Opening Rolls

 Rollouts of opening 21 and replies

 From: Alexander Nitschke Address: alexander.nitschke@ww.tu-berlin.de Date: 17 October 1997 Subject: Rollouts: Replies to opening moves Forum: rec.games.backgammon Google: 344752A1.6B3EE47B@ww.tu-berlin.de

```Im rolling out all replies to the standard opening moves. The method is
as follows: I take an opening move, eg 21 played 13/11 24/23. Then I
take all replies from 11 to 66 and make rollouts for each move which is
evaluated by JF 3.0 level 7 within 0.05 equity of the best move (take or
give a move by my consideration). The rollouts are full cubeless 864
games level 6.

This is one of the hardest subjects for rollout studies because of some
reasons:

1) Opening rollouts lasts very long compared to other types of
positions.

2) A very high number of games is needed to get statistically
significant results.

3) Jellyfish evaluates these opening positions quite good, so why do
these rollouts?

As you can imagine, this takes a long time even on a fast computer. I
have a 233 MHz Pentium and a 133 MHz Pentium. One rollout lasts about
1.5 hours and 2.5 hours respectively. For about 1500 rollouts this
procedure needs only 10 weeks 24 hours a day :-). If someone out there
is willing to help me with these rollouts, tell me, and I am willing to
coordinate the work.

Now to the results for the replies to 21 if played 13/11 24/23:

The first two columns are the roll and the move (self explanatory). The
next three columns are the equity estimates of JF 3.0 level 6 and level
7 and the rollout result. An asterisk marks the best play in each column.
In the next six columns are the figures for wins, gammons and
backgammons for both players where player 1 is the player who won the
opening roll and player 2 is the replying player.
The column SD contains the standard deviation of the rollout equity.
Based on these SD and the rollout equities I have calculated the
probability that the rollout came out with the wrong best move (wrong
in a statistical sense of true infinite rollout result, not wrong in a
sense of perfect play on both sides).

Equities         Player 2       Player 1
roll      move         L6 EV  L7 EV  L6 RO  wins G&BG  BG  wins G&BG  BG   SD   error

11  24/22 6/5(2)       *.122  *.105  *.111  54.2 14.6  .7  45.8 12.2  .3  .010
11  24/23 6/5(3)        .109   .099   .106  53.8 14.7  .6  46.2 11.7  .6  .010  36.2%
11  24/23(2) 6/5(2)     .103   .090   .084  53.1 14.6  .6  46.9 12.4  .1  .010   2.8%
11  8/7(2) 6/5(2)       .079   .064   .039  51.2 13.9  .7  48.8 12.6  .6  .011    .0%
11  8/5 6/5             .068   .058   .070  52.5 14.9  .7  47.5 13.0  .6  .010    .2%

8/7(2) 6/5(2) is clearly inferior, surprisingly close is the ugly 24/23
6/5(3). Maybe it is generally better to split to 23 than to 22.

21  24/21              -.099 *-.098 *-.099  46.4 10.1  .5  53.6 12.8  .5  .009
21  13/11 24/23       *-.099  -.101  -.117  46.0 11.3  .5  54.0 14.8  .8  .010   9.0%
21  24/22 24/23        -.115  -.113  -.129  45.5 10.5  .3  54.5 14.3  .4  .010   1.3%
21  13/10              -.129  -.132  -.124  45.4 11.3  .5  54.6 14.4  .6  .010   3.2%

24/21 came out clearly best, a surprise for me and maybe for level 6 too
;-)

22  13/11(2) 6/4(2)    *.141  *.138  *.154  55.5 15.9  .8  44.5 11.8  .5  .011
22  24/22(2) 6/4(2)     .113   .117   .125  54.1 13.9  .7  45.9  9.9  .4  .010   2.6%
22  24/20(2)            .105   .104   .137  54.5 12.0  .5  45.5  7.6  .3  .009  11.6%
22  24/22 13/11 6/4(2)  .089   .087   .110  53.9 15.2  .5  46.1 12.1  .4  .010    .2%
22  13/9 6/4(2)         .090   .086   .062  52.1 14.7  .6  47.9 12.7  .7  .011    .0%

24/20(2) is more close to 13/11(2) 6/4(2) than I would have thought.

