The problem of draws – a Christmas solution

Currently the Russian Championship Super Final has completed its ninth round, and of the 54 games played just 24 were draws. This comes to 44%, which is extraordinarily low for a tournament of this strength. Alexander Morozevich, who had won his previous six games in a row, actually lost one today. His drawing ratio is 11% (six wins, two losses and one draw).

Still it is not such extraordinary tournaments or hard-fought draws that are of concern to organisers and chess fans. It is short, unfought draws that cause distress, it is these that they want to eliminate. Above is a (genuine) snapshot of an organiser and his wife during the press conference after two world-class grandmasters had agreed to a draw after thirteen moves.

A number of proposals have been made and some actually implemented (links can be found at the end of this article). The main ones are:

1. The Sofia Rules: draw offers are generally not allowed, players can only claim a draw in case of perpetual check, threefold repetition or if the position is a theoretical draw. The system was first professionally implemented in 2005 MTel Masters and is the brainchild of Topalov manager Silvio Danailov.

2. The Bilbao System: count wins with three points, draws with one and losses with zero. It was used during the Bilbao Blindfold World Cup 2007 and has been intensely discussed in the articles to which we link at the bottom of the page.

One other system would be to simply invite Alexei Shirov and Alexander Morozevich to every top category tournament. This has not been formally proposed and is probably impractical, as is the whispered proposal to not invite some of the more notoriously drawing players. However there are some new ideas we like, especially the last one proposed by some unknown thinker. So on to the letters we have received from our readers.

New opinions and proposals

Alexander Minkin, Michigan, USA

As mentioned before, the whole reason for Bilbao system is to encourage battles on the chess board instead of GM draws. The reason 3-1-0 system does not work is algebra. It is easy to see that in a 10 round tournament a player with 0-0-10 has scored 5 points and gained 10 Bilbao points, while a player with 4-5-1 has scored 4.5 points ad gained 13 Bilbao points. So there is a problem, how can someone who scored less points overall claim better performance? He/She can not and should not.

There should be a way do differentiate between 4.5 point and 5 point score while also differentiate among all those who scored 5 points and reward based on victories. That is 5-5-0 player should be rewarded more than 0-0-10 player. The reason 1-0.5-0 scoring does not work is it does not differentiate within the same score. The reason 3-1-0 scoring does not work is it does not properly differentiate between different scores.

The simplest solution is to modify normal 1-0.5-0 system such that we reduce reward for a draw and leave reward for victory or loss the same. After doing simple algebra that I will not go into, one can see that 1-0.45-0 system will work for both purposes; it will differentiate between scores and within scores at the same time. With this 1-0.45-0 system in a 10 round tournament we will get next output:

This should be the simplest way to discourage draws in a tournament of any kind.

Jerry Olsen, Los Angeles, USA

I read with interest (and some amusement) the various solutions to the issue of "grandmaster draws", offered in response to Dorfman's article opposing the "Bilbao rule" (i.e. 3/1/0 scoring system).

Most amusing to me were: (1) The proposal to use the 2/0/-1 scoring system, which is mathematically identical to Bilbao! (2) The proposal to use the 1/0/-1 scoring system, which is mathematically identical to the standard 1/0.5/0 system!

Some people dismissed Dorfman's argument (that Bilbao would encourage cheating) on the grounds that it would be difficult and risky to actually arrange a swap of wins. These people have a point, but besides the "actuality of evil", we should be concerned about the "appearance of evil" and the "potential of evil". If a player wins a tournament largely because he swapped wins with a number of players while another player swapped draws, it is bound to raise suspicions, and perhaps even accusations, of cheating. Of course, the players will deny it (perhaps truthfully), but we'll never know for sure. At any rate, it would be an unsatisfying result and a bad image for chess.

Now, when solving a problem, one must first clearly identify the problem, and then find a solution that:

1. Is effective (eliminates or lessens the problem).
2. Has minimal side-effects (little or no impact on non-problem matters).
3. Is simple (complex solutions solutions can be confusing and probably have unforeseen side-effects).
4. Is realistic (not so radical that it would never gain wide acceptance).

