Game 1 | Glacier Gammon

bgLog Interactive Board #

Above this text is the interactive board that you can use to walk through the moves in the game. Here are the parts from the top:

  • Top Checker Top Player Name — The name of the player oriented at the top of the board.

  • bgLog Board — The display of the current board state. bgLog has various features that enable it to provide a lot of information at a glance. Note that for the first three listed, the bottom player’s information is at the bottom of the board and the top player’s information is at the top of the board.

    • Match Score — On the leftmost portion, you can see the current scores of each player out of the score required to win the match.
    • Pip Count — The pip count is the number of pips (each dot on a die face is a pip) you have to roll to bear off completely. Each player’s pip count can be seen on the middle portion.
    • Turn Indicator — The checker color of the player on turn will appear on the rightmost portion. If you can see the player’s checker on the rightmost portion, it is currently that player’s turn.
    • Point Labels — This board uses Chicago Point Labelling: the respective player’s 1-12 points are labelled on their side of the board while their 13-24 points are labelled in the middle (depicting the points on the opposite side). As an example in the starting position, the bottom player’s 1-point is where the two Top Checker checkers are while the bottom player’s 24-point is where the two Bottom Checker checkers are.
    • Doubling Cube Ownership — The current stakes for the match and who owns the cube is shown in the middle. This is similar to real-life play: if the cube is in the center and the 64-side face is up, no one owns the cube and the stakes are equivalent to one point (disregarding gammons and backgammons). If the cube is on a player’s side, the stakes are equivalent to the side of the cube facing up, and that player owns the cube.
  • Bottom Checker Bottom Player Name — The name of the player oriented at the bottom of the board.

  • XGID — The XGID of the current position is shown: you can copy this and paste it into GNUBG and XG with minimal problems in case you want to perform your own analysis. Clicking the XGID will also copy it to your clipboard.

  • Navigation Buttons — These buttons enable you to traverse the current match. If a button is greyed out, it is currently disabled (e.g. the first game in the match where there is no previous game).

    • Previous Game Previous Game (Numeric Keypad Shortcut: 9) — Brings you to the previous game in the match.
    • Start of Game Start of Game (Numeric Keypad Shortcut: 7) — Brings you to the start of the game.
    • Previous Move Previous Move (Numeric Keypad Shortcut: 4) — Brings you to the previous move.
    • Slower Slower Animation (Numeric Keypad Shortcut: -) — Makes the board animation play slower.
    • Play Play (Numeric Keypad Shortcut: 5) — Plays the board animation.
    • Stop Stop (Numeric Keypad Shortcut: 5) — Stops the board animation.
    • Faster Faster Animation (Numeric Keypad Shortcut: +) — Makes the board animation play faster.
    • Next Move Next Move (Numeric Keypad Shortcut: 6) — Brings you to the next move.
    • End of Game End of Game (Numeric Keypad Shortcut: 1) — Brings you to the end of the game.
    • Next Game Next Game (Numeric Keypad Shortcut: 3) — Brings you to the next game in the match.

Analysis Level #

There are various analysis levels used to analyze moves. Here are the common analysis levels used by XG:

  • Book — This usually means that someone placed the equities into XG’s opening book. While most of these are actual rollouts, some Book-level analyses are actually at the level of XGR/+/++.
  • Rollout — Rollouts are the closest we can get to finding ideal play (with current hardware).
  • XG Roller/+/++ (XGR/+/++) — These are truncated (less deep) rollouts that are way faster than running a credible rollout, but have a closer result to an actual rollout than an n-ply analysis.
  • n-ply — n-ply analyses are those that play the best moves for all 21 distinct two-die rolls at each succeeding turn (ply) for n plies, then uses the neural network to evaluate the outcomes that occur. One can think of it as a brute-force tree search for n plies then estimating the actual value of the position using a neural network. The strongest default ply for XG is 5-ply. At 1-ply, the neural network is only evaluating the position as it is and not the outcomes that occur from n plies of ideal play.

XG also uses 3-ply Red which is an approximated 3-ply. Its only relevance would be if you want a super-quick rollout with accurate enough doubling decisions, for which you choose 3-ply Red for doubling decisions.

GNUBG Equivalents for n-ply Analysis #

GNUBG defines plies differently: XG 5-ply is actually GNUBG 4-ply and XG 1-ply is actually GNUBG 0-ply. Since GNUBG calls their plies one-less, one might be misled to think that a GNUBG 4-ply is at a depth less than that of an XG 5-ply. This is incorrect, since they are operating at the same depth, and the only difference there would be how the respective neural networks were trained and how they operate.

