Your checker color
Checker movement
Checker Play Keyboard
Keyboard text size
Checker Play Error Type
Probability Details: Checker Play Hints
Probability Details: Cube Hints
Statistics
Theme
Language
Table 1
36 combinations of a 2-dice roll
| 1 - 1 | 2 - 1 | 3 - 1 | 4 - 1 | 5 - 1 | 6 - 1 |
| 1 - 2 | 2 - 2 | 3 - 2 | 4 - 2 | 5 - 2 | 6 - 2 |
| 1 - 3 | 2 - 3 | 3 - 3 | 4 - 3 | 5 - 3 | 6 - 3 |
| 1 - 4 | 2 - 4 | 3 - 4 | 4 - 4 | 5 - 4 | 6 - 4 |
| 1 - 5 | 2 - 5 | 3 - 5 | 4 - 5 | 5 - 5 | 6 - 5 |
| 1 - 6 | 2 - 6 | 3 - 6 | 4 - 6 | 5 - 6 | 6 - 6 |
Table 2
Number of pips per dice roll: On average, we advance 8.2 pips per dice roll
| Dice | 1 | 2 | 3 | 4 | 5 | 6 |
| 1 | 4 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 8 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 12 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 16 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 20 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 24 |
Table 3
Probability of hitting a blot
| Number to be made | Number of favorable rolls | Probability of hitting |
|---|---|---|
| 1 | 11 | 31% |
| 2 | 12 | 33% |
| 3 | 14 | 39% |
| 4 | 15 | 42% |
| 5 | 15 | 42% |
| 6 | 17 | 47% |
| 7 | 6 | 17% |
| 8 | 6 | 17% |
| 9 | 5 | 14% |
| 10 | 3 | 8% |
| 11 | 2 | 6% |
| 12 | 3 | 8% |
| 15 | 1 | 3% |
| 16 | 1 | 3% |
| 18 | 1 | 3% |
| 20 | 1 | 3% |
| 24 | 1 | 3% |
Table 4
Probability of a checker re-entering
| Number of available squares | Number of favorable rolls | Probability of re-entering |
|---|---|---|
| 6 | 36 | 100% |
| 5 | 35 | 97% |
| 4 | 32 | 89% |
| 3 | 27 | 75% |
| 2 | 20 | 56% |
| 1 | 11 | 31% |
| 0 | 0 | 0% |
Table 5
Probability of the last checker bearing off in a single roll
| Position | Number of favorable rolls | Probability of exit |
|---|---|---|
| Square 6 | 27 | 75% |
| Square 5 | 31 | 86% |
| Square 4 | 34 | 94% |
| Square 3 | 36 | 100% |
| Square 2 | 36 | 100% |
| Square 1 | 36 | 100% |
Table 6
Probability of the last two checkers bearing off in a single roll
| Position | Number of favorable rolls | Probability of exit |
|---|---|---|
| Square 6-6 | 4 | 11% |
| __ 6-5 | 6 | 17% |
| __ 6-4 | 8 | 22% |
| __ 6-3 | 10 | 28% |
| __ 6-2 | 13 | 36% |
| __ 6-1 | 15 | 42% |
| Square 5-5 | 6 | 17% |
| __ 5-4 | 10 | 28% |
| __ 5-3 | 14 | 39% |
| __ 5-2 | 19 | 53% |
| __ 5-1 | 23 | 64% |
| Square 4-4 | 11 | 31% |
| __ 4-3 | 17 | 47% |
| __ 4-2 | 23 | 64% |
| __ 4-1 | 29 | 81% |
| Square 3-3 | 17 | 47% |
| __ 3-2 | 25 | 69% |
| __ 3-1 | 34 | 94% |
| Square 2-2 | 26 | 72% |
| __ 2-1 | 36 | 100% |
| Square 1-1 | 36 | 100% |
1. Understanding GNU Backgammon's Analysis
The AI's analysis is based on equity calculations (the expected average value of a position).
Here is an example:
Cube analysis
2-ply cubeless equity -0.236
0.435 0.050 0.001 - 0.565 0.155 0.003
Cubeful equities
1. No Double -0.318
2. Double, Pass +1.000 ( +1.318)
3. Double, Take -0.855 ( -0.537)
Proper cube action: No Double, take (28.9%)
● The first section, 'Cube Analysis', refers to the current board state without considering the match or the cube (Cubeless). It indicates the equity for the game. Here, -0.236 means you are currently losing (the negative sign).
