mache

Chess engine testing on GitHub Actions, with no server to run.

mache runs a match between two versions of an engine on the GitHub-hosted runners a repository already has. The match is split across jobs that run at the same time, and the games are pooled afterwards into one elo estimate or one sequential test (SPRT). A repository calls it from a workflow of its own, on its pull requests or by hand, and the result goes in the run's summary. fastchess plays the games.

It suits an engine whose changes are still large enough to show within a few thousand games. A small change can take many runs to settle, and What hosted runners can measure says how many.

The tools that read the games also work without GitHub Actions, on pgn files fastchess wrote anywhere. Running a match without CI shows how.

The name is from mache (μάχη), Greek for battle, and reads as Measure A CHess Engine.

Why this exists

OpenBench is how engine testing is normally done: an instance hands out tests and client machines attach to it and play the games. In almost every case using OpenBench is a far better choice.

This tool exists for two reasons.

The first is that it was not planned. It grew as I wrote arche, my first chess engine, starting as a basic CI job that got out of hand.

The second is that OpenBench needs machines. Some engines develop against a shared instance and some projects run their own. mache is for the case where you have neither. It has no instance and no clients, and it runs on the hosted CI runners a repository already gets, as part of the pull requests and releases it already runs, so testing an engine needs no machine of your own. Both play their games with fastchess underneath.

Hosted runners are the point of mache and also what make it awkward. Their timing varies from one job to the next, and a job is stopped at a time limit, often long before a match worth reading has finished. So a match is split across jobs that run at once and pooled afterwards, which is most of what the tools below are for, and why they take the care described further down.

What is here

mache, a Python package with four tools:

Seven composite actions, which are the parts of a match workflow that are not about any one engine. A caller keeps its own jobs, its own matrix and its own toolchain cache, and calls these for the work inside them.

Each has a README.md beside it. Two things they deliberately do not do: build an engine, and write the manifest a run keeps about itself. A build belongs to the engine, and arrives as steps of the caller's own rather than as a command in a string. A manifest is the calling repository's record of its own run, and its shape is that repository's business.

Two reusable workflows, .github/workflows/strength.yml and calibrate.yml, which are a whole match as one call. A repository that wants a match rather than a job graph writes about ten lines and gives up three things: its own cache action, its own build as steps, and the shape of its own manifest. uses: is not an expression, so a reusable workflow cannot be handed a step by anybody. .github/workflows/README.md has the call, the build contract and the trade in full.

bin/ holds the shell tools a caller can run directly, which actions/setup puts on PATH. One of them is book_table.sh, the default book table: two standard books from official-stockfish/books, used whenever a caller does not pass a table of its own. There is no build script among them, and docs/BUILDING-A-REF.md says why, along with the one trap a build step written for this has to avoid.

What hosted runners can measure

A run of strength.yml with its defaults plays 500 games over five shards, which is 250 pairs. A sequential test given batches: 4 plays up to four such batches in one run, 1,000 pairs. It stops early if a batch settles the test, and otherwise hands back the counts for the next run to carry on from.

For an estimate on its own, the 95% margin in normalized elo, as mache works it out, depends only on the number of pairs:

The margin in logistic elo also depends on how the pairs scored, and so on how many games were drawn.

A sequential test runs until the pairs settle it, and the closer its bounds, the longer that takes. In the simulation below, halving the gap between the bounds took between three and four times the pairs. It ran 300 tests a row of the normalized test with mache's own code, judged every 250 pairs as with the workflow's default batch. The pair scores were drawn from a distribution in which three pairs in five score one point, shifted to each true difference:

Those are averages, and the spread around them is wide: about one test in ten ran to nearly twice the average or longer. At 1,000 pairs a run, the averages come to about four to seven runs for [0, 10] and about thirteen to twenty-six for [0, 5]. The normalized model is what match-estimate --model normalized and the sprt_model input of actions/summarise-match use. strength.yml takes its bounds in logistic elo, so its default of [0, 10] is not the first row above, and how long a logistic test runs depends on the draw rate as well as the bounds.

How long a batch takes depends on the time control, the engines and the runner, so it is worth timing one before planning a test around it. A shard is stopped at max_match_minutes, 150 by default, and reports the games it finished by then.

Both engines of a shard share one runner, so a slow runner slows both. An engine whose strength changes a lot with the time it is given loses more to a slow runner than one whose strength does not.

GitHub does not charge for its standard hosted runners on public repositories. A private repository uses the Actions minutes its plan includes. GitHub's billing documentation has the current terms.