So, let's clearly identify the problem in chess: The problem is not draws, it is short unfought draws. Now lets look at some solutions:

• Bilbao: May satisfy #1, but it seriously fails #2 (it punishes hard-fought draws and may lead to suspicions of cheating) and perhaps #4.
• Some solutions involved a variable scoring system, such as making a draw worth less than 0.5 (e.g. 0.1 or 0.3, etc.) if unfought. This may also satisfy #1, and maybe #2, but it badly fails #3 and IMO #4. It's too subjective. Some arbiter has to decide how to split the point, and this might determine the winner of a tournament?
• Some solutions involve affecting the clock, giving a greater reward to the person with less time. In my opinion, this may violate #2, #3 and #4, and perhaps even fail #1!
• Making each game a match (if the classical game is a drawn, they play a rapid game, and if thats a draw, a blitz, with different ways to split the point in each case.) This is interesting, but I think it violates all the points, particulary #1. The players can still have a short unfought draws in each game!
• Sophia rule (prohibit draws by agreement without arbiter's consent). I think this satisfies #2, #3 and #4 quite well, and it goes a long way to satifying #1. It keeps the players at the board until the result is clear. Granted, if both players REALLY want to draw, they can force a threefold repetition, but then the players must be quite blatant in their effort to draw, and it should be quite rare.

Addendum: Many who advocate the use of this rule in chess point to its successful use in football. However, when making comparisons like this, it's important to look for fundamental differences that could distort, and thus invalidate the comparison. With the comparison between football and chess, I think such a fundamental difference exists.

Suppose that a football game is tied with just a few moments left to play. Now, at least one of the teams might be very motivated to win (huge prize fund, fame, championship status, whatever), and that team may also have very talented players. It's not hard to imagine that this team might be sufficiently motivated and talented that they could produce a level of play sufficiently brilliant to force in the winning goal before the game ends.

NOT SO IN CHESS! In chess, we can easily arrive at a position that is simply drawn. No additional amount of incentive, and no amount of additional talent or determination will allow one player to force a win. This is a situation that has no equivalent in football. As a general rule then, it pointless to offer extra incentive to avoid draws in chess.

Charles Hall, Orlando, FL
The flaw in the author's logic is that in football, you have a clear metric – a tie game is numerically equal and nobody is "worse or better" in the position. Other than material, chess has a dynamic (and often persistive) qualitative element.

In other words, other than possession of the ball, there is very little else (except for general team skill) upon which to base a long-term evaluation. You don't have specific positions which dictate the "best" course to be to offer, accept, or play for a draw. Chess games have evaluations far beyond the material evaluation, and regardless of the material, the position often dictates the result either player should play toward. Only the truly unreasonable would deny that well-fought games deserve their due. As many say, it is the short, unfought games that are the problem.

The Rentero "carrot-stick" approach seems more effective than changing the rules or scoring. Honoraria is reduced, and a pool of money goes toward rewarding decisive games. Maybe even bringing back decisive-only brilliancy prizes. Those that choose to consistently avoid conflict (perhaps more than 1 short draw per x number of games) should simply face not being invited back to that event the next year.

Darshan Gupta, Delhi, India
I have touched this subject as far back as 1995. After analysing various alternatives, I successfully applied the formula of 7 pts. to winners, 3.0 pts. to draw. In one of my tournament of 8 rounds, player A won 7 rounds, lost one and secured 49 points, while B won 6 games and drew 2, so he got only 48 pts. There had been lot of discussion who is better, A or B – our ultimate conclusion is winning is better and tough as compared to making draws. I am holding so many tournament with this point structure. The system is liked and praised by all players.

Systems with 3-1, 5-2 , 9-4 and 11-5 points were also considered, but best suited for competition up to 11 rounds has found to be 7-3 points. Personally, I feel for 9 rounds it should be 9-4 pt and for 11 rounds it can be 11-5.