● The two sets of three numbers show the probabilities of winning a single game, a gammon, and a backgammon for you and your opponent (You: 43.5% probability of winning a single game, 5% of winning a gammon, and 0.1% of winning a backgammon. Your opponent: 56.5% chance of winning a single game, 15.5% of winning a gammon, and 0.3% of winning a backgammon).
● The second section, 'Cubeful Equity,' is the true value of the position, taking into account cube possession, future doubles, and the match score. It shows you the equity of the game, followed by the gain or loss of equity in parentheses. You will always see three lines: no double (nothing happens on the cube), double, pass (you double and your opponent passes), double, take (you double and your opponent takes).
● Finally, the last line, 'Proper Cube Action,' tells you the best decision to make, followed by the opponent’s best decision. Here it is a no-double, and if you had doubled, the opponent must take. Finally, in parentheses, 28.9% is the frequency at which the opponent must wrongly pass for the double to be justified.
2. Take Points
A 'Take Point' is the probability threshold of winning required to justify accepting a cube (Take).
The decision threshold varies depending on the game format:
- Money Game: 25%
- Match ('Dead' Cube / Last Point): 25% (the cube level reaches the match score / only one point remains to be scored to end the match)
- Match (2-away / 2-away): 30% (score is tied and each player needs 2 more points to win)
3. Decision in a race (8%, 9%, 12% rule)
In a race with no contact (no checkers can be hit), the decision to double or take depends exclusively on the difference in pip count relative to the opponent’s total.
| Leading player's advantage | Player's decision | Opponent's decision |
|---|---|---|
| Less than 8% advantage | No Double | Take |
| Between 8% and 9% advantage | Double | Take |
| Between 10% and 11% advantage | Redouble | Take |
| 12% advantage or more | Double | Pass |
4. Doubling Window (Money Game)
For doubling to be mathematically optimal, your chances of winning must fall within a specific range:
● Doubling Threshold: You must have approximately a 66% to 68% chance of winning to roll the cube.
● Pass Threshold: Your opponent must have less than a 25% chance of winning to pass.
● Too Good to Double: If your chances of winning exceed 75% and the potential for a gammon is high, doubling is a mistake because it allows your opponent to escape by giving up 1 point when you could win 2 or more.
'+' for your checkers, '-' for the opponent:
This feature is designed exclusively for educational and post-game use. The goal is to help you improve, not to assist an ongoing game. MBT does not offer any automation for real-time online play and cannot be held responsible for how you use it.
Minimalist Backgammon Trainer (MBT) is a simulator designed to isolate the essentials: the movement of your checkers and cube strategy. Its goal is to improve your ability to choose the perfect move or make the best decision in realistic game situations. No stakes, no stress, just you facing the best possible decision.
Why MBT
MBT was born from the observation that online training tools are often limited to quizzes or selected positions. Nothing offers training covering all phases of a game in a modern and responsive interface. MBT was designed to fill this gap and refocus training on the essentials: improving your accuracy and your decisions.
How to play
Start a simulation by pressing 'Play'. Use the virtual keyboard, your physical keyboard, or tap directly on the board to suggest the best move or make the best cube decision. Submit your answer to discover GNU Backgammon's analysis. You made the best choice, well done! If not, keep trying until you find it.
Features +
● Checkers and/or Cube: Freely switch between targeted training—checker play or cube decisions—and the complete mode: 80% checkers / 20% cube. Note that the complete mode retains your Checker and Cube preferences.
● Mode: Choose 'Mix', 'Opening', 'Middle', or 'End' to get simulations of the beginning, middle, or end of the game for checker play. Choose 'Mix', 'Money Game', 'Match to 5', or 'Match to 11' to get varied match and score configurations for cube play.
● Input: Use the virtual keyboard, your physical keyboard, or click on the board to enter your move (bottom of the center bar for 'OFF'). On your physical keyboard:
- 'm' for Checkers and/or Cube, 'c' to change the game type
- numbers, the / key, 'b' for 'BAR', 'o' for 'OFF'
- 'y' to double or take, 'n' to not double or pass
- 'g' to display Game Information, 'h' to display Hints
- the Enter key to start a simulation or confirm a move, 'a' to retry
● Game info: See the list of moves played during the simulation, as well as the resulting pip. The latter is not visible at all times to also train you in calculating the pip count.
● Error type: If the move you submitted is not the best move, MBT will indicate the type of error you made.
● Hints: For checker play, the best moves according to GNU Backgammon's analysis. For each move, you will see in parentheses the ply level used for the analysis, followed by the equity loss compared to the top move. For the cube, the analysis of the current simulation with the equity gains and losses for each decision. GNU Backgammon always displays hints from the point of view of the player concerned; if you choose the minimal or essential probability detail level, the take/pass values will be converted to show the hints from your position.
