Can a transposition table cause search instability

Question

I'm writing a chess engine and recently added a transposition table.

When running a few tests, I found that although the search still returned the same best move, the value of the move (how good it is for the maximizing player) fluctuated.

Is this normal behavior for a transposition table? I remember reading that a transposition table can cause search instability. Is this what that means? So is this a normal occurrence or a serious bug in my code?

Answer 1

Yes, transposition tables introduce search instability.

Fortunately, it occurs rarely enough that the advantages of transposition tables outweigh that complication by far.

1. What is the function of a transposition table?

After adding transposition tables (TT) to your program, you should notice two main differences:

1. Improve move ordering: The move from TT is generally the best possible move
2. Early cutoffs: When you reach a position again, which has been already searched with a greater distance, you can stop and use the value stored in the TT entry

In chess, the improved move ordering is the most important factor. Only in endgames, the likelihood of transposition increased, and you will see more early cutoffs.

So, what does search instability mean? It means that when you search one position with a given distance and later repeat the same search (same position, same distance), you will get the identical result.

2. Simple minimax/alpha beta search algorthm

Let us first ignore search extension and start with a simple minimax or alpha-beta search.

Note that you search will have the property that searches are repeatable, and will see no search instabilities. Even if you improve your move ordering with a move from a transposition table, you will still get the same result for every search. However, after adding TT, the extra cutoffs from a deeper search will in general break that property and introduce instabilities.

For instance, consider a position containing a deep tactic:

• A search with a low distance may not see it, but a search with a greater distance will.
• After that result is stored in the TT, a re-search with the low distance will see the tactic, too. It now behaves differently compared to the original search.
• Even worse, when the TT entry is overwritten, the improved knowledge gets lots again.

So, using extra knowledge to force early cutoffs is a factor that leads to instability. (But in practice, it is worth it, as it is more a theoretical problem.)

3. Search extensions

When applied to a simple alpha beta search, the improved move ordering itself does not lead to search instabilities. The situation is more complicated in real-world search algorithms which implement many extensions. Some of these extensions are sensitive to the move ordering, too.

One prominent example is called Late Move Reduction (LMR). It uses the fact, that the quality of move ordering is generally so high that only the first few moves have to be searched thoroughly, while the other moves are most likely bad ones and will only be searched with a reduced distance.

LMR is only one example where move ordering makes search less repeatable. But again, the advantages predominate.

4. How much search instability is normal?

There is no clear answer. In practice, you cannot eliminate instabilities completely but if the instability gets out of control, your search will become inefficient.

Of course, bugs can be the reason behind instabilities, too. So, is it a bug in your search? Well, I don't know. Could be. :-)