own flaw. Namely, black would always play for draw, no incentive to play for the win. OK, then let's fudge a little, I don't know, I leave that to the discussion of experts, let's assign a large enough value for c. Perhaps c = 0.2, that is 0.7 for black draw, 0.3 for white draw, would suffice? If we play tournaments this way and it turns out that is not enough and there are still some unfought draws, try c = 0.3. I think one can choose this constant to be large enough to prevent most if not all of unfought draws, and still make black worthwhile to play for a win, in most if not all cases.

Marcin Ksiazkiewicz, Zielona Góra, Poland
I have a feeling that any resolution to the problem of "grandmaster draw" will never solve the problem of cheating and "team playing". I liked the idea of a scoring system 3-1-0, but then I realized that in fact it worsens the problem of "team playing" (one player of the team wins all his games against other players from that team). Kung-Ming Tiong's solution doesn't change anything on that matter.

My solution to the problem is to change the whole system: All tournaments should be played like a cup – winners of a round advance to the next round BUT losers are still playing among themselves for lover places. Of course each round should consists of at least two games (equal number of games with white and black pieces). In case of a draw in a round (for example two drawn games, or one win each player) there should be two blitz games. Double blitz games should be repeated until there is a winner. Blitz games should NOT be taken into account when changing the rating of the players. They are played only to force-pick the winner of a round. Blitz games seldom end with draws, even among the grandmasters, so it should be a very fast process.

Most important is to differentiate the prize money from the change in the rating of the players! The prize money should be distributed according to the final places of the tournament, but the change in the rating of the players should be counted as it is today – each game counted separately. Even if a player loses in the first round he still will play his best to improve his rating.

Example:

• player A wins all his rounds but his only wins are in blitz games and all his normal games are drawn. Result: he earns top money, but if he is a very strong player his rating will decrease (all games drawn),
• player B loses his first round (draws his first normal game and loses his second on a blunder), but in the next rounds wins all his normal games with white and draws all his games with black (there are no blitz games, because they are not needed). Result: he earns less money, but his rating will increase (no matter if he is a strong or a weak player).

Some might say that it is not fair, because a very strong player will finish in the middle of the field if he loses just one game in the first round, and wins all his remaining games. Well he at least will record very significant improvement in his Elo rating, so it's not so bad either.

Why I think that this system would be better? All normal games will be very hard fought (at least by one player). Blitz games are like lottery, because there is too little time to properly analyze the position. Better players will tend to avoid the blitz games, and to win the round right away. Moreover if the first normal game of a round is won by one of the players, the other player will fiercely attack in the second game, because he has little to lose (except maybe rating points). All rounds should be very exciting, and probably the most exciting round would be the FIRST one! Most importantly my proposition solves the problem of "team playing" – it becomes pointless.

I've come up with an idea how to create a chess cup. I'll describe it on an example:

There are 16 players. Player with the highest Elo ranking has number 1 and with the lowest ranking has number 16. Pairs in the first round are: 1-16, 2-15, 3-14, 4-13, 5-12, 6-11, 7-10 and 8-9.

My idea is that there should be no fixed tournament tree. Normally the winner of 1-16 pair would play with the winner of 8-9 pair, the winner of 2-15 pair would play with the winner of 7-10 pair, and so on. I see the problem with unexpected results, for example 16 and 9 win their first round matches and the rest of the games are won by higher rated players. In such situation pairs in the second round would be: 16-9, 2-7, 3-6, 4-5 and in the lower part of the tree 8-1, 10-15, 11-14, 12-13. This is a bad situation because pair 16-9 is much weaker than pair 2-7, 3-6 and 4-5. Similarly pair 8-1 is much stronger than 10-15, 11-14 and 12-13.

I think that after each round the pairs should be made similarly to the beginning of the match. So in my cup the second round pairs are: 2-16, 3-9, 4-7, 5-6 and in the lower part of the tree 1-15, 8-14, 10-13, 11-12. The winners from the first set of pairs play for the places 1-4 and losers play for the places 5-8. The winners from the second set of pairs will play for the places 9-12 and the losers for the places 13-16.

Let's say that there are 4 surprises: 9, 7, 14 and 13 win their second round matches. The pairs in the third round should be:

Assuming that all these games are won by stronger players the pairs in the last round are: 2-5, 7-9, 3-4, 6-16, 1-11, 13-14, 8-10, 12-15. Assuming again that all these games are won by stronger players the final standings are: 2, 5, 7, 9, 3, 4, 6, 16, 1, 11, 13, 14, 8, 10, 12, 15.

Commentary:

• such a cup would be very exciting, because every round would very important,
• there would be no way of "team playing", because nobody will know who will he face in the next round,
• there would be no games in which one player doesn't really care for the outcome of the game – every game counts!

Tournaments based on playing in groups will NEVER solve all the problems with draws, cheating and "team playing".

Leon Piasetski, Matsuyama Japan
I find the discussion about grandmaster draws a bit irritating since it smacks of 'political correctness', a justification for controlling aspects of life that unfortunately often robs them of their vitality and spontaneity. Of course, I agree that grandmaster draws are a concern but what worries me is that in our zeal to eradicate this problem we may end up creating a slew of rules and punishments that extend to all players. Thus I suggest we take another look at this issue and consider it from several perspectives.

There are a limited number of grandmasters in the world of chess, perhaps 1000 or so players at this point in time. Of these, how many are at the top level where they receive sponsorship in the form of food, lodging, travel expenses, and a significant honorarium? These players should indeed be subject to 'rules of engagement' where their conduct is scrutinized, since they are supported by the chess community. However, there are also many GMs who are not at the top level and who must make ends meet by participating in second and third tier events. They may not receive much in the way of support and may even have to pay hefty fees like everyone else. This is common in the US, Canada and many non-European countries. Even in Europe there are some tournaments where so many GMs participate the organizers can simply not afford to pay all their expenses.

