Benchmarks

Moneygames with cube, Galaxy engine is best in class

Time is the average of one checker decision and one cube decision.

Ply notation: Galaxy, Sage and XG count the static evaluation as 1-ply, while GNU, Fox and Hedgehog count it as 0-ply. To compare like with like, GNU, Fox and Hedgehog are shown one ply higher than in their own notation on this page, so GNU 1P here is GNU 0-ply, GNU 2P is GNU 1-ply and GNU 3P is GNU 2-ply, and the same for Fox and Hedgehog.

Lines join the levels of the same engine. XG is eXtreme Gammon 2.10 at its Expert (1-ply), Professional (2-ply) and eXtremeGammon (3-ply) playing levels, placed from 7,632, 7,632 and 25,920 games against Galaxy 1P, 2P and 3P, without the Jacoby rule. XG's times (marked ~) are estimates, not measurements: they are read off XG's own published strength-vs-speed chart and scaled to our GNU timings, and XG 1P is not on that chart, so its time is a rough guess.

Hollow points are estimates from the 1,720 rolled-out positions database, not from simulations (hidden by default; turn them on with the "rollouts" buttons in the legend). Galaxy R1–R3, XG Roller+/Roller++ and Sage 1T/2T/3T are placed from their mean absolute equity error on 1,720 positions (against XG's and Galaxy's own rollouts, equal weight), using the relationship between that error and the simulated strength of the 1–3 ply engines, on a curve with diminishing returns (gains shrink as the error gets smaller). Galaxy R1, Sage 1T and XG Roller+ are drawn filled because they were measured in matches: R1 against Galaxy 3P (7,776 games), Sage 1T against Sage 3P on its Tiny filter (12,958 games) and Roller+ against XG's 3-ply (2,573 games); the curve is also calibrated on the R1 and Sage 1T results, and Sage 2T and 3T are shifted by Sage 1T's measured offset from the curve. Rollout times are per position; XG Roller++ time is a guess.

Cube decisions

Error on 1,720 rolled-out positions

Mean absolute error of the no-double and double/take equities, in millipoints, lower is better. Galaxy R4 plays 1,296 trials to the end of the game. The two references differ by 19.3 on average, and on 38 of the 1,720 double/take calls.

Detailed data

Checker play (cubeless)

Games played without the doubling cube, so only checker play counts.

Rollouts

Rollouts compared

Rollouts of the same 1,720 positions: mean absolute error of the ND and DT equities in millipoints against each reference, lower is better. Time is core-seconds per position for Galaxy.

Rollout	Core-s/pos	vs Galaxy R4	vs XG
Galaxy R41,296 trials, played to the end	–	ref.	19.3
Galaxy R3360 trials, truncated at 12	12.50	19.1	23.2
XG rolloutXG's own rollouts of the set	–	19.3	ref.
Galaxy R2324 trials, truncated at 9	7.10	20.9	24.0
XG Roller++	–	24.2	21.6
Sage 3T	–	24.7	27.4
Galaxy R1144 trials, truncated at 7	1.70	26.8	27.9
Sage 2T	–	29.1	32.2
XG Roller+	–	29.7	28.9
GNU Roller B	–	30.4	33.6
Sage 1T	–	35.1	37.2

Ratings

Points per game vs Galaxy 1P

± 1 standard error, fitted from the match-ups below and weighted by 1/SE². A difference of 0.01 ppg is one extra point per 100 games.

With the cube	ppg	± SE

Cubeless	ppg	± SE

XG 1,720 scoreboard

Error against eXtreme Gammon's rollouts

Millipoints per decision, lower is better: cubeless equity, no-double (ND) and double/take (DT) equity, and total cube error. Every engine at full depth with no move filter. Green marks the best in each column.

Engine	Level 11P				Level 22P				Level 33P
Engine	Cubeless	ND	DT	Cube err	Cubeless	ND	DT	Cube err	Cubeless	ND	DT	Cube err
Galaxy	23.9	52.3	63.4	3.38	16.7	36.7	57.8	1.76	12.6	28.5	41.2	0.74
Sage	32.0	63.1	90.5	5.98	22.6	51.9	65.2	3.21	18.8	34.6	57.2	1.82
eXtreme Gammon	–	62.1	87.3	6.17	–	49.0	61.5	3.04	–	35.0	55.2	1.77
GNU Backgammon	35.7	69.1	101.2	7.35	25.6	56.1	74.6	4.41	20.9	40.4	64.7	2.23

– not measured (XG reports no cubeless error at these settings). GNU is shown one level higher than in its own notation.

