Some time back I tried implementing a Principal Variation Search , but as I wrote about in my post PVS – Another Fast Fail , the results were not good. At the time I concluded that if PVS is not a win, it must mean that the cost of the researches is outweighing the nodes saved by doing zero width searches. For that to be the case, it must mean that too often the first move is not the best move, which points to move ordering.
Since then move ordering has certainly improved, as documented in this post on Move Ordering . So, I decided to give PVS another try. In my first attempt, it appeared to be another loss. Then, I decided to not do PVS at the root node, and now it appears to be a very small win.
A win is a win, so I’m merging the changes in, but I think there is more to do here. My suspicion is that, as move ordering improves, the benefits of PVS will increase. The most obvious way to improve move ordering is to add a depth preferred hash table (the current strategy is a very naive “always replace”).
It seems like PVS at the root should work as well, if the program can reliably predict the best move often enough. I know a lot of programs put extra effort into ordering the moves at the root. I remember reading that Bob Hyatt’s Crafty does a quiescence search at the root. So, this is on the backlog as well, and once complete I will revisit the idea of PVS at the root.
For now, it is on to the next thing – Late Move Reductions. I’m hopeful that will yield a significant ELO increase, perhaps finally putting P4 on par with P3.
In my recent post on move ordering, I identified a potential area of improvement to the criteria for deciding if a capture is “good” or “bad.” As I wrote in that post, a capture is good if:
It is a promotion (technically even non-capturing promotions are included)
The value of the captured piece is greater than the value of the capturing piece
The Static Exchange Evaluator (SEE) score is non-negative.
The issue is with knights and bishops. They are roughly the same value (which one is more valuable really depends on the position), but in Prophet the bishop has a slightly higher value. A knight has a material value equal to 3 pawns, but a bishop has 3.2 pawns. The consequence of that is that a simple Bishop x Knight capture would be categorized as “bad” and not tried until all non-captures have been tried.
I don’t have the link handy but I read an older post on talkchess.com where Tord Romstad, the author of Glaurang (pre-cursor to Stockfish), mentioned that he used different piece values for the purposes of move ordering than he did in the evaluation. He said he used 1, 3, 3, 5 and 10. That means Bishop x Knight captures, as well as Knight x Bishop captures would both be categorized as “good.” Also, by giving the queen a value of 10, it means that giving two rooks for a queen would be considered equal by the SEE, where giving a queen + pawn for two rooks would have a negative score.
Sure enough, that simple change seems to be worth about 6 ELO.
As suspected the change to move ordering to separate good captures from bad captures has already paid off. Moving bad captures to the bottom of the move order list made it trivial to skip bad captures in the quiescence search altogether. This is an idea I first read about in a discussion on r.g.c.c. between Bob Hyatt, Feng-Hsiung Hsu and others at https://groups.google.com/g/rec.games.chess.computer/c/H6XjY2L13eQ . Hyatt claimed a small improvement, though Hsu was skeptical. Time has proven Hyatt correct though; I believe this is something most strong programs do. In any event, it seems to be worth about 10 ELO for Prophet4 so it’s a keeper.
Improving move ordering has been on the radar of a while now. I started to suspect that move ordering needed some work when my initial attempts at a PVS search and aspiration windows both failed. I reasoned that, if move ordering is subpar, researches would occur too often causing an overall increase in node counts.
To know, you have to measure, so I added data to the logfiles and wrote a Python script to aggregate (1) time to depth, (2) effective branching factor, and (3) the % of nodes in which we get a fail high on the 1st move and first four moves.
Once I was able to measure, I changed the move ordering scheme FROM:
PV move -> Hash move -> All captures in MVV/LVA order -> Killer 1 -> Killer 2 -> noncaptures in the order they are generated
PV move -> Hash Move -> “Good captures” in MVV/LVA order -> Killer 1 -> Killer 2 -> noncaptures -> bad captures in SEE order.
A “good capture” is one that is a promotion, a capture in which the value of the captured piece is at least that of the capturing piece, or one with a non-negative SEE value.
The change doesn’t seem to add more than just a couple of ELO directly. However, in non-tactical test suites all the measured metrics were improved: time to solution is down, effective branching factor is lower, the percentage of fail highs on the first move is improved, and the percentage of fail highs in the first four moves is dramatically improved. Additionally, the number of nodes required to reach a solution is cut by about a third, with only a 7% or so decrease in speed (nodes per second). I believe this sets the stage to take another stab at PVS and aspiration windows. First though, I’m going to take a stab at pruning bad captures from the quiescence search.
One potential (probable) area of improvement is that knights and bishops have slightly different values (bishops being the more valuable). For the purposes of determining if a capture is “good” when classifying the captures, they should probably be considered equal.