Then why do they risk their own money to play in such events? Perhaps it's the same reason we all play - because the event looks interesting and there are chances to win big prizes - a gambler's motivation! Another reason may be that there are fewer quality events and more competition, thus one inevitably must take risks or give up playing altogether. My point is that life is not easy for many grandmasters and before we judge them perhaps we should also keep this perspective in mind.

My view is that all of us are in some way supporting the game of chess. Having paid for travel, lodging, food and entry fees, if one wins a prize and deducts these costs, how much is left over? Probably not much except in the best of circumstances! The same is true of organizers who put in a lot of time and effort and rely heavily on unpaid volunteers. The financial benefits mostly go to the hotel owners and food establishments frequented by the participants, not the players or organizers themselves except for the lucky few or unscrupulous ones.

Thus I think we need to shift our perception and recognize that we are playing chess because we want to, not because it's lucrative - otherwise try something easier, like poker. The grandmasters who choose to act conservatively and play for a draw because they need to make sure they have food on the table deserve some sympathy. In fact, even the best fighting players will take this option because it's a normal part of tournament tactics. It may be irritating for organizers or spectators to watch a lifeless last round, but for the players involved it's crucial and we have no right to condemn them unless we can promise them the kind of support they would get if they were professional athletes paid handsomely by their government.

We can and should create conditions that encourage more fighting chess - otherwise why play or watch? However, any rules we make may create more problems than they solve and should be carefully considered before being implemented. I am not in favor of rules that increase arbiter interference since we may eventually end up with ridiculous situations, such as national arbiters interpreting rules to favor their own players, just as we sometimes see in World Cup soccer games. I also feel that applying any rules to the greater chess public would be overkill since the problem of GM draws by definition is not a general phenomenon (Of course, I realize that ordinary players can and do agree to 'grandmaster draws' and this may have a degrading effect on a chess tournament. However, sponsors and the chess public at large are mostly paying attention to grandmaster games and my guess is if we focus on the elite group other players will follow along).

I have a simple solution to the grandmaster draw issue - although this doesn't address the underlying problem of lack of financial support. Grandmasters avoid taking chances because they want to maximize their earnings and minimize risk of losing everything. Why don't we distribute prizes in same point groups based on results against an average opposition with wins counting 3 times as much as draws (losses are ignored). So if player A scores 4 wins and 3 draws against an average opposition of 2500, the calculation would be (4x3+3) = 15 x 2500 = 37500, whereas player B scores 3 wins and 4 draws against an average opposition of 2600 . (3x3+4) = 13 x 2600 = 33800. We can decide whether players need a minimum average opposition to be considered for prizes, whether we divide up all the prizes and distribute them proportionally or simply follow the organizers original prize list, and what factor to give wins (I suggested a multiple of 3 but it's completely arbitrary). In any case, this would encourage GMs to risk more if they want to get a better prize. This solution does not change the rules of the game as has been proposed by many mathematical models - instead it addresses the key point, who gets the money.

However, this doesn't take into consideration why we should even try to penalize players for making a draw. In fact, what is wrong with a well-played draw? There are drawn games that have far greater artistic merit than many mundane wins. Perhaps we need to reeducate the chess public to appreciate draws rather than devoting all our attention to their elimination!

One final note: The recent Corus and Linares tournaments show that top-level players are paying attention to this discussion and adjusting their approach to make events more competitive. Clearly, this type of discussion is healthy as long as we don't become a police force trying to root out any evildoer - or I predict one day we will have 'sting operations' against GM cartels, Perhaps with a few simple adjustments grandmasters will wake up and start playing for all their worth. Incidentally, waking up early for a last round is one of the reasons some GMs make a quick draw!

Tsering Dawa Lama, Zell am See, Austria
The Christmas Rule, mentioned by Brian Karen, Chessbase, December 29, 2007; touted as a promising rule by ChessBase, specifies that when a player proposes a draw, the draw offer would stand for the rest of the game. According to Mr. Karen, this would mean that only a player who is certain the position is "dead draw" would make the draw offer and once offered, it allows the opponent to play sharper lines while keeping the draw in hand. Agreeably, this would result in interesting and enterprising lines of play after the draw offer (it does not, however, ensure that a game would be interesting and enterprising up to the point before the draw offer) but this in effect creates an artificial situation as the player offered the draw now has, literally, nothing to lose and has the incentive to win "to prove to the player offering the draw that the draw offer was a mistake". Thus, out of fear (perhaps), the first player would not offer the draw. This artificial situation clearly benefits the second player. If the first player had misevaluated the position when offering the draw (and this definitely could happen), he is at a disadvantage as there is the possibility that he could now end up losing the game. It is true that the draw offer is discouraged but would the win by the second player be justified when it was achieved under a "nothing to lose" situation where in the normal course of the game (if the draw was not offered), the second player may not have played the interesting and enterprising lines. Certainly (in my opinion), the win can be considered as botched and unworthy.

Now read my own solution carefully and thoroughly: once GM-A makes the draw offer GM-B can decline and continue to play for a win until he finds that he cannot possibly win and he himself is not getting mated in the next 10-15 moves after accepting the draw! Wait a second, here comes the interesting part. When GM-B accepts the draw offer, at that moment GM-A has 10-15 moves to checkmate GM-B, or else it is a well fought worthy draw. Doesn't this give the Christmas Solution a great twist, worthy to be considered? In conjunction with this Christmas Solution you can also add an appropriate and non-complicated scoring system such as (3:1:0) or (1:1.1:0.4:0.6:-0.1:0.0).