For distinction, I will be using XG terminology by default, and will be calling GNUBG’s n-ply as n-ply lookahead.

Equity Information #

XG provides the equity for the player after a move is done. It then sorts the moves based on equities to have a ranking of moves. XG also shows the equity difference for non-best moves, so we can see how much worse the other moves are comparatively. Do note that this is the cubeful equity produced by the neural network, which is an equity that accounts for the cube ownership and value when simulating outcomes.

Bottom Checker Bottom Player Category Top Checker Top Player
Intermediate (-0.0298) Total Error Distracted (-0.4333)
Distracted (-0.0745) Checker Play Expert (-0.0114)
World Champ. (+0.0000) Cube Play Distracted (-1.0662)
14.90 Performance Rating 216.58

The table above is the Game Overall Rating. It is similar to the Match Overall Rating except this table shows the ratings for the current game.

The text below shows who won the opening roll.

Bottom Checker Bottom Player wins the opening roll.

Move 1

The heading below shows the move the player made. Each heading of this kind shows the checker color of the player that made a specific move. It also shows whether the player committed an error.

Checker play moves are represented with the roll and move sequence. The opening roll is depicted with the left number as the top player’s roll and the right number as the bottom player’s roll. The move sequence uses standard backgammon notation. To demonstrate this, this match has various examples.

Bottom Checker  46:  24/14  ?!

Computer Analysis
1. Book1 24/18 13/9 +0.0128
50.34% (G:14.11% B:1.40%)
49.66% (G:14.12% B:1.17%)
Conf.: ±0.0030 (+0.0099...+0.0158) - [99.5%]
2. Book1 24/14 +0.0075 (-0.0053)
50.51% (G:12.69% B:1.14%)
49.49% (G:13.70% B:1.00%)
Conf.: ±0.0028 (+0.0047...+0.0103) - [0.5%]
3. Book1 8/2 6/2 +0.0008 (-0.0120)
49.66% (G:16.45% B:1.88%)
50.34% (G:14.68% B:1.21%)
Conf.: ±0.0028 (-0.0020...+0.0037) - [0.0%]
4. Book2 24/20 13/7 -0.0756 (-0.0884)
48.25% (G:12.91% B:0.56%)
51.75% (G:13.63% B:0.59%)
5. Book2 24/20 24/18 -0.0871 (-0.0999)
48.74% (G:11.19% B:0.49%)
51.26% (G:14.41% B:0.51%)
1Generated by Steven Carey on 07/05/2013 using eXtreme Gammon 2.10
46656 Games rolled with Variance Reduction.
Dice Seed: 63058600
Moves: 3-ply, cube decisions: 4-ply

2Generated by GameSite 2000, Ltd on 21/05/2011 using eXtreme Gammon 2.00
Analyzed in XG Roller++

This is a doubtful move.

If the player committed a doubtful move, the heading will show “?!”. Doubtful moves are moves that do not lose much equity but might change the course of the game.

Attached to each move is a computer analysis of the position shown.

Player Winning Chances #

The probability that the player will win (along with the magnitude of their win) is depicted by the player winning chances. This is the information shown on every second row, and shows how likely a player is to win the game, how likely it is for them to win by a gammon, and how likely it is for them to win by a backgammon. They are not supposed to add up to 100%.

Rollout Information #

Thanks to the work of various individuals, a majority of the opening roll plays have been rolled out. A modern rollout is a Monte Carlo simulation that uses a computer program to look at the outcomes that stem from a position multiple times. This usually rules out which position is better than another, especially for close plays.

Using a rollout provides additional information that we can consider. XG tells us the confidence interval of the equity (if you are familiar with statistics), but it also does additional processing to give us much more important information: the probability of being the best move.

In the computer analysis table, the probability of being the best move is enclosed in square brackets ([]). This probability is the aspect of the rollout that rules out which position is better than another. A probability of close to 100% would mean that the position is almost certain to be the best move in the position.

Footnote Information #

At the footnote section of the computer analysis table, you can find additional rollout information. Examples would be who generated the rollout and when using what (for opening book information), the number of samples used, the dice seed (XG uses a Mersenne Twister PRNG), and the play level (deeper/higher plies are more accurate) of checker play and cube play decisions when the outcomes are simulated.

Top Checker  21:  13/11* 11/10  ?