Using the tools

pip install mache gives the four command names used below. Under the composite action nothing is installed, and the same tools are python3 -m mache.<tool> with underscores where the command name has hyphens.

Each tool prints its report on stdout. Anything worth an alert goes to stderr instead, a fault or an unfinished game, so a workflow can raise it from there rather than reading it back out of the report.

match-estimate

A shard is one pgn, written by one job of the run. fastchess plays it with -repeat, so a round is two games on one opening with the colours reversed, and --candidate and --baseline name the engines as fastchess named them.

match-estimate strength-1-1-shard-*/games.pgn \
  --candidate new --baseline ce8b662 --tc 10+0.1

+56 ±37 Elo (150 games)

75 pairs from 150 games. The 95% interval is +19 to +93 elo, and the likelihood of superiority is 99.9%. In normalized elo the difference is +85 ±56, which is the figure to compare across books and time controls.

| pair score | 0 | 0.5 | 1 | 1.5 | 2 |
| --- | --- | --- | --- | --- | --- |
| pairs | 2 | 9 | 36 | 19 | 9 |

| shard | games | score | faults |
| --- | --- | --- | --- |
| strength-1-1-shard-0 | 50 | 57.0% | 0 |
| strength-1-1-shard-1 | 50 | 59.0% | 1 |
| strength-1-1-shard-2 | 50 | 58.0% | 0 |
| pooled | 150 | 58.0% | 1 |

The block match-terminations prints follows that, and the last line of the report names the version that read the games. --tc and --baseline are recorded rather than read, so a baseline that is not a release tag can go in as its sha.

--elo0 and --elo1 read the same pairs a second way, as a sequential test:

match-estimate strength-1-1-shard-*/games.pgn \
  --candidate new --baseline ce8b662 --tc 10+0.1 --elo0 0 --elo1 10

which puts this paragraph in the report:

SPRT [0, 10] inconclusive. The log likelihood ratio over the 75 pairs of the test (75 from this batch and 0 from the batches before it) is 1.32 against bounds of (-2.94, 2.94). The games so far settle it neither way. Launch another batch with prior_pairs set to 2,9,36,19,9.

The counts at the end of it are what the next batch carries in, so that the runs accumulate into one test:

match-estimate strength-1-1-shard-*/games.pgn \
  --candidate new --baseline ce8b662 --tc 10+0.1 \
  --elo0 0 --elo1 10 --prior-pairs 2,9,36,19,9

SPRT [0, 10] inconclusive. The log likelihood ratio over the 150 pairs of the test (75 from this batch and 75 from the batches before it) is 2.64 against bounds of (-2.94, 2.94). Over all of them the difference is +56 ±26 elo, which is the figure the trailer carries. The games so far settle it neither way. Launch another batch with prior_pairs set to 4,18,72,38,18.

Three flags each replace the whole report. --line prints what release notes carry:

+56 ±37 Elo (150 games), SPRT [0, 10] inconclusive, LLR 1.32 (-2.94, 2.94)

--trailer prints what a commit carries:

Elo: +56 ±37 (sprt [0, 10] inconclusive, 150 games, 10+0.1, vs ce8b662)

--json prints all of it as data, for a reader that is not a person:

{
  "format": 1,
  "tool": {
    "name": "mache",
    "version": "0.1.0",
    "command": "match_estimate"
  },
  "candidate": "new",
  "baseline": "ce8b662",
  "tc": "10+0.1",
  "games": 150,
  "pairs": 75,

format is which shape the object is in, and shape 1 is a contract from 0.1.0 on. Fields are added to it. None is removed and none is given a new meaning under the name it has, and a change that cannot be made that way raises the number. The rest of the object holds the pentanomial counts, the sequential test, a row per shard, the terminations, and the line and trailer strings above.

rating-estimate

The ladder is one argument, name:rating per opponent separated by commas, with the names as the pgn spells them:

rating-estimate gauntlet.pgn arche-0.5 \
  'stash-v33:1876,cheng-4.39:1932,supernova-2.1:1801,winter-0.7:1978'

| opponent | ccrl | w-d-l | score | implies |
| --- | --- | --- | --- | --- |
| stash-v33 | 1876 | 12-6-12 | 50.0% | 1876 |
| cheng-4.39 | 1932 | 9-7-14 | 41.7% | 1874 |
| supernova-2.1 | 1801 | 16-5-9 | 61.7% | 1884 |
| winter-0.7 | 1978 | 7-6-17 | 33.3% | 1858 |

1873 ±56 (95%) on the ccrl blitz scale (120 games)

Read by mache 0.1.0.