Kenneth Calitri, Mahwah USA
How many times do I have to send in the simple solution:

You reward points for winning games. Draws are not rewarded, so the tournament leader cannot coast to victory by drawing games. The player willing to play for a win is rewarded by his/her risk. Plus awarding two points for a win and –1 for a loss allows for a greater swing in one game. Therefore and aggressive player can afford to lose a game here and there, especially if they beat a key competitor. For example:

• Player one has 5 wins and 5 draws: 7.5 points in the normal scoring system; 10 points in the revised system.
• Player two has 6 wins 1 losses and 3 draw: 7.5 points in the normal scoring system; 11 points in the revised system. Player 2 wins.

Go over any major tournament and it will dramatically change not only the winners but the top five positions. Conservative or drawing GMs go home. Not that I am picking on him, but Boris Gelfand's great showing the last World Championship would have actually put him in the lower portion in the field – he drew too many games. On the other hand Magnus Carlson would have won several recent major tournaments rather than tying. Try it – pick a bunch of tourneys and redo the crosstables based on the 2, 0, –1 scoring system.

David Valovage, Fargo, ND, USA
Do we assume chess to be a draw? I would assume so, and I believe the vast majority of qualified chess professionals and analysts to assume so as well. Assuming chess is ultimately a drawn game, how can we justifiably modify the scoring system to make draws "more appealing"? We're applying an objective change to fix a subjective problem. While Kung-Ming Tiong's essay on draws appears to be quite exhaustive and relatively formal, it is wholly unsatisfying since it is clear that ANY modification to the scoring system will simply unbalance a game that SHOULD be balanced, and a panel of arbiters overseeing every single game is quite unpractical. Perhaps in the case of a proposed draw, a panel could check (possibly against computer analysis) to confirm, but otherwise the implementation of multiple GM's per match would be nigh impossible. While well-intentioned and well-thought, the proposal simply changes too much to be the solution.

I think a democratic action would be most appropriate, as a statistically approved method (by GM's and analysts) would have the highest probability of being the correct solution. Personally, and from reading so many of the same slight correction to the Christmas solution, it would appear the answer is simply a 10-move (or thereabouts) sustain of every draw offer.

Raymond Cheng, Virginia Beach, USA
Mr. Tiong asserts that his proposed solution S1-S4 to the perceived problem of "grandmaster draws" is "effective, with minimal side effects [sic], simple and realistic." Um, on which planet??

Kerem Yunus Camsari, Lafayette, IN, USA
The concept of draws in chess has been there since the invention of the game. Given the absolute symmetry of the black and white structure (with the slightest skew of White's initiative in the beginning) it is quite logical to observe draws in classical chess. Personally, I think that the ultimate chess game (where no players make a mistake) is a draw. Therefore, I have a few comments about the current developments. I will try to convince you that the current system is one of the best among what has been proposed.

First of all, you can't take the 'HUMAN' aspect out of it. People are making a living out of this. It is chess players' job to play chess. And they are ALWAYS going to be calculating the possible outcomes of a particular chess game. It is the REAL experimentation of game theory. And as one of us suggested, if both players INDEPENDENTLY came up with the idea that drawing is their best option, we have to accept it and learn to live with it...! It's their job and profession. It is even a kind of art for those who live at the top. Just listen to what Kramnik said about it: A painter simply paints... He doesn't ask for rules, he shouldn't be restricted by these puny attempts. No matter what complicated rule we come up with, they are always going to be vulnerabilities, exploitations, secret agreements, team plays...

Do you think that can you avoid such things by ABSOLUTE logic? We are all missing the humanistic point of view here. These guys are not gladiators. They don't have to kill if they don't feel like it. That's what makes their brilliant victories brilliant. If you force them out of their own style, they will even be worse than what they are now. Just get over it and accept that they can't always please you. 95% of you even do not understand if it's an unfought draw or a well-fought draw. Stop teasing the GMs ...!

IM Mark Diesen, Conroe, Texas, USA
All systems that attempt to discourage non competitive games are fraught with problems. Alternate numerical scoring systems are too 'unnatural' and too difficult for the average chess fan to comprehend. My proposal is that in the event of a "non-competitive" game that these games be evaluated by a group or committee, and that a small $ fine on both players be imposed – to be deducted from each players honorarium and/or prize fund.

The small fine would be sufficient – let us propose as an example $200 per incident, as it would be somewhat humiliating and more of a psychological penalty than true financial penalty. The 'small' financial penalty would apply for games agreed drawn 'wherein the committee looks at number of moves, amount of play left in the position, or even possible collusion. Fines would mainly be applied to games less than 30 moves and/or games agreed drawn where there appears to be significant imbalance left – games judged to be "non-games". The fines being small allow the current system to continue on, but apply subtle but real pressure for players to fight harder.

Dan Mowers, Peterboruhgh, Canada
Why not define the draw out of existence. In the case of perpetual check, the person giving this gets the full point. Perpetual check is defined as a win. Why add up the point on the board and eliminate this draws where one player has more points on the board than the other. In the case of a draw and the points are equal then the player with the greater space advantage wins. Just the number of possible squares that each player can move to.

Christian Sasse, Vancouver
The discussion is hyptothetical for now. Recent tournaments at top level have shown quite the opposite: Linares was super-exciting with a few draws (so what) and Atatürk Istanbul showed even fewer draws. Let's enjoy the games, so many new ideas happening!

Adnan Bicaksiz, Ankara, Turkey
Of course, all proposals to solve the problem of draws have their own merit, as analyzed by the Malaysian mathematician and logician Kung-Ming Tiong. I will make a practical and clear cut proposal: since all proposals need fundamental rule changes in the game, let us have only one outcome for the game: win (1) for one side and loss (0) for the other. No draw offer allowed during the game. Players must play to the very end. Games ending in with no party having enough material to checkmate should be decided by "drawing lots" under the supervision of the arbiter to select the winner. Then see what happens.