Scored against Galaxy R4

The same scoreboard, against our deepest rollout

The 1,720 positions scored against Galaxy R4 instead of XG's rollouts. Cubeless is left out because R4's cubeless equity comes from cubeful trials.

Engine	Level 11P			Level 22P			Level 33P
Engine	ND	DT	Cube err	ND	DT	Cube err	ND	DT	Cube err
Galaxy	53.8	65.6	3.74	37.0	58.8	1.93	28.8	41.1	1.09
Sage	64.0	89.1	5.80	52.2	63.1	3.12	34.2	55.0	1.84
eXtreme Gammon	63.3	88.5	6.30	49.6	62.9	3.20	35.7	56.2	2.06
GNU Backgammon	69.8	98.8	7.17	56.2	72.1	4.32	39.7	61.7	2.29

Every head-to-head match-up (38 match-ups)

Mean is points per game for the first-named engine, with its 95% confidence interval. Where a match-up was run more than once, the runs are combined into one row: games are added up and the results are averaged, weighted by their precision. The engine that was ahead is in bold; bold numbers are significant. Galaxy 3P and XG 3P vs Sage 3P use Sage's Normal filter to match XG. Matches with Galaxy 2P and 3P, and every match against XG, are played without the Jacoby rule; the others with it. Fox and Hedgehog have no cube model of their own and use a fixed cube-efficiency formula.

Mode	Match (A vs B)	Games	Mean ppg (A)	95% CI

How to read the benchmarks, and rollout settings

Levels: 1P, 2P and 3P search 0, 1 and 2 plies ahead, in Galaxy, Sage and XG notation.
Ratings come from head-to-head matches of 5,000 to 250,000 games each, all with variance reduction. One rating per engine and level is fitted so that the difference between two ratings matches their head-to-head result.
Rollout points in the top chart (turn on "Rollouts") are placed from their error on the 1,720 positions, using the link between that error and the simulated strength of the 1–3 ply engines. Galaxy R1, Sage 1T and XG Roller+ are drawn filled because they were also measured in matches: R1 against Galaxy 3P (7,776 games, +0.0073 ± 0.0033), Sage 1T against Sage 3P on its Tiny filter (12,958 games, +0.0091 ± 0.0027) and Roller+ against XG 3-ply (2,573 games, +0.0111 ± 0.0068).
Galaxy R1: 144 trials, truncated after 7 half-moves. Checker play 1P, cube 2P, truncation at 1P, bear-off database at truncation.
Galaxy R2: 324 trials, truncated after 9 half-moves. Checker 2P for the first 2 half-moves, then 1P. Cube 2P.
Galaxy R3: 360 trials, truncated after 12 half-moves. Checker 2P for the first 4 half-moves, then 1P. Cube 2P.
Galaxy R4: 1,296 trials, every game played to the end. Checker 2P for the first 4 half-moves, then 1P. Cube 2P.
Sage 1T / 2T / 3T: 72 / 360 / 360 trials, truncated after 5 / 7 / 7 half-moves, at 1-, 2- and 3-ply.
XG Roller+ / Roller++: 360 trials with variance reduction, stopping early at 0.010 confidence (minimum 180), truncated after 7 moves at 2-ply / 3-ply.

Features

Play vs AI

Matches from 1 to 17 points or money games, with hints, Jacoby, beavers and the Crawford rule. Set how strong the engine plays.

Analyze Match

Import .mat, .txt, .sgf and .xg files. Get every error, your error rate and Galaxy PR, and a chart of the turning points. Batch analyse up to 1,000 files at once.

Transcription

Record an over-the-board match move by move with keyboard shortcuts. The engine analyses as you go and nothing is ever lost.

Built for YouTube streaming

Allows transcribers, commentators and producer to be in sync. Live sessions share every move and the analysis as it happens.

Coach

Turn on Coach for a plain-language explanation of why the best play is best, for every position you review.

Set Up Position

Paste an XGID or GNU ID, or build any position by hand, and analyse it in seconds.

Play from position

Practise by playing out positions, and Gammon.ai scores them like a chouette or a manual rollout.

Rollouts R1–R4Star Pro

Cubeful rollouts tuned for Galaxy, from a 144-game quick check to 1,296 games played to the end. Or set up your own.

