The case for seeking draws in chess tournaments

Being quick on the draw can be completely rational in certain circumstances and where prize money is at stake. Just do the maths

John Foley

The re-emergence of weekend tournaments has drawn attention (no pun intended) to the use of draws. Chess purists would say that you should always try to win a game. By contrast, game theorists would say that you should always try to obtain the best payoff i.e. financial outcome. This divergence of perspectives gives rise to different draw strategies. We need to set aside the emotions and make a rational case for seeking a draw as players reach the last round.  It is more rational to be realistic rather than optimistic.

Photograph: R Nial Bradshaw

Last-round strategy

Let’s say you are in the fortunate position of coming into the last round of a tournament in joint first place, you are paired against someone with the same number of points and you are both a point ahead of the chasing pack. Let’s make this more concrete and assume that the first prize is £400 and the second prize is £200, and that these are the only prizes and this is shared among those in the top places. These figures are not atypical on the English chess scene. Not a lot of money, but enough to give pause for thought for an impecunious chess player.

What is the right draw strategy?  There are three outcomes arising from the game:

You win:          sole tournament victory and £400

You draw:        joint tournament victory and £300 (being half of the total prize money)

You lose:         zero 

The game theorist says you need to consider the probability of each outcome.  As a first approximation, there is an equal chance of a win, draw or loss. The “expected value” of the game is therefore:

(⅓ x £400) + (⅓ x £300) + (⅓ x 0) = £233

It is rational to offer a draw because you are guaranteed a return greater than the expected value from playing the game out. You avoid the possibility of defeat and get a share of the pooled prize money.  You are £67 better off than leaving it to the vagaries of a contested game. To express this in percentages, you get a 29% improvement in expected prize money by agreeing to a draw early on.

Young and ambitious players may prefer to slug it out. Youth knows no fear. Or they may lack objectivity and overestimate their chess skills. More seasoned performers will assess the opposition and, unless they are clearly superior, will often seek a draw.  Tournament organisers are wise to this temptation and seek to impose measures designed to avoid early draws. Nevertheless, the economic incentive remains. 

Penultimate-round strategy

By a similar argument it can be shown that, based on a reasonable set of assumptions typical of local weekend tournaments, if the tournament leader accepts a draw in the penultimate round, their expected value of the prize money is £267, whereas if they take their chances and play out the game the expected value is slightly lower at £256. The tournament leader can thus secure a small financial margin of £11, on average, by taking a draw in the penultimate round against the nearest challenger. That’s the price of a couple of beers if you live in London.

The outcomes can be summarised in this payoff matrix. This shows that it is always advantageous to seek a draw in the last two rounds. This decision must be made prior to or at the outset of the game. Try for a win only if you have grounds for believing you can beat the odds. Once the game is underway, then this analysis is superseded and depends upon the chances in your current position. Then the conventional strategy applies: If you are ahead, then go for victory; if you are at a disadvantage, try to get a draw.

The expected value of settling for a draw in the last two rounds of a Swiss

There are more substantial benefits of taking a draw before the final game. Nimzowitsch, in an article titled “The Technique of Tournament Play”, explained how he won Carlsbad 1929 ahead of Capablanca and others due to taking short draws to save energy.  The message is to save your efforts for the last round,when you may also have another drawing possibility.

Offering a draw can also have a psychological impact. Your opponent may believe you are lacking in confidence and therefore start focusing on you rather than the board. They may lose objectivity and take a more risky line. As a result, you may outperform original expectations. It is not as if you are bluffing. You are taking a rational approach to winning prize money.

We should acknowledge the legitimate fear that taking a draw could become habitual. We all know players who have a reputation as draw specialists. They are the chess equivalent of people who hug the middle lane on the motorway – ultra-cautious and annoying.

However, what is being advocated here is highly circumscribed. Firstly, the prescription is only relevant to Swiss tournaments where there are only a few top prizes and there is a shared prize pool for people scoring the same number of points. If you are in an all-play-all, then try to win each game. Secondly, it only applies to those two or three people in the lead – if you are in the chasing pack, then try to win your game.

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