Robert Luck, Tualatin
The "mathmatical solution" is hard for me to argue with since I have promoted it for years, though I hadn't considered punishing White for losing. The shortcoming is that, though more complicated, it still very likely allows for draw odds coasting for the tournament leader in the later rounds. Lately I've favored not counting draws at all in tallying the final score, as Fischer wanted in matches; except possibly as a tiebreak system that favors Black. If only wins count, then taking chances in an effort to bring about a decisive outcome becomes a viable tournament strategy, and one that will seldom allow a tournament leader any comfort in taking short draws.

Kai G. Gauer, Waterloo, Ontario, Canada
There's at least one very simple method to solving the deterrance of encouraging GM draws: anyone who has scored more than 2/3rds of their game points (wins or losses; but just not draws) during the tournament shall have incentives such as their billeting fee or return portion of their travel fare reimbursed. Those who have not attempted to play in accordance to the primary goal of chess (i.e. checkmate, as indicated as the goal in the preface to the FIDE rules, where stalemate, etc. is only covered in a highly numbered section much later on – shows the strategic precedence for which is the rule and which is the exception) can find their own way of getting home or choose another way to make a living, or at least enjoy a well-fought-out tournament.

Telmo Escobar, La Plata, Argentina
I don't agree with any artificial measure to restrict the right of chessplayers to declare a draw by agreement, without the obligation to give any explanation to third parties. Players lose face when people believe they are not playing for a win – for whatever reason, "legitimate" or not – and this must be their only punishment. Also, directors and/or sponsors of top class closed tournaments are entitled to invite the players they want to have, so they can, in effect, seriously damage the career of nonfighting masters. Indeed this has happened often in the past.

Concerning ordinary tournaments, I understand the preoccupation about short draws, but think that the proposed cures could be much worse. For example, it has been stated that giving arbiters – maybe in consultation with some silicon monster – the right to cancel draw proposals when they are apparently not justified, could be an intelligent solution to the problem. I vehemently disagree with these kind of measures because the consequences could be disastrous and the problem would be vastly augmented. I'm not so confident about the honesty of arbiters and/or organizers, and don't like the idea of enhancing their power over chess players.

In my view, the main problem of chess tournaments is the main problem of human life generally speaking: money. Capitalism is a cancer. It's only because of money that grandmasters are doomed nowadays to perversely short time controls, they are often forced to dress in a way they ordinarily don't like, they are forced to attend silly press conferences after playing, and so on, and so on.

Harry Cohen, Ellicott City, MD USA
I'd like to propose a practical solution to the problem of GM draws. I suggest that games be played with a single sudden death time control (e.g. game in 150 minutes) and an increment (e.g. five seconds). When a draw is reached, for whatever reason (agreement, repetition, or 50 move rule), the clocks are paused, the players switch colors, and a new game is started with each player having whatever time remains on his or her clock. This continues until there is a decisive result.

Jean-Michel Laprise, Montreal, Canada
If a player wants to make a draw, let him. "Exciting" players get invited to a lot more tournaments than "boring" ones. And the "boring" ones deserve to get some invites anyway, because everybody has different tastes and many actually prefer the kind of players whose solid style and less fiery personality generates more draws.

Though I personally have no major problem with unfought draws, I was interested by a more recent proposition, that once a game is drawn, the clocks keep going and the players switch colors and play another game until a decisive result occurs or one player's clock runs out. This would increase the importance and the subtlety of clock management, and also require better "rapid chess" skills, but I feel would harm the game in some important ways.

When faced with a novelty, a player will typically spend a great deal of clock time working out the intricacies involved over the board. But this would be almost suicidal in the proposed scenario, as even if the player managed to make a draw, he would likely have a huge time disadvantage in the rematch (one hour versus five minutes, for example). Even if he somehow managed to draw that one, he would eventually be placed in an impossible situation and lose on time or on a horrible blunder. In the long run, long thinks would basically disappear from the game, and time management would become more important than correct play.

In the end, out of all the solutions proposed, the only one that would not denature the game is the Sofia rule. If you think draw offers hurt the game, then you simply ban them without the arbiter's consent. Every other proposition would hurt the game's simple nature. Each tournament director and sponsor can choose for himself the kind of tournament he wants through his invitations and the imposition or not of the Sofia rule. And we can show our preference by following more closely the tournaments that are run according to our tastes. I prefer Corus to Dortmund, but I don't see why my preference should be imposed on everyone.

Jonathan Estey, Providence, Rhode Island
I am quite frankly a bit frightened by many of the "solutions" to short draws proposed both by ChessBase readers and by experts, because they are cases of the cure being worse than the disease. Let us not forget, as many others have pointed out, that a perfectly played game of chess should be a draw. Penalizing draws under the Bilbao system or with fines (or removing draws from the rules altogether) simply ignores that fact and erodes the quality of chess as a game.
Let us also not forget that the vast majority of tournament games are NOT played by professionals but by amateurs like myself. When I run, play in, or work at tournaments, there are very few draws and almost no short draws. As a player, I don't want to go through head games to decide when it's safe to make a Christmas draw offer, nor do I want to save a tough draw against a stronger opponent only to not get any points for it, nor do I want to show up for a slow chess tournament and find that my score is dependent on my rapid chess skill, and I especially do not want to play through a dead ending for an hour when I could be analysing with my opponent or relaxing. As a sometimes tournament director who still does his Swiss pairings by hand, I DEFINITELY do not want to have anything to do with tenths of a point. The 1/.5/0 system is beautiful in its simplicity, and there is no reason to change it or the fundamental rules of chess. 90% of chess tournaments have few spectators, few incentives to short draws, and zero need of radical anti-draw measures. The rest can hire extra arbiters and use the Sofia rule to make sure that all draws are at least sporting. Don't change the game I play just because Leko is boring the spectators.