Javier Araujo, Fort Worth, TX
The Sofia rule and any rule based on number of moves will show its problems in a near future. Took the GMs a few decades to become shameless enough to have 10 and 15 move draws, how long will it take them to shuffle pieces for 40 moves?

The Bilbao rule, on the other hand, has a complete different kind of problem: It ignores a fact of chess: ratings are more important than tournament results. Since we don't have a tournament a year where all professional chess players compete (like in the case of soccer) we need ratings in order to compare the professional players to each other. And the same hold true for "D" players.

If I understand ratings correctly they are based on expected performance, not on expected points. On a field of 11 GM playing a 10 round robin tournament, where all of them are rated 2600, the expectancy is that they all obtain a 50% performance. That doesn't mean 50% of the points, if someone draws all its games he will have done what's expected from him and thus his rating will not change. On this scenario: Player A has +4 =1 –5 he will have 13 points but 45% performance so his rating will go down. Player B has +1 =9 –0 he will have 12 points but 55% performance so his rating will go up. Player A won the tournament but lost the points, player B didn't win the tournament but won points. Guess what route the GMs are going to take?

What I suggest is to abolish the draw altogether. Make Black play without time increment and give him draw odds. White will have advantage that can win on time, but can't lose on time. Black will have the advantage that he can repeat moves while White can't. And the 20-30 min less on the clock justifies Black draw odds. We will not see any more drawish lines, because white can't afford them. Draw offers will be thing of the past, and all games will have to go until the bitter end. Black players will probably try to trade everything off looking for insufficient mating material situations, and is up to White to demonstrate that passive play brings defeat. or at least that takes too long.

IM Julio Kaplan, El Cerrito, CA, USA
The analogy with soccer misses an important point that make chess unique: soccer games are not repeatable. Chess games are. This has immediate, important consequences.

The number of "fighting moves" in a game has nothing to do with the length of the game itself. If you follow a well-known drawn game for 25 moves, make a minor innovation on move 26, and then draw on move 32, in a position that is almost identical to the original game, did you really fight? Take chances in order to win?

The interest of a chess game, and the sense in which it was a real fight, corresponds to its history.
For example, take many of the Ruy Lopez, Marshall Variation games played today. If we were seeing this for the first timer, we might say that Black "daringly" sacrifices a pawn in the opening. A few moves later White sacrifices an exchange on e4, offering to remain behind in material but take over the offensive – what an exciting concept! Black refuses the offer, angling instead for an endgame in which he hopes that his activity and two bishops will be enough to draw. Finally, the game is drawn in the endgame – what a marvelous struggle!

By the twentieth time we see a game that meets this description, with minor variations late in the game, this is totally boring, and even suggests that the players, Black especially, are aiming for a draw. Exact same game, totally different interpretation.

As for the statistics on chess tournaments at the end of the article, the resoning is circular and totally flawed. If you define "bad" draws as draws under 31 moves, then of course, anything that prevents those would be a "success". The new rules have also given us a number of games where a dead-drawn position was played on for many moves, until only kings were left, so as to satisfy the rules. This is, in general, not an improvement. However, it brings me to the only thing I think is useful about the Sofia rules:

They force players to play out positions that, while clearly drawn for any competent grandmaster, are still full of fight as far as the public can see. I think it is important for games to be continued until the public at large can see that the fight has been exhausted. For this purpose (and for this purpose only), I think requiring permission before a draw is agreed is a good thing.

W. Laurence Coker MD, Overland Park, KS USA
At the Lone Pine tourneys in the USA in the 70s one solution for draws was found: give a prize for the best game of each round, and make the prize significant enough to encourage fighting chess. Obviously boring draws do not win a prize.