Prophet4 finally has a proper testing rig! A few weeks ago, I purchased a Dell Alienware system — an 8 core (16 logical) AMD Ryzen 7 5800 with 32 GB of RAM and an AMD Radeon RX600XT graphics card.
This replaces the single core laptop I have been using. This is pretty exciting as it will allow P4 testing to go at 8x the speed it did before. Just to break the machine in, I ran the first ever gauntlet with P4. Here are the results:
This closely matches the results I obtained a few years ago when I announced Prophet3 20180811 is released . One notable exception is TCB – it seems to have done much worse on this machine, for whatever reason.
So, it seems P4 is already on par with P2, and is within 78 elo or so from P3. This is encouraging, as the P4 rewrite is still not complete. I’m feeling pretty confident that when it is, it will be at least as strong as P3, and then the real work of improving can begin. And, with the fast feedback from a proper testing rig, I don’t think that should be all that difficult. My goal is to achieve +100 elo over P3 before doing a release.
Note– the versions of the chess engines used in this gauntlet are quite old by now; many of them likely have updates that could be significantly stronger. During the rewrite process, I’ve tried to keep everything “as is” — the goal is to compare P4 to P3, not to other engines. Once the rewrite is complete and P4 grows in strength, new testing engines will be cycled in as the current set is cycled out.
“Tree shaping” is an important component of a strong chess program. There are various ways to shape a search tree. One is by extending lines that seem interesting in some way; particularly those that cannot be fully resolved within the search horizon (see https://en.wikipedia.org/wiki/Horizon_effect). Other methods of shaping the search tree include reducing or even pruning lines that seem less promising. The quiescence search is also a form of tree shaping, as the search becomes more selective in which nodes it expands – typically just captures or captures + checks and check evasions.
One of the simplest, and perhaps the most effective extension is the “check extension.” Whenever a move is made, if the move gives check to the enemy, the search depth is increased by one. That is, instead of this:
val = -search(pos, depth-1, -beta, -alpha)
bool gives_check = in_check(pos)
int ext = gives_check ? 1 : 0
val = -search(pos, depth-1+ext, -beta, -alpha)
Disclaimer: that is probably a little too naive, as it doesn’t really guarantee the line will terminate. There are surely positions that would cause the extension as written above to explode the search tree. But, on average, it’s a win.
I implemented the check extension in Prophet4 and indeed it seems to be a big win.
Prophet4 with check extension vs without, 5+0.25
In an effort to add some sort of terminating criteria to it, I also tried limiting the check extension to capturing moves, and while still a win it didn’t work out as well.
P4 with capture only check ext vs without, 5+0.25
I also tried another form of extensions entirely – promoting moves. However, it had no measurable effect at all and may have even been a small loss, so I abandoned it.
After settling on the “naive check extension” I measured P4’s standing against P3.
Prophet4 vs Prophet3, 10+0.5
The last time I measured, P4 was -164.29 vs P3, so it’s definitely gained some ground.
Next on the list is to take a careful look at move ordering before moving onto another form of tree shaping – reductions. I expect Late Move Reductions (LMR) in particular to give another large jump. But, the algorithm is very sensitive to good move ordering, so it’s worth taking some time to study that first.
I’ve been pretty busy as of late, but in an effort to get some momentum going I picked some items that have been on my to do list that would take far more processor time than programming time – validating some evaluation terms that have been part of Prophet for many years now. The goal, really, was to validate what I was sure was true- that these evaluation terms do help; if they are removed, surely performance would drop as well. As you’ll see, it didn’t quite work out that way.
Here’s a list of evaluation terms that were tested, with results below.
Knight tropism – the idea that keeping your knight as close as possible to the enemy’s king is generally a good thing.
Rooks on open files, or even half open files.
Passed pawns – pawns with no enemy pawn in front or on an adjacent file should be rewarded, since the likelihood of promotion increases dramatically.
Isolated pawns – pawns with no friendly pawns on an adjacent file should be penalized, since they are weakened considerably without the supporting pawns.
Doubled pawns – pawns that occupy the same file as another friendly pawn are a (small) positional weakness.
Major pieces (rooks, queens) on the 7th rank with the enemy king on the back rank are usually very deadly, especially when “connected.”
This term works by penalizing a knight by 2 x distance_from_enemy_king centipawns. Distance from the enemy king is the max of difference in ranks and difference in files.
I actually started out running this one with chess4j, the Java engine, before deciding to use Prophet4 going forward. As explained in a previous post, the overhead of restarting the JVM between matches is just too high, and not restarting the engine between games isn’t great either, so doing these fast tests with a lightweight executable that can be quickly restarted seems preferable. At any rate, the outcome was nearly the same so I’ve combined the results into one table.
Also, since these are validations of existing terms, player A was the “control” player, and player B the “without” player. The hypothesis is that “Player A is better than Player B.”