Dr Hans Richter, Cambridge, UK
I am really surprised with the extreme measures proposed to eliminate not only short draws but any kind of draw altogether. I am not surprised that not many GMs, who strive hard to make a life out of such a demanding competitive job, have sent any insightful comments so far. People participating in this long debate seems to forget that

1. they are not paying to follow hard-fought games, so basically they can't claim to see any particular type of game,
2. professional players, specially GM strength, are not swimming in a sea of money, but maybe quite the opposite,
3. draws are an integral part of the game, very often with fierce attacks being neutralized by imaginative defences, so a draw may well be just the outcome of correct play,
4. strong GMs play so well and deep nearly all the time, that mere amateurs will seldom understand why a game ended in a draw (it's like a nursery school kid just getting to know the letters suddenly critisizing a literature Nobel Prize for writing this or that way)...

I guess a 2600 GM who works on his chess eight hours a day may well be right when determining that a draw is a good result, either to improve his intakes/Elo rating or save energy/recover from illness or a previous defeat (all very valid scenarios to my mind). All this discussion stems from weak players who, together their last version of the Fritz program, feel free to critisize decisions made by strong GMs. In conclusion, I would like to see more respect for professional Chess players, so before aiming to change the job conditions of a job we are not actually doing but only looking at (ie, high level competitive Chess), ask ourselves: Would I be able to make any money by playing competitive Chess? If I were a professional Chess player who has not made enough/any money for several months, would not I take a short draw in the last round to secure first prize? A couple of simple questions, just to start with...

Sartaj Hans, Sydney
Dear ChessBase reader, what makes you think that your outrage at the number of draws in elite GM chess should be addressed ? You follow chess on the internet, read free news on chessbase.com, dont pay any money to watch the game live, dont do anything to make these Super GM tournaments happen. What part of your chess existence gives you a right to winge about the proliferation of draws ?

The elite GMs play these tournaments with an aim to place as high as possible at the end of the event. They use their own tactics, they understand their own strengths and weaknesses, and use what they perceive is the best possible strategy to achieve their objectives. This is their life, this is their tournament, they can do whatever they want.

If some party has a right to demand a tougher fight, that party is the organizing sponsor. Their motivation in sponsoring such tournaments is self publicity and nurturing of the game. If they believe that the game they want nurtured is being abused by the GMs, then sure, they have a right to change the conditions of contest.

You, dear reader, should stop spamming the Internet with your pointless demands.

Paul Ladanyi, Budapest, Hungary
The too many grandmaster draws are only the second biggest problem in chess today. Even worse is that it is a team play. It is not as bad as it used to be when after the games were adjourned, the players went to sleep while their team analyzed the position all night. Today the teams work on openings and the player with the most money will buy the best team members and will have a big edge on his opponents.

The obvious solution that solves both problems: play Fischer Random. Today an amateur like me skips the first 10-15 moves when replaying a grandmaster game since it is known that they follow theory and won't be able to suprise each other in the opening. It is very likely that they get to a balanced position and agree to a draw possibly only after 20 moves. Playing Fischer Random with its 960 possible opening position would guarantee exciting chess from the start.

Hanro Viljoen, Sandton, South Africa
"Match fixing or game fixing in organized sports occurs when a match is played to a completely or partially pre-determined result" – answers.com.

GM Chess tournaments often contains games that are as fixed as a Zimbabwe election. I think that spectators are disappointed that chess undergoes so much match fixing and feel cheated when they come to watch a game with a predetermined result. I believe that pre-arrange draws fall into the above definition. Do short draws fall into this result? Many articles I've read regarding this matter have one of the following views: Players are entitled to this pre-determined result; or that it must be stopped some way or another. I aggree with the latter and my reason is that match fixing is unethical and damages the sport when it is allowed so freely.

Please note that I am merely proposing a concept not trying to create a hard and fast rule. Even if you don't agree with my proposed solution I believe point 1 is still valid and match fixing should be punished in chess or any other sport.

I propose that all draws in the tournament (assuming a GM tournament) must be evaluated and if the arbiter feels that the game was a "short draw", both players should be awarded 0 and not the usual 0.5. I realise that "short draw" will have to be defined in some or other way to standardise the rule, but I will leave this to FIDE or the discretion of the arbiter. I am merely trying to illustrate a concept.

Of all solutions that pose to address the problem (not including the solutions that state the problem should be ignored or accepted), this idea will change the nature of the game the least. I believe you cant blame spectators or sponsors that wish no part in a fixed result.

Wuthrich Guillaume, France
In a tournament invite four Tals and four Moros and you'll have no short draws. Now invite four Lekos and four Svidlers and you have only short draws. Isn't the solution clear?? Chess players gain their fame from the public, the players the public do not want to see, you don't show... This will cultivate the right player's state of mind, just like in Chinese Chess...

Michael Vidler
I've been only partially following the debates and proposals on dealing with the draw problem and "grandmaster draws" in chess, so apologies if this has been proposed before. I just wondered whether, with the sophisticated computing power we have in terms of databases, whether the games could be subjected to an analysis as they are played to score the game in terms of "originality", that is, divergence from previously played games held on record? Of course, it does not get around the problem of coincidentally playing in all innocence down a drawing line, but it need not be the only scoring system or rule for determining the level of determination to play a full game by the players, and could be used as a more objective part of a scoring system for taking the quality of the game into account at, for example, the prize stage or tie breaks.

Mark Liew, Singapore
I believe the solution to preventing short 'planned' chess draws is simply to change the monetary prize system in such a way to benefit decisive games while discouraging draws. Some of the following examples can be used: deduction of prize money for games which end in draws before move 40, Cumulative bonuses for consecutive wins, big financial rewards for best fighting game of the tournament..etc. However, the changes of the prize money system have to be significant in order to attract more fighting chess. I believe the Sofia rule, which does not permit players to offer draws is also a good rule to keep.