Jonathan Estey, Swarthmore, Pennsylvania
I was happy to read Dragan Solak's pointed argument on the deficiencies of the Bilbao system, and I think he goes to the heart of the matter. The major difference between chess and football is that draws are an integral part of chess: the proper result of a chess game with no mistakes is a draw. Changing the scoring of tournaments to penalize the game's default ending may lead to more wins, but it will also lead to bad chess. As a spectator, I want to see top players playing good games, and draws that are hard-fought and well-earned are good games. (Would any spectator feel cheated by Fischer-Tal 1960, for example?) Fiddling with the scoring to discourage draws is missing the point: what we want to discourage is unfought draws. To that end, the ban on draw offers, which Solak argues for, is a much better strategy: games that should end in draws do so, but only after both players have exhausted all possibilities for play and have put on a show for the world. Solak has identified the true enemy of exciting chess: not good defensive technique, but cowardice.

Jackson Showalter, Lexington, Kentucky
Classical Chess (time control and scoring system) has the the advantage of long standing tradition. Yes, "professional draws" do happen, but usually because the GMs involved mistaken overestimate the value (monetarily or strategically) of a draw. They are great chess players, but not necessarily risk analysts! This is why 'cutthroat' players like Morphy, Tal, Fisher, and Kasparov earned high ranking, championships, money, and will always be remembered, whereas other excellent but 'careful' players such as Karpov and Kramnik, not quite so much. In short, public sentiment and economic incentive already greatly rewards our current generation of largely exciting players such a Morozovich, Svindler, Shirov, Grishuk, Polgar, Anand, Radjabov and Carlsen over such boring types such as Leko and Kramnik. Once the organizers and players themselves become fully cognizant that erring on the exciting side is good for their image and purse, then Bilboa will be redundant. In large American Swiss System tournaments (aside from frequent last-round losses of nerve) the GMs have already figured it out. Still, I would like to see some experimental, Bilboa tournaments.

Jens Christensen, Copenhagen
Dragan Solak makes some good points. Curiously though, in his attempt to show how the Bilbao scoring system wouldn't work, he almost managed to convince me that it was a good idea. Here's why: He uses a couple of examples where in 'normal chess' the game would end by repetition whereas in 'Bilbao chess' black would choose to go into a slightly inferior position with winning chances. He speaks as if this is a bad thing, but from my perspective (the Average Joe spectator) this sounds like a stunningly good result. If the Bilbao scoring system stops players from taking early (or even late) draws and continuing to play I say we implement it yesterday rather than tomorrow. Unfortunately I don't think things are that simple.

My biggest problem with the Bilbao system is still, and probably always will be, that it unfairly penalizes the players who play a 'proper' draw to the same extent that it penalizes the players who take a 15-move draw. I think that it would be very interesting to see the Bilbao system tried out in some real GM tournaments (not rapid or blind) as that would give us a better indication of whether it would actually work in chess. The problem is not the draw itself, it's the unplayed draws, which brings me to Mr Solak's last suggestion, one which I can wholehearted agree to. Simply remove the draw offer. The draw offer is NOT a necessary part of the rules of chess. The rules of chess would work absolutely fine without it, so why not just remove it. And lastly, why not do both. Ban the draw offer and implement the 3-1-0 scoring system. We could call it the Bilbofia system. That should get the fighting chess to the forefront.

Mihael Ankerst, Munich, Germany
There have been a lot of suggestions posted how to tackle the problem of unfought draws. Knowing the international tournament scene quite well, I would like to suggest a new format which, to my knowledge has not been suggested before, yet it has quite an appeal. I will just outline my idea briefly, however I am willing to describe the idea in more detail in case it caught some attention.

To address the problem of unfought draws, let's first list the main objectives: a) It is not in the spirit of the chess sport to have an outcome which is partially based on agreement and not on the performance. b) It is unfair to the remaining players of the tournament. c) It detracts sponsors as well as visitors of chess tournaments. There is a single reason the rule of offering a draw is in place: To spare an inevitable outcome of draw, which would be otherwise reached by e.g. repetition or the 50 move rule since chess is deterministic.

Acknowledging the points above, the suggestion is to prevent draw offers which come up in positions which are not inevitable draws. The measure of prevention is the right of an arbiter to have the player who offered a draw playing his position again a computer. A practical approach could be: a) From all games which prematurely ended in a draw upon agreement, a random sample is selected. b) The person who offered a draw and was selected has to play a blitz game against a strong computer program starting from the position. c) If the person draws (or wins) the draw is valid and gives 0.5 point. If the person loses he/she loses the official game.