● Sharing: In 'Hints', use the 'Save' button to generate an image including the board, the dice, and GNU Backgammon's analysis, or the 'Share' button to share a link to the simulation. In 'Game Info', you can find the Match ID and the Position ID of GNU Backgammon to reproduce the position on other applications.
● Statistics: Find your performance level for each type of game as well as your Error Rate for all games played. Please note that only your first answer is recorded in the statistics (shares, custom positions, and replayed blunders are not counted).
● Blunders: wait ten days to replay your biggest mistakes. MBT saves up to 100 blunders; make a better decision to make them disappear.
● Evaluation: Whenever you like, run an evaluation based on 20 simulations (16 checker moves and 4 cube decisions). Limited to one evaluation per 24 hours. Track your actual progress using the trend graph and the history of your last 40 tests.
● Custom Position: manually enter a backgammon position, for example from a real game. This is an easy way to review your decisions after a game, understand what you could have played differently, and practice situations that cause you problems.
● Cheat Sheet: some essential statistics on dice, moves, cube, ...
● Settings: choose your checker color, board orientation, show/hide virtual keyboard, probability detail level in hints, light or dark theme (compatible with all screens, including E-Ink), preferred language, and export/import your statistics.
Technical data - General +
● MBT uses the GNU Backgammon engine to provide simulations and analysis.
● MBT is designed to be used exclusively in portrait mode. This deliberate choice allows for optimal one-handed ergonomics and ensures maximum readability of the board and all the elements surrounding it.
● MBT is a PWA (Web App) that you can install on your home screen for full functionality, even in airplane mode.
● MBT utilized Gemini as technical support for optimizing its most complex code segments.
Technical data - Checkers +
● Each simulation is a unique game without the Jacoby rule or doubling cube.
● By selecting 'Mix', MBT will play between 0 and 27 moves. By selecting 'Opening', MBT will play between 0 and 4 moves. By selecting 'Middle', MBT will play between 5 and 16 moves. By selecting 'End', MBT will play between 17 and 27 moves. The number of moves is determined randomly within these ranges.
● The dice roll is managed by GNU Backgammon.
● The evaluation performed by GNU Backgammon during the simulation to decide on these moves is based on a depth of 1 (ply 1). The final evaluation, which will be used as a rating, is performed at a depth of 3 (ply 3). Why not more? To ensure a smooth experience.
● At the end of the simulation, if there is only one possible move or no possible move, a new game is started to avoid obvious situations.
● MBT only evaluates a playing decision at a given position, without cube decisions or the context of the entire game, so the ER obtained is not equivalent to a PR for the entire game. However, the values are correlated, and you can consider that multiplying your MBT ER by approximately 1.35 (1.2 > 1.5) provides a fairly accurate estimate of your actual PR.
Technical data - Cube +
● The match score is defined randomly for matches to 5 and matches to 11, taking care to exclude scores where both players are each one point from victory.
● A number of moves to play is defined randomly between 8 and 20, the range where cube decisions are most relevant.
● Each simulation starts a new match in which the beaver and Crawford rules are not activated. The Jacoby rule is only activated in money games.
● The evaluation performed by GNU Backgammon during the simulation to decide on these moves is based on a depth of 1 (ply 1). The cube analysis is performed at a depth of 2 (ply 2).
● To ensure relevant puzzles, MBT analyzes the equity in the background. It excludes situations that are too obvious (overwhelming or too weak an advantage) to force stops where the decision is most difficult. MBT also introduces randomness to alternate naturally between attacking positions (Double/No Double) and defensive positions (Take/Pass).
● This monitoring yields approximately 60% attacking simulations and 40% defensive simulations. Regarding difficulty, MBT achieves approximately 20% expert-level simulations (Gap < 0.030), 40% competition-level (Gap 0.030 - 0.120), and 40% learning-level (Gap > 0.120).
● Given that cube decisions represent only about 10 to 15% of the total decisions in a game, and because MBT filters for highly relevant cube positions, the Cube ER obtained will naturally be higher than in a full game. This makes it difficult to correlate with a match PR. Consequently, MBT prefers not to provide a conversion rule for the cube.
Definitions +
● Ply: this is the unit of measurement used to define the depth of analysis. A ply of 0 corresponds to an immediate and static evaluation of the position after the move, without taking into account dice rolls or future responses. A ply 2 analyzes your move and the opponent's best response. A ply 3 analyzes your move, the opponent's response, and your next move. You will never see a ply 1 because it is an approximation of a ply 2, which GNU Backgammon intentionally ignores. It differs from a rollout, which is not a theoretical analysis but a statistical simulation that plays out thousands of games to determine the best move.
