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Nacbracs (explained in detail)
Posted By: Nack Ballard In Response To: What is the meaning of " and = in nacbracs (Taper_Mike)
Date: Friday, 16 December 2011, at 8:54 p.m.
I concur with Stick's and Mike's answers.
I'll elucidate more generally. A good example will be provided by one of Neil's rollouts, originally posted here but for convenience it is copied below.
is Player 2
score: 0
pip: 158Unlimited Game
JacobyBeaverpip: 167
score: 0
is Player 1XGID=-a----EaC---dE-a-c-e----B-:0:0:1:32:0:0:3:0:10 to play 32
1. Rollout1 24/22 13/10 eq: -0.2754
Player:
Opponent:43.40% (G:10.50% B:0.41%)
56.60% (G:15.38% B:0.70%)Conf.: ±0.0017 (-0.2771...-0.2736) - [56.0%]
Duration: 8 hours 04 minutes2. Rollout1 24/21 13/11 eq: -0.2756
Player:
Opponent:43.67% (G:10.88% B:0.45%)
56.33% (G:16.00% B:0.82%)Conf.: ±0.0018 (-0.2774...-0.2738) - [41.4%]
Duration: 8 hours 14 minutes3. Rollout1 24/21 6/4 eq: -0.2773 (-0.0020)
Player:
Opponent:43.93% (G:10.83% B:0.46%)
56.07% (G:16.99% B:0.92%)Conf.: ±0.0019 (-0.2792...-0.2754) - [2.5%]
Duration: 8 hours 51 minutes4. Rollout1 24/22 24/21 eq: -0.2789 (-0.0036)
Player:
Opponent:43.37% (G:9.77% B:0.39%)
56.63% (G:14.84% B:0.59%)Conf.: ±0.0017 (-0.2806...-0.2772) - [0.0%]
Duration: 7 hours 44 minutes5. Rollout2 13/10 6/4 eq: -0.2888 (-0.0134)
Player:
Opponent:43.54% (G:10.91% B:0.44%)
56.46% (G:16.51% B:1.10%)Conf.: ±0.0032 (-0.2920...-0.2856) - [0.0%]
Duration: 2 hours 43 minutes6. Rollout2 6/1* eq: -0.2920 (-0.0167)
Player:
Opponent:42.84% (G:11.57% B:0.38%)
57.16% (G:15.68% B:0.90%)Conf.: ±0.0032 (-0.2953...-0.2888) - [0.0%]
Duration: 2 hours 48 minutes1 101088 Games rolled with Variance Reduction.
Dice Seed: 29794098
Moves: 3-ply, cube decisions: XG Roller
2 32400 Games rolled with Variance Reduction.
Dice Seed: 29794098
Moves: 3-ply, cube decisions: XG RollereXtreme Gammon Version: 2.00.154.alpha
Six plays have been rolled out. In describing the position (instead of diagramming it) and eliminating and the less important details such as win/gammon/backgammon percentages, we might summarize the data into blue typeface as follows:The far-side player opened by rolling 63 and played 24/18 13/10.
The near-side player replied with a roll of 32. The equities of his top six plays are listed below, with relative equities (compared to the best play) shown in parentheses:24/22 13/10 . –.2754 (best) .....101088 trials
24/21 13/11 . –.2756 (–.0002) .101088 trials
24/21 6/4 ..... –.2773 (–.0020) .101088 trials
24/22 24/21 . –.2789 (–.0036) .101088 trials
13/10 6/4 ..... –.2888 (–.0134) ...32400 trials
6/1* ............ –.2920 (–.0167) ...32400 trialsExtreme Gammon version 2. Moves: 3-ply. Cube decisions: XG Roller.
If Neil had chosen to display his rollout with three decimal places instead of four, the summary would look like this:
The far-side player opened by rolling 63 and played 24/18 13/10.
The near-side player replied with a roll of 32. The equities of his top six plays are listed below, with relative equities (compared to the best play) shown in parentheses:24/22 13/10 . –.275 (best) ....101088 trials
24/21 13/11 . –.275 (–.000) .101088 trials
24/21 6/4 ..... –.277 (–.002) .101088 trials
24/22 24/21 . –.279 (–.004) .101088 trials
13/10 6/4 ..... –.289 (–.013) ...32400 trials
6/1* ............ –.292 (–.017) ...32400 trialsExtreme Gammon version 2. Moves: 3-ply. Cube decisions: XG Roller.