Eric Duker, Columbia, Missouri, United States
Mr. Fernandez's arguments regarding the draw rates in Bilbao vs. previous tournaments are poorly conceived. First, sample size must be taken into effect. One tournament cannot be used to make sweeping statements regarding the effectiveness of a system. Second, Bilbao was a blindfold tournament, and such a style of chess is prone to blunder losses, which were seen here. If you made a 30 game tournament (as Bilbao was), and gave it the same win/draw rate as is expected at the tournaments Mr. Fernandez provides statistics from, but change 3 draws to 3 "blunder wins", that provides a 10% change, which appears consequential, but would never occur if the players could see the board. Blindfold chess is going to provide larger swings than normal chess, since gross miscalculations are more likely, and wild swings are going to lead to more wins. The only thing Mr. Fernandez's statistics prove is that if you want more decisive games in chess, make them all blindfold!

Third, length of draws are meaningless, especially when the Sophia Rule is in effect. Since that rule exists outside of the Bilbao Rule (see the Sophia tournament it is named after), it can't be used as an advantage to this new idea. Length of draw is not proportional to competitiveness of the draw. I can play a B+P v B ending for hundreds of moves (assuming you discount threefold repetitions) and the ending will always be a draw, but it will never be competitive. Since Mr. Fernandez's statistics only show length and not competitiveness (if such a thing is even objectively measurable) and the consensus of previous replies seems to be towards to latter, I don't understand their purpose in advancing his claim.

In regards to the second part of his position in which he invokes comparisons to football, I would argue that the importance of excitement in football is different than it is in chess. Chess cannot be played in front of massive, cheering crowds as football can. Nor is it exciting to the average viewer. The pace of play is slow and the positions are filled with unseen meaning that the average fan will not see on his own. I can see the excitement and understand the score of a football match even if I lack the skills of Ronaldinho, but I will never see the board the way super GMs do unless I possess the talents of them, which is unlikely. Because of these differences, excitement plays a fundamentally different role in these two activities, and thus they cannot be viewed as comparable situations. Further, increasing sponsorship for chess has numerous problems (some mentioned above, such as its inherent nature) that football, especially in Europe, doesn't have. A weak governing body, which some argue is corrupt, that has trouble formulating and sticking to a championship system that has its headquarters in a country that appears increasingly to exist in a state of corporate lawlessness is not appealing to any potential sponsors that don't have people at the top with a personal interest in chess.

Alexander Aguilar, Los Angeles, CA
Are draws really all that bad or do they just have a bad reputation? I think the bad reputation stems from the fact that draws inherently do not draw much interest – especially when they are quick, not fought, and boring. But there are good reasons why players seek to play for a draw. The Sofia rules seem to be reasonable in that – it simply attempts to correct the problem of unwarranted draws in a way that reflects the spirit of the game in the first place – i.e., draws obtained as a natural course of the game. There's nothing wrong with that. But it is also important to recognize that playing for a draw is the right of a player. To prevent abuse of that right, we just need to come up with reasonable rules (or corrections) that will help minimize draws without making it too hard for the players.

Here are some positive things about playing for a draw:

1. There is nothing wrong with a player seeking to play for a draw as long as it is done in the spirit of the game. After all, even that takes skill to achieve especially when your opponent is desperate to win and you are playing black. Without getting into too much details or citing too many scenarios, playing for a draw can be a way out of defeat or even a way to win a tournament. It takes good discretion to know when it's best to play for a draw.

2. Getting a draw is like a way to retreat during a battle so that you can recuperate and put up a better fight next time. Wouldn't it be better to play for a draw in some games so that you could recuperate and have a better overall performance in the tournament. That can be a good tournament strategy.

3. A draw allows a player to have less stress and be refreshed for the next game where he could produce a beautiful game. I would rather see players drawing their games every once in a while and produce some beautiful games at their moments of strength than see players forcing the issue and commit blunders because their brains are simply overworked. I don't think games full of blunders help chess especially in top level competitions; but beautiful games are immortal.