--line prints the estimate and nothing else. --json prints the fit, the ladder it was given and a record per opponent, in the same format 1.

The figure is on the scale of the list the ratings were read off, and the line names it. That is ccrl blitz unless --scale says otherwise, so a ladder read off the 40/15 list is fitted with --scale 'ccrl 40/15'. The summarise-gauntlet action takes the same thing as its scale input.

match-terminations

match-terminations strength-1-1-shard-1/games.pgn

games: 50
normal: 49
adjudication: 0
time forfeit: 1 (new 1)
disconnect: 0
stall: 0
abandoned: 0
illegal move: 0
unterminated: 0

Every ending is printed, zero included. The line about the one that ended by a fault goes to stderr beside the block. --json prints the same counts, with the engines an ending fell on as a mapping rather than as the sentence.

book-slice

book-slice --openings 34700 --pairs 250 --shards 5 --shard 3 --seed 7

758

That number is one based, which is what fastchess's start= takes. Every shard of a run asks with the same --openings, --pairs, --shards and --seed, and its own --shard, so the slices are worked out from the run's own numbers and no two of them hold an opening in common.

A sequential test pools its batches the same way it pools its shards, so the rule holds across them too, and --batches with --batch is how a caller says so. What is then reserved is the whole test rather than one batch of it, and a batch takes the slice after the batch before it. This matters where the batches are chained inside one run, because they share a seed: each reserving its own games alone would start every batch where the first one started, and the pooled estimate would count those positions twice with nothing failing. A caller that passes neither plays what an unbatched run plays.

Running a match without CI

None of the four tools needs GitHub Actions. They read pgn files, or in book-slice's case a few numbers, so they work on games played anywhere: on one machine, or on a few machines that each play part of a match. pip install mache gives the command names. fastchess and an opening book are yours to provide. In a clone of this repository, bin/book_table.sh fetch 8moves_v3 . downloads one of the two books the actions use and checks it against its recorded hash.

Each machine plays a shard. book-slice says which opening a shard starts at, so that no two shards play the same one. Every shard asks with the same numbers and its own --shard:

openings=$(grep -c '^\[Event ' 8moves_v3.pgn)
start=$(book-slice --openings "$openings" --pairs 100 --shards 2 --shard 0 --seed 7)

Then fastchess plays the shard. -repeat pairs the games as match-estimate expects. -rounds is the number of pairs and has to match --pairs above. nodes=true is what the report's table of clocks and nodes counts moves by, and timeleft=true gives its last column. Without them the table reads as zeros.

fastchess -engine name=new cmd=./new -engine name=old cmd=./old \
  -each proto=uci tc=10+0.1 \
  -openings file=8moves_v3.pgn format=pgn order=sequential start="$start" \
  -rounds 100 -repeat -concurrency 2 \
  -pgnout file=games.pgn nodes=true timeleft=true

fastchess adds to a games.pgn that is already there, so start each shard in an empty directory. A shard played twice into one file would be counted twice.

With each shard's games in a directory of its own, one command pools them. The directory names become the rows of the shard table:

match-estimate shard-0/games.pgn shard-1/games.pgn \
  --candidate new --baseline old --tc 10+0.1

--elo0, --elo1, --prior-pairs and --model run the sequential test here the same way they do in a workflow. A test played in several batches passes --batches and --batch to book-slice as well, so that a later batch does not replay an earlier one's openings.

The part that is not obvious

A sharded match is not a long match cut up. Three things have to hold or the number it produces is wrong.

The estimate is over the pool. fastchess prints one, but only for the games its own process played. With five shards that is a fifth of the evidence, and averaging five such figures is a different calculation. match-estimate reads the games themselves.

The error bar is over pairs, not games. Under -repeat the two games of a round are one opening with the colours reversed, so they are one observation. Counting them as two understates the spread.

A sequential test looks only at batch boundaries. A per-shard SPRT that stopped when its own games settled the question would be one look per shard at a bound priced for one, on a sample chosen by what it said. Here the shards play their slices out with nothing watching and the test is judged once over all of them. A run is one batch, and --prior-pairs carries its pairs into the next, so repeated runs accumulate into one test rather than several.

Openings follow from a seed rather than a shuffle, so a schedule can be played again from what the run recorded.

The clocks and the search are in the report

A match report carries what each side's clock and search did: moves thought about, nodes, time, nodes a second, and the tightest its clock ever got. The figures are per engine rather than per colour, since -repeat plays every opening both ways, and they pool across shards the way the estimate does.