Tobias Nordquist, Sandviken, Sweden
I have a suggestion to add upon the The Christmas Rule: Let the players that suggested a draw have another chance to force a draw by suggest a new draw after 10 moves (or so). If this new draw also is rejected then we have, the same situation as in Armagedon-games, one point for the players who offered a draw if he won or played a draw, we have one point for the refuting player if he wins. Comments: This is a way to give fare conditions to both sides in the Christmas Rule. I guess that the players who play for draws will stop offering draws and just gonna play on forever.

Julio Claudio, Santiago, Spain
I would like to give an opinion about trying to avoid too many draws in chess tournaments. My suggestion is simple and quite straightforward:

• On the one hand, if a forced draw is reached in a game (Fifty move, Threefold repetition, Perpetual check, or Stalemate rules are applicable) then every player obtains 0.5 points, as always.
• On the other hand, if the draw is agreed by both players, having all of the above mentioned rules been discarded, then every one obtains just 0.25 points.

I think this is a sort of penalization to unfought games, forcing the players to keep on the battle up to reaching on the board two kings alone. As it can be seen, theoretical draws are to be included by means of using the rules mentioned under the first item. It can also be seen that this idea is useful for tournaments only, becoming pointless when applied to usual matches. It would be interesting to hear about the drawbacks the readers find on this idea.

Iman Khandaker, Watford
A major reason for unplayed draws is the ease of predicting the range of possible results towards the end of a tournament. Adoption of 1 point for a win, 0.55 for a draw with black, 0.45 for a draw with white and 0 for a loss, would greatly increase the number of possible results. This would create sufficient uncertainty to deter many draw offers, without resorting to the coin-tossing non-determinism that has been suggested. I concede that the tables would look messy, but they would be accurate.

The idea of a permanent or sustained draw offer appears to be gaining traction, but I have doubts. The objective should be the reduction of unplayed draws rather than all draws – anything else would change the balance of chess. A permanent draw offer places the offerer under a substantial disadvantage - in a position where all results are equally likely, the offerers expected yield is 25%. Seeing your odds dropping from 1-1 to 3-1, is out of all proportion to the crime of offering a draw (almost equivalent to dropping a pawn!). Draw offers sustained for a set number of moves would reduce this imbalance, but by an amount strongly dependent on position.

In contrast Robert Bernard's 'drawing cube' idea penalizes the draw offer by only an imperceptible amount. The game continues as normal, except that the right to offer a draw passes to the opponent. Giving away this small advantage might be enough to deter players from speculative draw offers. A major source of these offers is the weaker player making early draw offers with the white pieces - black knows that he is worse, but turning down the draw offer commits him to the psychological burden of outplaying his opponent. The idea of giving black the first option of offering a draw is excellent, because it eliminates the aforementioned problem ... and goes some way towards reducing blacks disadvantage in the opening position. This would require draw offers to be represented on the scoresheet - I suggest =? Any takers?

On the theme of minor changes, FIDE rules Article 15.1(d) says: "It is forbidden to distract or annoy the opponent in any manner whatsoever. This includes the persistent offering of a draw." And Article 16.5 requires arbiters "to impose penalties on the players for any fault or infraction of the Laws. These penalties may include a warning, a time penalty (by adding to the player's used time or to his opponent's unused time) or even the loss of the game." Since a draw offer increases the analysis required, it seems only fair to compensate the disturbed party by an extra minute to consider the offer. The elegance of this solution is that it just requires one word to be removed from the rules of chess – the 'persistent' in 15.1(d). Proposed rule changes should be as small as possible and this seems a good place to start.

Saeid, Abdoli, New York, USA
I have seen many interesting ideas about how to split the score between Black and White in order to discourage short draws, However, I am not sure if anyone has been considering the number of moves in their account yet. For instance, if we assume anything less than 40 moves to be considered as a short draw and anything beyond that a normal draw, then perhaps we can bring the number of moves into the equation like this:

Number of moves = n
White's score = (n / 40) * ½
Black's Score = 1 - White's Score

	     W1	D(n18)	B1	D(n34)  D(n25)   Total
GM A	1.0	0.775	0.0	0.575	0.3125	2.6625
GM B	0.0	0.225	1.0	0.425	0.6875	2.3375
Original system = 2.5 points each

* White's Score = ½ * (18 / 40) = 0.225
* Black's Score = 1 - .225 = 0.775

** White's Score = ½ * (34 /40) = 0.425
** Black's Score = 1 - 0.425 = 0.575

*** White's Score = ½ * (25 /40) = 0.3125
*** Black's Score = 1 - 0.3125= 0.6875

In this case at least the players will be discouraged to have short draws.

Vugar Fatali, Strasbourg
I read the last two articles about solutions to short draws with the aim to see something interesting but, franlkly speaking, was extremely disappointed. Why? Because all of the proposed solutions are unsatisfactory and the great majority of them are simply too stupid to discuss.

The draw is a natural part of chess. Chess cannot be compared to soccer, hockey, baseball or anything else, so we cannot introduce scoring rules from other sports to chess. (Let alone some "innovative" scoring systems like 0.4 to white/0.6 to black in case of a draw, and minus 0.1 score for white loss - they are just obviously ridiculous in their automatic assumption that white holds a 0.1 point advantage at the start of the game!). As for short GM draws, I understand that people (including me) don't like to see them because they are unspectacular and "uncompetitive". But they constitute only a relatively small number of all chess games played.

So we all love the game of chess as it is in its entirety, but we happen not to like only a very minor part of it (which is short draws). However, if we intend to find a solution to the problem of short draws, we must realise that such a solution should not hurt the game itself. All of the suggestions voiced in the last two articles, while aiming to resolve this problem, have a very negative side-effect: all of these suggestions, if adopted, would result in a dramatic change of the game itself! So I would ask people not to offer ridiculous "solutions" which arguably aim to eliminate short draws, without thinking first how it would risk changing the nature of the game we all love!