My point is that we don't have to be so negative about playing for a draw – it is a necessary part of chess and chess competitions. It is as much a part of the dynamics of chess competition as playing to win. Of course, it is always more exciting when one plays to win and it helps the cause of popularizing chess more, but it should not be an issue to be forced on players by making rules (such as the Bilbao rule with its scoring system and flaws already pointed out by others) which effectively underestimates the overall benefits of playing for a draw – both to the players and to the game. Although I like the idea of playing out the game, being able to achieve a drawn position early in the game requires skill and should have its own reward. In this sense, the Sofia rule might be a little over-restrictive when players are forced to play out games that they already know to be theoretically drawn. Or what if the player is feeling sick or exhausted in the middle of the game and chooses to find an easy way out by offering a draw. If the goal is to limit the number of draw offers, then why not do just that - say like once every four games with a minimum number of moves restriction. We simply need to find a good balance and if the Sofia rule is not enough or is too much, we can make adjustments without losing sight of the true spirit of the game and the player's cause. The game owes its popularity mostly to all those who invested a big part of their life just for the love of the game. I'd like to hear what they have to say about this. After all, they are the ones who will play through the rules and feel all of its effects – positive or negative.

An unusual proposal

James Conway, Blacksburg, USA
Maybe we are trying to solve the problem of fighless draws through the wrong avenue. So far, most of the solutions use tournament rules to inspire a fighting spirit. The problem is that it's the tournament situations that inspire short draws in the first place. Even fighting players are prone to short draws against highly rated players, in an effort to save energy for the next fight the feel they can win.

Maybe the solution lies in something that trancends tournament results, the rating system. It really is quite simple; deduct a few rating points for each short draw. My solution would apply to agreed draws, and for each move less than 45, ratings are calculated as if your opponent was two points lower. Logically, this makes a lot of sense. If you didn't demonstrate the skill to fight a highly rated player to a draw, you don't deserve all the rating points associated with that result. Another way of thinking about this is that it is just as much skill to make a short draw with a high rated opponent than a lower rated one, but the longer you play the more skill is required and the more points you earn. For example:

Player A (2700) draws Player B (2700) in 25 moves. Thats 20 moves less than 45, so each players' ratings change as if they drew a 2660 rated opponent (40 points lower).

Player A (2650) draws Player B (2750) in 30 moves. Thats 15 moves less than 45, so each players' ratings change as if they drew an opponent 30 points lower. As if Player A drew a 2720 opponent and Player B drew a 2620 rated opponent.

There are a few points why this might be more effective than tweaking tournament rules. First, this applies regardless of the tournament situation. Maybe a draw is all that you need, but you still have to play the game out to get full rating points.

Second, only one player has to care about their rating to refuse a quick draw. If a 2650 player gets an advantage after 20 moves and offeres a draw to a 2750 player, the 2750 player might refuse in a worse position, because he thinks he can play well enough to EARN the draw and earn full points.

Third, ratings affect much more than just ratings. They affect invitations, seeding, world championships, sponsorships, and more. For professional players, it will be in their professional interest to play out almost every game.

Fourth, habitual offenders are punnished more than the occasional offender. Consider a four player round robin. Player one makes four quick draws. The other players make one quick draw (with player one) and play out their other games. Players one's results are going to be relativly worse than the other players.

One posible criticism of this system might be that it does not directly affect the draw rate, in that is does not necesarily encourage players to take risks and play for a win. If a player wants to draw, they can still play for a draw; they just have to play longer and work harder for the draw if they don't want to hurt their rating.

Our Favourite

Brian Karen, Levittown, NY
Somebody once proposed that when a player offers a draw it should last for the rest of the game. This allows the opponent to sharpen the position while keeping a draw in hand. Only a player who is certain that the position is a 'dead draw' would make such an offer. Admittedly, it doesn't deal with problems of collusion but at least makes collusion a little harder. After all, who gets stuck having to offer the draw?

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