Just finished writing customizing a chess engine by basically adding a bitboard to the freely availably tscp engine. Now I'm testing it out in winboard and notice that often the two machines will play the same game multiple times in a match. I'd like to add some variety to the games by at least having it pick equal moves at random. I'm just using alpha-beta search with simple move ordering. I'm thinking about just adding a small random number to the leaf nodes to break ties but I don't really like this solution because some of the smaller bonuses that the evaluation function uses are 3-5 centipawns. So I don't have enough "room" for random number to break the ties.

my other thought was to have the engine pick randomly which move to keep when it found an evaluation == alpha. I don't really like this because I suspect it favors moves ordered last in the search.

Question is how can I pick from the equal scoring leaf nodes randomly? and also evenly?



It's a good idea for your engine be deterministic. There is no reason to select a move randomly. You would only do it to lower your engine strength. If you make your engine non-deterministic, you will find it very hard to debug and reproduce a bug. My recommendation is not to do it.

You shouldn't modify your engine. You may want to use an opening book, and pick a line randomly. Many chess GUI can do that, for example, the CuteChess software. Arena GUI can do also that.

But if you insist:

Let's take a look at the Stockfish source code.

 Move Skill::pick_best(size_t multiPV) {

    const RootMoves& rootMoves = Threads.main()->rootMoves;
    static PRNG rng(now()); // PRNG sequence should be non-deterministic

    // RootMoves are already sorted by score in descending order
    Value topScore = rootMoves[0].score;
    int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValueMg);
    int weakness = 120 - 2 * level;
    int maxScore = -VALUE_INFINITE;

    // Choose best move. For each move score we add two terms, both dependent on
    // weakness. One is deterministic and bigger for weaker levels, and one is
    // random. Then we choose the move with the resulting highest score.
    for (size_t i = 0; i < multiPV; ++i)
        // This is our magic formula
        int push = (  weakness * int(topScore - rootMoves[i].score)
                    + delta * (rng.rand<unsigned>() % weakness)) / 128;

        if (rootMoves[i].score + push > maxScore)
            maxScore = rootMoves[i].score + push;
            best = rootMoves[i].pv[0];

    return best;   }
  • Stockfish starts multi-PV (not supported in TSCP, so you'll need to code it yourself!)
  • Compute a random number and add it to the score for each PV
  • Compare each weighted PV, and pick the best one

You may find the following links useful:

Recommendation: Don't do it unless you want to weaken your engine.

  • the book approach worked great, thanks! I have posted a follow-up question regarding transposition tables and triangular arrays.
    – nak3c
    Feb 12 '17 at 0:48

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