Control vs “without knight tropism”, 5+0.25
As you can see, the knight tropism is worth a few ELO. Not a game wrecker by any means, but it does have a small positive effect. We’ll check this one off the list.
Rooks on Open Files
Rooks on open files or even half open files are known to be a strategic advantage. It allows the player to move their rooks around easily, projecting strength and penetrating into the opponent position.
Rooks on files with no other pieces are given a 25 centipawn bonus. Rooks on files with just enemy pieces are given a 15 centipawn bonus.
Control vs “No rook on open files”, 5+0.25
This term is obviously doing the job. Check this one off the list.
Passed pawns become promoted pawns. Passed pawns are awarded 20 centipawns.
Control vs “no passed pawn bonus”, 5+0.25
Another one validated. That’s not to say it’s tuned correctly, but at least we can say it does help.
Isolated pawns don’t have any friendly pawns on adjacent ranks to give them any support. They are a weakness. In Prophet and chess4j, isolated pawns are penalized 20 centipawns.
Control vs “no isolated pawn penalty”, 5+0.25
That is NOT a good result! I was in such disbelief after the first test that I ran a second test, and though the result doesn’t seem quite as bad, it’s still bad. As it stands, the isolated pawn penalty is hurting. I haven’t disabled it, because the major focus right now is rewriting the engine before improving it, and I want to be able to compare apples to apples after the rewrite. However, I have put an item on the backlog to study this in more detail. The heuristic should work. Either the implementation isn’t quite right, or it’s too expensive, or the weights aren’t right. I’ll have to get to the bottom of this.
Doubled pawns also known to be a positional weakness. They are penalized 10 centipawns (note this penalty gets “awarded” to each pawn).
Control vs “no doubled pawn penalty”, 5+0.25
Another surprising and disappointing result! Investigating this has also been added to the post-rewrite backlog.
Majors on 7th
This evaluation term awards rooks and queens on the 7th rank when the enemy king is on the back rank. If so, 50 centipawns are awarded. Additionally, if connected to another major piece on the 7th rank, an additional 80 centipawns are awarded – the idea being this is likely a deadly / mating attack.
I can’t remember how long this term has been around, but it’s been a looooong time. Sadly, the results aren’t so good.
Control vs “without majors on 7th”, 5+0.25
Clearly, not a good outcome! I wondered what would happen if I just disabled the “connected” part but left the award for having a major piece on the 7th when the enemy king is on the 8th?
Control vs “without CONNECTED term”, 5+0.25
Disabling the “connected” bit may help a little, but still, the heuristic is hurting overall, not helping.
Out of the six evaluation terms to be tested / validated, three of them were found to be helpful and three are actually harmful. The “majors on 7th”, doubled pawn, and isolated pawn heuristics have all been added to the post-rewrite backlog for further study.
The moral of the story here is, do NOT assume anything. Always test! This has been my philosophy for a good while now, but these eval terms were all added at a time that I wasn’t as rigorous in my testing as I am now. (And, frankly, I don’t think many in the computer chess community were before 10-15 years ago.)
If there is any upshot, it’s that there is a guaranteed strength improvement to be had, even if it’s just removing the terms altogether. But, since I know they really should work, I’ve opted to leave them for now. Also, when the Prophet4 rewrite is complete, I really want to be able to run some benchmarks against Prophet3 and be able to make comparisons. The rewritten codebase should “stand on its own.” Improving the evaluator now would cast some doubt on those comparisons.
The premise of the book is to teach one how to — think. And learn. It’s targeted primarily towards software developers, but anyone wanting tips / tricks / advice / insight on how to think critically, and problem solve more effectively would benefit from Andy’s work. There are several metaphors likening the brain to hardware and software that programmers would be familiar with, but the book is really about cognitive science.
Some of my take aways:
Software is created in your head, not your IDE. This makes it appropriate in my view to schedule time to do nothing but think. “Thinking walks” are encouraged, or even kicking your feet up on your desk. This may look like goofing off to non-programmers, and even programmers that are of the mindset that “work means your hands are on the keyboard,” but thinking is an important part of the craft.
A corollary to that is, it’s important to invest in your skills. It should be OK to incorporate that into your work schedule – in moderation of course. Do you expect a doctor to keep up with important advances in medicine? Would you expect him to do that after hours ? What about a lawyer? The same holds true for any knowledge worker. There is an unnecessary stigma around reading / learning at work. We need to keep the sword sharp to be effective in the long term. The book points out the need to be deliberate about your learning. It doesn’t happen by accident, and if you relegate it to “when I have time” you never will. Create a plan and a schedule.