Nactation and "nacbracs" (Nactation brackets) provide ways to further condense the above summary:
- The position is referred to by a hyphenated move sequence. For example, "63S-32" means that the opening roll of 63 was played as "S" which means Split (24/18 13/10), and the reply roll under consideration is 32.
- Before the brackets, the match score is given; e.g., –2–5 means the player on roll needs 2 points, and the opponent needs 5 points. Other abbreviations: d = dmp, s = (gammon) save, g = (gammon) go. If no score is indicated, assume money/unlimited.
- Each candidate play is abbreviated with a single character (usually a letter).
- Absolute equities (–.275, etc.) are generally ignored and only the relative equities (–.000, –.002, etc.) are imparted.
- The minus sign is omitted from the relative equities, which are given in thousandths of a point; i.e., the decimal place is moved three places to the right. This representative margin (error size) is shown after each (single-character) play.
- The bot, followed in symbol form by the version, the number of ply for checker play, and what number of ply for cube decisions if different, are listed after the brackets.
- Finally, the number of trials (in thousands, rounded down) for each play are listed, where *(asterisk) repeats a number.
Using these abbreviative techniques, the earlier sea of blue becomes:
63S-32 [Z=S E2 U4 N13 H17] "<=101***32
Let's break down the three symbols immediately following the brackets (fundamentally, and then in more detail).
Pre-symbol:........ ".. refers to the second version of a bot (currently applies only to XG).
First symbol:...... <.. refers to XG (Extreme Gammon) 3-ply.
Second symbol:.. =.. refers to XG RollerThe pre-symbol: A single quotation mark (') refers to XG1. A double quotation mark (") refers to XG2. When you see no pre-symbol in old posts (before XG2 came out), it means XG1 was used. If you see no pre-symbol in more recent posts, it generally means XG1 was used, though it might be that XG2 was used and the writer forgot to include the pre-symbol (I've occasionally lapsed myself). It's a relatively unimportant element of the overall data, though. In a list or repetitive textual situation for which XG2 is mentioned as the bot used or it is otherwise understood, it is common to omit the " -- else it is cumbersome.
First symbol: The bot/ply symbols translate as follows: ~ is Snowie 3-ply, / is Gnu 2-ply, | is Gnu 3-ply, \ is Gnu 4-ply, < is XG 3-ply, ^ is XG 4-ply, > is XG 5-ply, = is XG roller, + is XG roller+, & (formerly ++) is XG roller++.
Second symbol: The same bot/ply translations apply. The first symbol applies to checker play and the second to cube decisions. If there is no second symbol, the one symbol applies to both checker ply and cube ply which are the same.
An "e" in the after-bracket vicinity (usually following a lone symbol) stands for "evaluation." An "a" stands for "aggregate" (typically an average or weighted average of all available rollout data from different bots).
Finally, let's address the number of trials. By way of example, 101***32 means that the first play was rolled out to 101000+ trials; i.e., some number between 101000 and 101999. [If for some reason you want to know the exact number, you need to consult the rollout display, but people almost always input a multiple of 1296, as Neil did is in this case: 101088.] Each asterisk following it indicates the number is repeated, so the top four plays were all rolled out to 101000+ trials. No asterisk is ever necessary after the final number; the "32" here indicates that ALL subsequent plays (the fifth and sixth in this case) were rolled out 32000+ trials.
For reference, I'll recap the nacbrac of Neil's rollout:
63S-32 [Z=S E2 U4 N13 H17] "<=101***32
Even when the equities in a rollout are shown to a fourth decimal place, it is most usual to represent margins in a nacbrac to the third decimal place. However, if one wants to show the fourth, one can add a decimal point to the margins like this (isolating just the part inside the brackets): [Z S0.2 E2 U3.8 N13.4 H16.7]. Or if one wants to represent only the closest plays to four places and the less close plays to three, a punctuation mark such as a comma can be inserted as a divider: [Z S0.2 E2 U3.8, N13 H17].
Nack
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