Computer Analysis
1. XG Roller++ 24/23 13/11* +0.0721
51.37% (G:13.40% B:0.48%)
48.63% (G:11.81% B:0.47%)
2. XG Roller++ 13/11* 11/10 +0.0386 (-0.0335)
50.63% (G:13.71% B:0.53%)
49.37% (G:12.60% B:0.57%)
3. XG Roller+ 13/11* 6/5 -0.0079 (-0.0800)
49.98% (G:13.56% B:0.58%)
50.02% (G:14.35% B:0.85%)
4. XG Roller+ 13/11* 8/7 -0.0515 (-0.1236)
48.77% (G:13.56% B:0.51%)
51.23% (G:14.02% B:0.84%)
5. 3-ply 24/22 6/5 -0.2555 (-0.3275)
44.34% (G:10.55% B:0.40%)
55.66% (G:15.02% B:0.66%)

This is an error.

If the player committed an error, the heading will show “?”. Errors are moves that lose equities beyond an error threshold (XG uses -0.0200 by default) but do not qualify as blunders.

As stated, this match will have various examples on the notation used on this site.

On this move we can see that the player used the two to hit the blot on the 11-point and moved the attacker forward right after.

Move 2

Bottom Checker  55:  Bar/15* 13/8(2)  ??

Computer Analysis Joker
1. XG Roller++ Bar/15* 15/10 13/8 +0.4690
59.50% (G:17.96% B:1.20%)
40.50% (G:9.21% B:0.31%)
2. XG Roller++ Bar/15* 13/8(2) +0.3253 (-0.1437)
56.51% (G:17.41% B:1.15%)
43.49% (G:10.94% B:0.40%)
3. XG Roller+ Bar/15* 8/3(2) +0.3148 (-0.1542)
55.69% (G:19.19% B:1.47%)
44.31% (G:11.17% B:0.45%)
4. 3-ply Bar/15* 15/5 +0.2422 (-0.2268)
55.23% (G:15.34% B:0.89%)
44.77% (G:10.82% B:0.39%)
5. 3-ply Bar/15* 13/3 +0.1641 (-0.3049)
53.53% (G:15.28% B:0.90%)
46.47% (G:12.00% B:0.57%)

This is a blunder.

If the player committed a blunder, the heading will show “??”. Blunders are moves that lose equities beyond a blunder threshold (XG uses -0.0800 by default).

On this move we can see that the player reentered into the bar while hitting. The player also moved two checkers down from the 13-point into the 8-point.

Another notable feature to this move is that the Computer Analysis dropdown has a yellow smiling emoji. This means that the player rolled a joker. A player’s joker is a roll that gives considerably more equity to them than every other possible roll; that is, if the players play ideally. Since we are looking at the game from the perspective of the bottom player, their jokers are considered our jokers.

Top Checker  Double  ?? /  Take

Computer Analysis
Rollout No Double Double/Take
Player Winning Chances 43.550% (G:11.709% B:0.744%) 44.327% (G:12.203% B:1.332%)
Opponent Winning Chances 56.450% (G:18.314% B:2.874%) 55.673% (G:21.761% B:4.764%)
Cubeless Equity -0.2828 -0.5256
Cubeful Equities
No Double -0.3261 ±0.0221 (-0.3482..-0.3040)
Double/Take -0.8910 (-0.5648) ±0.0303 (-0.9213..-0.8607)
Double/Pass +1.0000 (+1.3261)
Computer Recommendation: No Double/Take
Percentage of wrong pass needed to make the double decision right: 23.0%
Rollout Details
1296 Games rolled with Variance Reduction.
Moves: 2-ply, cube decisions: 3-ply Red

Double Decision Confidence: 100.0%
Take Decision Confidence: 100.0%
Duration: 5 minutes 20 seconds

Here we can see a double error. If their opponent responds ideally, the double error will give the player less equity than if they had not doubled at all.

In double action analysis, the cubeful equities along with the equity differences are also shown. There is also additional information of what XG recommends.

Rollout Information #

Using a rollout to analyze a double action will provide additional information like the confidence intervals and the number of samples. The analysis level of “ideal” play that the computer uses during the rollout will also be shown. The ever useful probability of the computer recommendation being the best move is also available as the Double and Take Decision Confidence.

Cubeless Equity #

Ever since the massive involvement of computers in backgammon, the equity that most people refer to as equity is cubeful equity. However, cubeless equity is still sometimes useful and close to the cubeful equity. It is shown in double action analysis for No Double and Double/Take along with the player and opponent winning chances. Of course for Double/Pass we know that the cubeful and cubeless equity is always +1 for the doubling player.

Top Checker  33:  Bar/22 13/10* 6/3(2)  ?!

