The Value of a Tempo

What's the value of the first move in chess? Most people would say it's a tempo, but there's a problem here.

Let's say that White passes on the first move. I know the rules of chess don't allow a player to say 'Pass!', so let's call it a thought experiment. If White passes, then Black has exactly the same advantage of the first move that White just had. Now here's the problem: If White gives up a tempo thereby giving Black an extra tempo, then the difference between the positions is two tempi. But White only passed on one move, so how can this be? Let's use a simple algebraic formula to illustrate this...

X - 1 = -X

... where 'X' is the value of the first move for White, '-1' is the value of the lost move, and '-X' is the value of the new situation for Black. Solving for 'X' gives X = 1/2. This means that the value of the first move is not a tempo; it's a half-tempo. QED?

A few years back I wrote a couple of posts -- One Imbalance Leads to Another (February 2013) and A Pawn Equals 200 Rating Points (ditto) -- based on GM Larry Kaufman's work. One of the observations from his work was...

• 0.4 - Value of a tempo
• 0.2 - Value of first move

...where a Pawn is worth 1.0. Kaufman's observation confirms the X = 1/2 calculation. Why bring this up again? While reading the September 2017 issue of Chess Life, I noticed that GM Lev Alburt gave the following diagram in his monthly column, 'Back to Basics', after the moves 1.c4 e5 2.Nc3.

Most people would accept that statement as obvious and continue with the column. We've all seen similar statements many times and accepted them without question, but it might not be so straightforward. According to Kaufman's work, White's advantage might be *only* a half-tempo.

I plugged the position after 1.e4 c5 into an engine, looked at the analysis, entered a null move for White, and looked again at the analysis. The difference between the two analyses (before and after the null move) was not a half-tempo, it was closer to a full tempo. Why is the value of a move a half-tempo at the start of a game and a full tempo later? I think it's the difference between 'having the move' and 'making a move'. Once you make a move the advantage of having the move passes to your opponent.

I'm a big fan of chess960. I've always assumed that different start positions have different values. According to the analysis above (X - 1 = -X), every position starts with the same fundamentals -- a tempo is a tempo no matter what the start position might be.

So why do some chess960 start positions seem to offer a better opportunity for White to gain an advantage? Maybe it's for the same reason that some moves in the traditional start position (as in the diagram above) offer a better opportunity than other moves. After all, 1.d4 and 1.e4 are better moves than 1.a3 and 1.h3. A move that accomplishes two objectives is better than a move that accomplishes a single objective; similarly, a move that does nothing is better than a move that makes the position worse. Just don't say, 'Pass!'.