● Equity loss: Difference between the best possible move and the move actually played. The lower the equity loss, the better. You can consider that you have played an excellent move if your equity loss is less than 0.02; you have made a small mistake if it is between 0.02 and 0.08; and a big mistake (a blunder) if you lose more than 0.08.
● Jacoby: The Jacoby rule applies in money game (outside of match play). In this case, a gammon or backgammon (double or triple win) only counts if the cube has been used.
● Beavers: A beaver is a special response to a double: when the opponent doubles, it is possible to accept and immediately redouble (without giving them a choice). The cube goes to double the proposed value, but does not change hands.
● Crawford: The Crawford rule applies in match play: when a player reaches 1 point from victory, the next game is a Crawford game. During this game, the cube is forbidden. After that, the cube becomes usable again.
● Cubeless: the position is analyzed as if there were no cube. Only the chances of winning or losing the game itself are analyzed.
● Cubeful: the use of the cube is taken into account in the analysis.
● ER (Error Rate) / PR (Performance Rating): The ER gives the average number of errors per move, equity losses. The lower the ER, the better the player is. It is used to calculate the PR (Performance Rating), which indicates the level of play. The lower the PR, the stronger the performance. In summary: ER measures errors, PR translates this into performance level. PR ranking for information purposes:
- Robot: 0 - 1
- World class: 1 - 4
- Expert: 4 - 7
- Advanced +: 7 - 11
- Advanced: 11 - 16
- Intermediate: 16 - 22
- Beginner: 22+
● Error type:
1. Minor optimization
- Slight pip adjustment / Slight positional choice: Positional adjustment with no critical impact
- Equivalent move: Playing this move or the best one makes no meaningful difference
2. Safety error
- Unnecessary blot: Creating a blot with no tactical justification
- Vulnerable to hit: Dangerous exposure of blots to an opponent's hit
3. Missed attacking opportunity
- Passive in dynamic position: Overly cautious play when the position calls for aggression
- Missed obvious hit: Overlooking a direct hit that would have changed the dynamics
- Missed tactical hit: Omission of a tactically advantageous capture of an exposed opponent checker.
4. Structural miss
- Missed point consolidation: Failure to close a strategic point or reinforce a stack
- Breaks prime: Dismantling a prime
- Loss of defensive point: Loss of an anchor or an important defensive point
- Loss of timing: Loss of flexibility in the position, forcing deterioration of one’s structure.
5. Racing inefficiency
- Non-optimal pip gain: The move does not efficiently maximize the racing advantage
- Significant pip loss: Significant loss of racing advantage
- Inefficient bearing off: Suboptimal bearing off
6. Passive error
- Gives up initiative / Overly cautious: Overly passive play or giving up pressure on the opponent
- Loss of containment: Inability to keep the opponent’s checkers contained.
- Major strategic error: Incorrect overall reading of the position
Friends Of MBT +
● The Backgammon Cafe: The definitive backgammon learning platform. Master the game with expert lessons, interactive drills, and a global community of players.
● Chicago Point: A prime source of backgammon information featuring US tournament rules, a tournament calendar of events and results, backgammon clubs in the United States, and links to other backgammon sites.
Privacy policy +
● Minimalist Backgammon Trainer does not collect, store, or share any personal data. All game statistics and preferences are saved exclusively in your browser's local storage, on your device only, and are never transmitted.
● Minimalist Backgammon Trainer uses GoatCounter for anonymous visit statistics. GoatCounter does not use cookies, does not collect your IP address, and is designed to respect your privacy and the GDPR. You can consult their privacy policy at goatcounter.com.
● No account is required. No data leaves your device.
MBT is offered without any warranty. Despite all the care taken during development and testing, you may encounter problems. If so, please be kind and feel free to report them to me :)
Credits +
● GNU Backgammon 1.05.000 May 31 2021
Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004 by Gary Wong
Copyright (C) 2015 by Gary Wong and the AUTHORS
● Porting GNU for the web by Theodore Hwa
● 'LE BACKGAMMON Stratégies et tactiques' by Henri Borentain / ISBN 2-85182-398-1
● Minimalist Backgammon Trainer developed by Alwin M. with the help of Gemini
● English version by DeepL
● Web analytics by GoatCounter
● www.backgammon-trainer.ovh / backgammontrainer634@gmail.com
Version 1.8.1 - April 2026