David Ottosen, San Jose, Costa Rica
As one of the early proponents on the Xmas Draw offer rule, it irritates me to see constant comments such as "the game after the Xmas draw offer will be unrealistic, or of no use to study". Less useful to study than a blank scoresheet (as we would see if the draw was accepted immediately?). And LOL at the Hydra suggestion.

Jerry Olsen, Los Angeles, USA
I've read the suggestions of Kung-Ming Tiong and several more suggestions from readers. I am relieved that most of the suggestions are so drastic that I'm quite sure they would face stiff resistance and never be implemented. The problem, I believe, has been blown out of proportion. GM draws aren't THAT big of a deal. They occur once in a while, and they are a minor annoyance, but they haven't ruined any tournaments nor have they spoiled professional chess. I have the sense that we're trying to kill a fly with a bazooka.

Most of the suggestions have unpleasant side-effects. For example, lets not forget that we often want to merely show the outcome of a game, and for for this purpose we normally use the shorthand "1-0" meaning "white wins", and "0-1" for "black wins", and "1/2" for "draw". If we change the scoring system, do we now have to use "-0.1-1.1" for a black win, or "0.4-0.6" for a draw? If so, it is very cumbersome, but if not, it creates confusion about who scored what.

I keep coming back to the same point: The problem is "Games that end by agreement even though the position still contestable". The most obvious and direct solution is therefore: "Forbid games from ending by agreement when the position is still contestable". This is the Sofia rule. It can easily be implemented, and it has been effectively implemented. So why make the problem bigger than it is, or make the solution more convoluted than necessary?

Jacob Woge, CPH, Denmark
I think short draws is not a problem in chess today. You have events where nobody seems to be able to win, but in general people fight. Maybe we are just lucky, but currently there seems to be a lot of ambition in top flight chess. However, I think it should be stated clearly in the rules that the same player cannot offer a draw twice, without a draw offer by his/her opponent. The right to offer should change sides. Since a few years ago draw offers must be recorded, so this is now possible to clarify.

Second, I kind of like the Monte Carlo method: draws score 1/4-1/4 and you play a second game with reversed colours for the other half point. This was used in some of the mega-tournaments around 1900. I use it in private events, with reduced playing time for the second game for practical reasons. For official events, this was abandoned more than 100 years ago, presumably with good reason. But I still think it's fun for the odd event.

Finally, notwithstanding my first statement, I find the idea of a sustained draw offer interesting. If applied, I think the limit should be one single move, i.e., you offer a draw and promise one more move. But it might be just that, interesting, and not applicable.

David Valovage, Fargo, ND, USA
I thought Paul Drearey of England made an elegant amendment to the Christmas solution. He proposed that the offer of draw to an opponent could not be rescinded for a number of moves equal to the remaining bishops, knights, rooks, and queens on the board at the time the offer was made.

I find Paul's amendment appealing for a number of reasons. First, a set number of moves, while solving the problem, appears too arbitrary to be "fair" (Who decides what number, and why?). Additionally, when the pieces whittle down, a draw offer would be too tedious for the player offering since pawn-play linearizes the game irreversibly. Moves become more critical and mistakes more costly. The fixed number of moves would become more valuable in the endgame, and endgames with pawns only (although highly nontrivial as Chessbase has demonstrated) would hold higher certainty of a draw! Clearly, the number must decrease with the pieces, and Paul's solution does so very mathematically as the game of chess would want.

The only difficulty would be if the number of pawns was low and a few pieces still remained. If both players had a knight and two bishops, the position would probably be drawn, but a draw offer would last for six moves. Therefore, perhaps the rule should state that "The draw offer will stand for a number of moves equal to the remaining bishops, knights, rooks, and queens OR the number of remaining pawns, whichever is the lesser number at the time of the offer."

The chess community should err only on the conservative side of change. Draws are a fact of chess, and many readers seem to want to reduce chess to gambling by affecting the NUMBER of draws. It's not the number that's the problem; it's the quality. Don't like short draws? Extend the length of the offers. Don't like boring draws? Encourage the players to fight. The perceived "too-many-draws" problem has been already solved with rapid/blitz/bullet chess; watch those if you're getting bored. The world shall surely feel a loss the day chess serves as instant gratification.

Albert Frank, International Arbiter, Brussels, Belgium
I don't understand all this discussions about short draws and GM draws. In high level chess tournaments (maybe don't consider some local players in it, specially for the past), there was always about 50% of draws, absolutely nothing has changed. I think there are a lot of really important problems (possibility of cheating, sold games, ...) and there should not be anything done about the draws. Of course, as said in Dr. Nunn's article, if a GM really makes a lot of short draws, just don't invite him any more.

R. Gibert, Dana Point, USA
Here is my proposal for dealing with GM draws: if a game ends in a draw, a second tiebreaking, faster (30 minute perhaps) sudden death game is played. The player of the White pieces again plays as White, but must give draw odds i.e. a second draw is scored as a win for Black.

Assuming players of equal ability and assuming the player of the White pieces generally scores 55%, then the above scheme is a coin-flip with a draw percentage a tad over 37%. A draw percentage of 50% would give Black a 55% edge. A draw percentage of less than 37% would give White the edge. So the above scheme rewards dynamic enterprising play. In this way, all matches would be decisive encounters with all games very hard fought.

One might object that at the highest levels a draw percentage below 37% is not realistic, so Black might then have a small edge, but so what? Does it really matter if Black has a small edge instead of White? Why should it?