Computer Analysis
1. XG Roller++ Bar/22 13/10* 8/5(2) -0.1071
51.30% (G:17.32% B:0.68%)
48.70% (G:14.20% B:0.97%)
2. XG Roller++ Bar/22 13/10* 6/3(2) -0.1077 (-0.0006)
51.54% (G:16.23% B:0.75%)
48.46% (G:13.84% B:0.87%)
3. XG Roller+ Bar/22 24/21 13/10*(2) -0.1604 (-0.0533)
50.21% (G:13.72% B:0.51%)
49.79% (G:13.20% B:0.61%)
4. XG Roller+ Bar/22 24/21(2) 13/10* -0.1771 (-0.0700)
49.85% (G:12.66% B:0.46%)
50.15% (G:12.00% B:0.39%)
5. XG Roller+ Bar/22 13/10*(2) 6/3 -0.2205 (-0.1133)
48.44% (G:13.47% B:0.56%)
51.56% (G:16.79% B:1.17%)

Here is an example of a doubtful move. Although the idea behind is the same (hitting and making a point in the home board), the succeeding rolls could be favoring one move over the other. However, doubtful moves are very close, and another possibility is that deeper analysis like a rollout would show that the doubtful move is in fact the best move.

Move 3

Bottom Checker  66:  Cannot Move

Computer Analysis
1. XG Roller+ Cannot Move -0.1162
41.98% (G:10.80% B:0.56%)
58.02% (G:21.63% B:0.99%)

If the player cannot make any valid moves (such as being unable to reenter from the bar), the analysis will still show the current equity of the player.

Top Checker  66:  13/1*(2)

Computer Analysis Anti-Joker
1. 4-ply 13/1*(2) +0.4457
64.46% (G:39.27% B:0.60%)
35.54% (G:8.90% B:0.56%)
2. 4-ply 22/4 10/4 +0.3586 (-0.0872)
65.51% (G:26.28% B:1.28%)
34.49% (G:7.57% B:0.32%)
3. 4-ply 24/18(2) 22/10 +0.2944 (-0.1513)
65.72% (G:18.09% B:0.64%)
34.28% (G:6.47% B:0.18%)
4. 4-ply 22/10 13/7(2) +0.2922 (-0.1535)
63.80% (G:24.02% B:1.43%)
36.20% (G:8.40% B:0.40%)
5. 4-ply 13/1* 8/2(2) +0.2781 (-0.1676)
60.16% (G:33.86% B:0.65%)
39.84% (G:11.36% B:0.80%)

If the Computer Analysis dropdown has a blue neutral face emoji, the player has rolled an anti-joker. A player’s anti-joker is a roll that gives considerably less equity to them than every other possible roll; that is, if the players play ideally. Since we are looking at the game from the perspective of the bottom player, their anti-jokers are considered our anti-jokers.

Bottom Checker  Redouble  ?? /  Pass  ??

Computer Analysis
XG Roller++ No Redouble Redouble/Take
Player Winning Chances 35.722% (G:9.175% B:0.574%) 35.765% (G:8.616% B:0.479%)
Opponent Winning Chances 64.278% (G:39.619% B:0.552%) 64.235% (G:38.778% B:0.564%)
Cubeless Equity -0.5882 -0.5677
Cubeful Equities
No Redouble -0.4488
Redouble/Take -0.5677 (-0.1189)
Redouble/Pass +1.0000 (+1.4488)
Computer Recommendation: No Redouble/Take
Percentage of wrong pass needed to make the double decision right: 7.0%

Here we can see a take error. The take error will give the player less equity than if they had chosen the other option.

Note that although this situation also has a double error, the equity loss is attributed to the wrong take (this can be thought of as a “bluff double”).

Bottom Checker Bottom Player wins a single game (2 points).
The table below is the Game Detailed Rating. It is similar to the Match Detailed Rating except this table shows the ratings for the current game.
Bottom Checker Bottom Player Category Top Checker Top Player
1 (1)
-0.1490 (-1.482%)
Move Errors
Equity Lost (Cost)
-0.0341 (-0.348%)
Double Errors
Equity Lost (Cost)
1 (1)
-0.5648 (-5.618%)
Take Errors
Equity Lost (Cost)
1 (1)
-1.5677 (-39.311%)
1 (1)
-0.1490 (-1.482%)
Total Error
Equity Lost (Cost)
3 (2)
-2.1666 (-45.278%)
-0.3960 (-16.356%)
+0.3960 (+16.356%)
Level of Play
Performance Rating

Conclusion #

After reading through this section, I hope you now know how to efficiently navigate through any match analysis found here on Glacier Gammon. You may proceed to the next game if you’d like, but it is actually just a demonstration of the appearance of a Crawford game and the effects of resignation errors.