They are there because an elo figure does not say why. A result that is really one side being handed more time, or more nodes for the time, shows as a ratio away from one here and nowhere else in the report. A registration that says a surprising number is re-read against the clocks and the node counts is answered from this table.

It is in the report, and the report goes to the log and to the run's summary. That is the point of putting it there rather than leaving it in the games: a later session reading back a run can reach a log, and may not be able to reach the artifacts. Book moves are left out of the counts, since the engine did not think about them, and still hold their place so the moves after them are attributed to the side that made them.

The test keeps no state

mache stores nothing between runs. The pairs the earlier batches of a sequential test played are an argument: a run prints them at the end of its verdict and the next run is handed them back with --prior-pairs. That is a decision and not an omission.

Carrying five numbers is the price. A caller that loses them has lost the test and has to start it again. actions/summarise-match hands them back as carried, beside the verdict that says whether another batch is wanted at all, so a caller writing its own job graph passes them on rather than a person retyping them between runs. What it buys is that a run says on its face what it was judged over, so a reader checks the count against the batches that were played rather than trusting a file nobody looked at. Stored state would also have to be one thing per test, and a tool that cannot see which test a run belongs to would be guessing at that.

An accumulator that keeps the counts in an artifact is a later addition if anyone wants one. It is not missing by accident.

The version is in the output

A change to the estimator can price the same games differently. So a report names the version that read them, --json carries it in its tool object, and the composite action hands the version on the path back as an output, for a caller to write into whatever it records about a run. A figure kept without it cannot be checked against the code that produced it.

--line and --trailer are one line each and carry no version. They are quoted beside a report or a manifest that does.

Logistic and normalized elo

The headline figure is logistic elo, read off the score with -400 log10(1/p - 1). How far a given improvement moves the score depends on how often the games are drawn. The same change reads as fewer elo on a balanced book than on an unbalanced one, and fewer at a long time control than a short one, so two runs that differ in either are not comparable in it.

The report also gives the difference in normalized elo, which is what fastchess prints as nElo. It is the score's distance from a half divided by the spread of the pairs, scaled so that a small difference in a match with no draws reads about the same in both. Because it measures how clearly the games separate the two sides, it compares across books and time controls better than logistic elo does, and its margin depends on the number of pairs alone. For the same pairs the figure here is the one fastchess prints. --json carries it as nelo and nelo_margin.

The sequential test takes its bounds in either. --model normalized reads --elo0 and --elo1 as normalized elo, and the default, --model logistic, reads them as logistic elo as before. Under the normalized model the number of games a test needs to settle depends on the bounds, and much less than under the logistic model on the book or the time control, so the same bounds cost roughly the same whichever is played. A normalized test names itself as SPRT [0, 5] nElo in the report, the line and the trailer, and --json carries the model in its sprt object.

Every batch of one test is judged under the model it started with. The pair counts carried between batches are the same under either, so nothing stops a caller changing it part way, but the error rates only hold for a test that did not. actions/summarise-match takes it as sprt_model.

The ratio under the normalized model fits, for each hypothesis, the distribution over the five pair scores that is likeliest to have produced the pairs while being that many of its own standard deviations from a half. It does that as a convex fit at each spread and a search over the spread, rather than by the fixed point iteration fastchess uses, which does not converge from every set of counts. Where both converge they agree. Hypotheses are limited to 100 normalized elo either side of nought, which is wider than the bounds a test normally uses.

Reading a rating estimate

rating-estimate holds every opponent at its published figure and fits the one free parameter, so the figure is the rating at which the expected score equals the score actually made.

The ± is a 95% interval and it describes the games and nothing else. Whether one rating can describe the results at all is asked separately: when the opponents disagree with each other by more than chance allows, a note says so, and the interval is an understatement rather than an estimate.

A placement against a published list carries a systematic error no number of games reduces. The opponents earned their ratings on other hardware at slower time controls. Treat the figure as a placement worth about a hundred points either way, not as a rating.

Install

pip install mache

The engine side needs no install. The action puts the package on the path.

Status

Alpha. mache is used by arche, which is where it was written, and it has not yet been used by an engine that is not arche. Until it has, expect the rough edges of a tool with one user.

mache is written with heavy AI assistance.

Licence

MIT. See LICENSE.

The generalized log likelihood ratio follows Van den Bergh's note on the pentanomial model, written from the note and checked against fastchess: for the same pairs the number here is the number it prints. Two test cases are fastchess's own, attributed where they are used. fastchess is MIT.