Nahim Zahur, Singapore
Your coverage of the draw death problem has been quite extensive and I have certainly enjoyed it, but I have one suggestion to make. When you're publishing hundreds of readers' responses, it makes more sense to do so in a forum of some sort rather than a news article. You'll agree that not all of the readers' responses are equally interesting, and some raise intriguing points that deserve to be debated further. The problem with the current format in which you publish them is that it makes responding to a specific suggestion by a reader quite difficult and unwieldy. Having a forum instead would solve that and probably lead to more lively and in my opinion more useful discussions, since each suggestion would be developed and refined further; whereas right now all we have is each person stating his/her opinion. Hope you consider this point in the future.

Crispin wiles, Bristol, UK
I've been following the unfought draw articles with interest. People generally seem to be divided into two main camps on this:

• Changing the scoring or some such, resulting in what one reader described as an "Americanization" of the sport (reminding me somewhat of the humorous suggestion in a beer advertisement of what an American solution to draws in soccer might be – added time multi-ball!); or
• Accepting grandmaster short draws as part of the game.

Whilst sponsors and followers of chess want to see titanic six-hour battles from every player every day, this is simply not how the modern game works, or how humans survive. Even the most popular players such as Carlsen sometimes play short draws, but you don't hear many people complaining about Carlsen being boring to watch! One of the key for this is that he very seldom plays this way. My proposed solution to the spectator/sponsor problem of grandmaster short draws is this:

Simply, put a limit on it. It is usually very obvious when a game has been played in this way, but for players (if not spectators) short draws can be a valuable strategy. Therefore, permit a maximum number of short draws per player, perhaps 1 game in 7 or 8. Then, if a player plays more than the maximum permitted number of short draws in a competition, that player is penalised by one of the following:

1. No points are awarded to any player who, having reached the short-draw limit, plays a further short draw. If the opponent has also reached the short-draw limit then neither player is awarded any points. If not, the opponent is awarded the customary ½ point. This not only would provide a real incentive not to reach the short-draw limit but also have a nice poetic justice to it - no points for no effort!
2. Being banned from that tournament next year. After all, with Kasparov gone, many top players are very close in skill level. For every Leko there's a Shirov, for example, (not to besmirch Leko's name - he is a very fine grandmaster and I'm not accusing him of anything) so tournaments have a wealth of amazing players to invite. The further down the ratings list you go, the more this is true.
3. Players could have points docked.

Concerning the issue of players using short draws as a form of inappropriate team play to save energy for defeating the weakest of the group, players should simply be permanently banned from the tournament, with immediate effect.

Howard S. Sample, Toledo, OH, USA
No one's ever called me the eternal optimistic type (and no one ever will), but personally I highly doubt if any ideal solution to the problem of too many short "grandmaster draws" will ever be found. People have been coming up with ideas – some of them ridiculous – for at least 40 years. But if no solution has been found then probably none will appear.

Tommy Leblanc, Boston, MA USA
It is wonderful to read the discussion on draws. Only with discussion will the solution be found. However, if one sits quietly in meditation, one will find there is one and only one answer to the problem. That solution is simple and easy. One must make slight changes to the rules of chess to eliminate all draws so that the final result will always have a winner and loser. The rules needing change are small and actually go back to rules previously used. The present rules are an outgrowth of a macho attitude of who is the better chess player when it was used as a betting game. It was a macho sign that the player could win no matter what advantages were given the other player. Thus wins had to be overwhelming. In todays society we live in a very different era. Now it is necessary to have winners and losers in a sporting contest. There is no longer the need to prove superiority based on crushing wins.

Madu Ezejiofor, Nsukka, Nigeria
I strongly believe that the only solution to this menace that is about to destroy chess can only be settled by changing the scoring system, where if a game is drawn White gets 0.4 point while Black gets 0.6, instead of half point per player when the game is drawn. if White loses he/she gets -0.1, while Black gets 0.0 for losing. If White wins he/she gets 1 point while if Black wins he/she gets 1.1. According to Kung Ming Tiong, the mathematician and logician from Malaysia, the scoring system will not only eliminate unfought draws but will solve the problem of tie breaks, because in most tournament some players will play more black than white and will play very well, while he/she might end up tying with some one that has played more white than black. So with this scoring system it will be clear who is the best. Other forms of tie break like playoff or crosstable format and strength of opponents will be phased out. Since it is a generally acceptble fact that White has a slight advantage by starting first, Black should equally be compensated for fighting so hard from a slightly disadvantageous position. I perfectly believe that this scoring system is not biased since every chess player will definitely play white and black, so under this new scoring system it will be extremely difficult to accept a draw when you know that it will have far-reaching consequences on the player that is being offered an unfought draw.

I am a Pharmacist and Lecturer at the University of Nigeria, and a great lover of chess!! Will be most grateful if my opinion is published.

Rauan Sagit, Stockholm, Sweden
Why do two powerful minds agree on a short draw? What is the reason? It is fear, fear of losing a game because of being in bad shape? Is it respect, respect of the opponent having equal chances, being equally strong? Is it always the same reason? I believe we need to terminate the discussion of how organisers can prevent premature or unfought draws. Because the discussion stands on destabilised ground. Talk to the grandmasters that play or have played unfought draws. Anonymously. Ask them why, prompt them to explain the mechanism that drove them to make the choice. Ask them to explain the reason. Because without knowing the reason, how can the chess community speculate about possible solutions?

Peter Henderson, Charlottesville, Virginia, USA
Let the grandmasters themselves decide if they want to play for a win or draw. Why should spectators make the rules? I wouldn't tell Picasso how to paint; why should I tell Anand how to play? Lots of draws are very interesting. Rules that forced games to a decision would ultimately hurt the game by forcing players to play unsoundly. Positional play would be punished. As a fan I appreciate Tal and Petrosian equally. I don't want rules that invalidate the search for the best move. After all, that's the ultimate measure of skill, and sometimes the best move is not the most double-edged one.

Previous ChessBase articles on unfought draws