The theory of Infinite Resistance May 2005

Rowson quotes Ian Rogers, who explains: …The theory postulates that when a player makes a serious mistake or reaches a bad position, if he or she continues to try to find the best possible moves thereafter he or she can put up virtually infinite resistance and should not lose…

During the first round of an Australian championship, a number of people mentioned my theory of infinite resistance. This had been attributed to me by Ian Rogers, who was quoted in "The Seven Deadly Chess Sins" by Jonathon Rowson.

This theory has never been written down before, so I am writing it down here.

Aside from losing on time, being forfeited for whatever reason or resigning prematurely, to lose a game of chess you need to be checkmated. If you cannot be checkmated you cannot lose.

Checkmate can happen because of a direct attack on the king, regardless of the material situation. Often the attacker has sacrificed to enhance the attack.

Checkmate may also happen because one side has overwhelming material (sometimes as a result of pawn promotion) and the stronger side leisurely mates the opponent. When I was seven years old (and knew no theory) I worked out that if I reduced the opposing side to just a king, it was easy to checkmate.

If you can avoid the direct mating attack on your king, don't allow you opponent to promote and don't lose material, you cannot lose.

A pawn down for nothing is objectively a lost game.

The reason a pawn up is a won game, is that you can use it to queen a pawn, so either you have a passed pawn while your opponent has none or you have one more passed pawn than your opponent. Often an extra pawn is drawn, if a passed pawn cannot be created. A simple example is Ph3Ph4Kg3kg7ph7. In other positions an extra doubled pawn may win, because of extra waiting moves etc.

Theory says a pawn is worth about 3 tempi early in the game. In the late middlegame perhaps it is worth 4 tempi. The more dynamic the position is, the less tempi a pawn is worth. In a quiet blocked position, a pawn may be worth many tempi.

A typical positional mistake is worth about 1 tempo. That means on average to get a 'lost' position you need to make about 4 small mistakes. Not only that, you need to make 4 mistakes MORE than your opponent. Even GMs are making small mistakes up to 10% of the time.

If you are making half as many mistakes as your oponent, (which suggests a large difference in strengh) he will need to make about 8 small mistakes to your 4 before he gets a lost position. Eight mistakes is quite a lot.

Even if the pawn up (or equivalent) for nothing has been reached, you may only need a few small mistakes (or fewer or one larger mistake) to reduce the advantage below a pawn for nothing.

While in theory, a pawn down for nothing is lost, in practice you need to be 2 pawns down for nothing to be lost (because) of the possibility of errors. Hence players often resign when losing a piece for a pawn or more.

Of course, a serious tactical mistake can cost you the game, you might lose your queen or get mated in one move. Sometimes a positional mistake can be more worse than a loss of one tempo.

COMPENSATION

In practice it is difficult to win a pawn for nothing. Usually the opponent gets some compensation, perhaps time at least.

If your pieces remain active, then you can resist being materially down for a long time.

If your position is worse, but material is equal, if you continue to find the best moves you have very good survival chances.

What happens if one side has an advantage, but both sides play well?

GM Hug writes that nearly every position has resources.

In your positional technique is reasonable (so that serious positional errors are rare) and you don't make serious tactical errors (blunders), you can survive a long time.

AN EXPERIMENT

An interesting idea suggested by GM Spraggett, is to play a game where one side deliberately plays the second best move. Its not so easy to put him away. The key thing is to avoid the really big mistakes.

WINNING GAMES STRATEGICALLY

Games can certainly be decided strategically without tactical errors.

One side builds up overwhelming force near the opponent's king position, then launches a decisive attack.

One side is able to create one (or more) decisive passed pawns.

One side has a weakened pawn structure. Over time there are too many weaknesses to defend and a pawn (or more) must fall. This may take many moves. Hence the advantage reaches the one pawn margin.

One side exchanges into a strategically winning ending.

ADVANTAGE GROWS OVER TIME

Something easily observable is that in many cases the side ahead increases its advantage as more moves are played, even if both sides play at the same strength. This happens for a number of reasons.

As more moves are played, more pieces tend to be exchanged. This will increase a material advantage (as a ratio of forces) or an advantage in pawn position.

The weaker side tends to make more mistakes.

For example, white is a piece up. 20 moves later his position has improved considerably.

Another example is when one side has a large space advantage. 20 moves later their overall advantage may have increased, the reason being that that side can do more with their position than their opponent.