Rolled-out opening book

Every opening roll and reply, already rolled out for money and for match scores, so the first moves show rollout numbers straight away.

Library and quizzes

Save positions into your own folders, import XG position files and quiz yourself on your own blunder database.

Profiles

State of the art stats breakdown of your game.

Skill adjusted error rate

The new Galaxy Performance Rate (PR) weighs each decision by how difficult it is. That makes it different from the two similar metrics, Galaxy's Error Rate (ER) and XG's Performance Rating (also called PR). Mochy has been asking for this invention for decades, and we finally solved it.

Advanced analysis

Dice distribution analysis
Swing roll analysis
Match score table analysis

Runs on your computer

The engine is installed with the app and uses all your processor cores. Analysis keeps working offline for up to 48 hours.

Read the user guide for every page and feature, step by step.

Star and Star Pro

Included with your Galaxy membership

Gammon.ai comes with a Backgammon Galaxy Star or Star Pro membership. There is no separate account or password: sign in with Backgammon Galaxy and the app reads your membership.

What you get	Star	Star Pro
Play vs AI, Analyze Match, Transcription, Set Up Position
Library, quizzes, Profiles, Batch Analysis
Analysis at 1-ply, 2-ply and 3-ply
Rolled-out opening book
Live sessions
Rollouts R1 to R4 and custom rollouts	–
Super Deep and UBC match analysis presets	–

Download

Get Gammon.ai

Free to download. Sign in with a Backgammon Galaxy Star or Star Pro account to start.

Download for Mac BetaApple Silicon · macOS 12 or later Download for Windows BetaWindows 10 and 11 · 64-bit

Mac

System: macOS 12 Monterey or later
Processor: Apple Silicon (M1 or newer)
Install: Open the .dmg and drag Gammon.ai to Applications

Windows

System: Windows 10 or 11, 64-bit
Rights: No administrator rights needed
Install: Run the installer; .mat files then open in Gammon.ai

Account

Sign in: Your Backgammon Galaxy login
Membership: Star or Star Pro
Offline: Up to 48 hours after your last sign-in check

FAQ

Questions players ask

More detail on every page of the app is in the user guide.

Do I need a separate Gammon.ai account?

No. You sign in with your normal Backgammon Galaxy account in your browser, and the app checks your membership. There is no extra password.

What does it cost?

The download is free. Using the app needs a Backgammon Galaxy Star or Star Pro membership. Star gives you everything except rollouts; Star Pro adds rollouts and the deepest match analysis presets.

Does it work without internet?

Yes. The engine runs on your own computer, so analysis keeps working offline for up to 48 hours after your last membership check. Sign-in, Coach and live sessions need a connection.

Can I use my eXtreme Gammon and GNU Backgammon files?

Yes. Gammon.ai opens .xg, .mat, .txt and .sgf match files, reads XGIDs and GNU Position IDs, and imports XG position files (.xgp) into your Library.

Is my error rate comparable with XG and GNU?

Yes. Error rate is measured the same way as in GNU Backgammon and eXtreme Gammon. Gammon.ai also shows Galaxy PR and a level of play from Casual to Super Grandmaster.

Is it stronger than XG?

Yes! Galaxy is significantly stronger than eXtreme Gammon at 1-ply, 2-ply and 3-ply.

How do you know Galaxy is the strongest engine?

We play it against other engines over tens of thousands of games per match-up, and score every engine on eXtreme Gammon's own 1,720 rolled-out positions. At matching depth Galaxy came out ahead in every head-to-head we ran, and it has the lowest error at every level. The numbers are in Benchmarks above.

What do 1P, 2P, 3P and R1–R4 mean?

1P, 2P and 3P are how far the engine looks ahead: its direct judgement, one roll ahead and two rolls ahead. R1 to R4 are rollouts, where the position is played out 144 to 1,296 times and averaged.

Does it run on Intel Macs or Linux?

Not yet. The Mac version needs Apple Silicon (M1 or newer), and Windows needs a 64-bit PC with Windows 10 or 11.

Backgammon Galaxy family

Backgammon Galaxy

Play online

Play backgammon online against players from around the world, join tournaments and manage your Star or Star Pro membership.

Go to Backgammon Galaxy

Trackgammon

Automatic match transcription

Go to Trackgammon

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Live tournaments

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Analyse your next match with Galaxy.

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