R-mode thinking (traditionally called “right brain”) is the more creative side of our brains, and where intuition comes from. It is often underutilized. You can’t force it, but you can foster it. To me, this is a good reason to play chess! Chess exercises both sides of the brain – L-mode (left brain) for analysis / calculation, and R-mode (right brain) for pattern matching and intuition. I’m going to try 10-15 minutes of puzzle solving each morning as I drink my coffee to get the juices flowing.
Mind maps! I admit I rarely ever use them, but the book makes a strong case for using them as a tool to organize your thoughts. Apparently kids in Europe are taught this at a young age.
Often times, the real value in documentation isn’t the documentation itself, it’s the act of documenting. This is similar to an observation I’ve already made when preparing to give a lesson, sermon, or a talk. I almost always prepare notes, but often times don’t reference them very much.
There is no substitute for experience. Don’t be afraid to jump in and try things. Make it safe to fail. Sometimes it’s better to play first and RTM later, once you’ve gained some context.
Pressure kills creativity. I’ve always hated deadlines – particularly artificial ones (ones created internally). I think they are usually counter productive. The book validates my thoughts on this. Pressure (such as deadline pressure) encourages shortcuts and errors. It forces you to get something done, at all cost. The pressure also has negative long term effects on your health. Avoid deadlines as much as possible. Sometimes it’s a trust issue.
So many people sit in a chair for eight hours a day (or more), but that doesn’t mean they are productive the entire time (and likely are not). This is assembly line thinking. When it comes to our work time, we need to emphasize quality over quantity. For knowledge workers, it’s important to have blocks of uninterrupted time to get into a flow. Personally, I’m best in the morning after having that first cup of coffee. Don’t sit like a rat looking for a pellet in front of your email – it is about the most unproductive thing you can possibly do. Shut down the email client, turn off notifications, and just get into a flow. Email, conversations with co-workers, and especially meetings are expensive. That’s not to say they aren’t important (well, sometimes), but they can almost always wait. In other words — schedule your interruptions so you can be more productive.
One of the things that really struck a chord with me was the notion of a Pragmatic Investment Plan. Andy introduces the notion of a “knowledge portfolio,” and likens it to a financial portfolio. It’s important to have a goal, with short term and long term objectives to reach that goal. The plan may change, and that’s OK, but always have a plan. Diversify your investment – it’s important to not put all your eggs in one basket. And, invest actively. That is, stop and reevaluate your portfolio from time to time to see if your objectives need to change. I have recently set a goal of becoming more proficient in the area of Machine Learning. This is an area I did some work in during my grad school days but not a lot since, so there is a considerable learning curve in front of me. Andy’s work has convinced me of how important it is to be purposeful about creating objectives towards that goal.
All in all, a great read, and I’ve gotten a lot of practical…. err, pragmatic tips from it. I’m glad I finally got around to it.
After the failure with aspiration windows I decided to implement PVS . The idea here is that, with proper move ordering the first move is usually the best. That being the case, it makes sense to search all of the moves after the first with a minimal alpha/beta window, the goal being to prove or disprove the first move was best rather than to get a usable score. If the first move is in fact best, you’ve saved some time. If not, you have to research with the “regular” alpha/beta window.
With PVS vs without, 5+0.25
This result is a little surprising and depressing. I’m not going to give up on PVS, but clearly the time isn’t quite right for it. I’ll have to revisit it later. This leads me to believe I should take a step back and look at move ordering. It seems to me that if PVS is a loss, that could mean the “first move is best” assertion is wrong more than we’d like, meaning move ordering is not where it should be. There are some tasks on my board related to move ordering, such as deferring losing captures until after non-captures and implementing a static exchange evaluator to aid in ordering the quiescence moves. I’ll leave the branch open and revisit this when move ordering has improved.
Earlier this week I implemented aspiration windows to chess4j. It’s a very simple concept. In the iterative deepening loop, the depth 1 iteration is processed as usual, with an alpha bound of “negative infinity” and a beta bound of “infinity.” On subsequent iterations, the alpha bound is initialized to the previous score minus some margin (1/3 pawn in this case), and the beta bound is initialized to the previous score plus some margin (again, 1/3 pawn). If all goes well, and the score is within those bounds, the search should finish faster as there are more cutoffs. However, if the real score is not within that search window, then a research must be done.
My intention was to start with the 1/3 pawn windows, falling back to a “wide open” search if it fails. Once testing confirmed that was a win, I could play with the margins or incrementally expanding the window. Unfortunately, this was a pretty fast fail.
My first run was terminated after 2002 games, and the second after 2965 games.
With aspiration windows vs. without, 5+0.25
I did expect this to be a win so I’m a little puzzled by the result, but that’s why we test. Perhaps when the search matures a little more and can hit deeper depths the scores between iterations will stabilize ? I’ll just queue this up to revisit later on.
On the plus side, SPRT saved a lot of time by terminating a 20,000 game match after 2-3k games. That’s a big time saver.