31  8/5 6/5            *.068  *.058  *.071  52.6 14.9  .7  47.4 13.0  .6  .010

32  24/21 13/11       *-.084 *-.080  -.100  46.9 11.3  .4  53.1 14.9  .7  .010  44.1%
32  13/10 24/22        -.091  -.095  -.100  46.6 11.8  .6  53.4 15.2  .4  .010  44.1%
32  24/21 24/22        -.099  -.098 *-.098  47.0 10.1  .5  53.0 13.8  .6  .009
32  13/8               -.116  -.112  -.146  44.8 11.3  .3  55.2 15.2  .6  .010    .0%
32  13/10 13/11        -.110  -.116 *-.098  46.5 12.3  .4  53.5 14.4 1.1  .010
32  24/21 6/4          -.147  -.144  -.148  45.5 10.0  .4  54.5 15.6  .7  .010    .0%

Here you have 4 equally good moves. Pick your choice!

33  24/21(2) 13/10(2)   .139  *.148  *.180  56.1 13.8  .5  43.9  8.2  .2
.009
33  24/21(2) 6/3(2)    *.140   .141   .155  55.0 13.6  .5  45.0  8.4  .3  .009   2.5%
33  13/10(2) 6/3(2)     .119   .124   .114  54.0 15.7  .7  46.0 12.2  .8  .010    .0%
33  8/5(2) 6/3(2)       .126   .117   .092  52.1 16.9  .7  47.9 12.1  .5  .010    .0%
33  24/18(2)            .098   .089   .108  54.6 12.1  .4  45.4 10.5  .3  .009    .0%

Level 6 makes the wrong move here. This affects level 6 rollout for the
opening move as I will discuss below.

41  6/2* 2/1*         *-.064 *-.069 *-.093  46.7 11.9  .5  53.3 14.3  .8  .009
41  13/9 24/23         -.089  -.092  -.109  46.1 12.0  .6  53.9 15.1  .6  .010  11.7%
41  13/8               -.116  -.112  -.144  44.9 11.3  .4  55.1 15.3  .6  .010    .0%
41  24/20 24/23        -.105  -.114  -.109  46.4 10.7  .4  53.6 14.4  .4  .010  11.7%

The double hit is best, but it is only close; it is worse than JF
estimates.

42  8/4 6/4            *.016  *.012  *.008  50.1 14.0  .7  49.9 13.5  .8  .010

43  13/9 24/21        *-.077 *-.077 *-.076  47.2 12.4  .5  52.8 14.3  .6  .010
43  24/20 13/10        -.079  -.091  -.083  47.3 12.1  .6  52.7 14.9  .7  .011  31.9%
43  24/20 24/21        -.104  -.094  -.088  47.1 10.4  .6  52.9 13.6  .5  .009  18.6%
43  13/9 13/10         -.097  -.095  -.112  45.6 13.1  .6  54.4 15.2  .9  .011    .8%
43  6/2* 24/21         -.101  -.105  -.081  47.0 11.7  .5  53.0 13.7  .7  .010  36.2%

6/2* 24/21 follows the rule Hit and Split. So ugly a hit on the 2 with
so many return hits is, this move yields the second place very close
behind the conventional 13/9 24/21.

44  24/20(2) 13/9(2)    .277  *.276  *.308  60.8 14.7  .5  39.2  5.9  .2  .009
44  24/20(2) 6/2*(2)   *.282   .275   .263  58.6 16.4  .6  41.4  7.6  .3  .010    .0%
44  8/4(2) 6/2*(2)      .254   .253   .265  57.1 22.7 1.4  42.9 11.3  .5  .011    .1%
44  13/9(2) 6/2*(2)     .240   .250   .219  56.7 18.7 1.2  43.3 11.0  .5  .010    .0%

Again a big error of JF level 6. Note: Trailing 2 away 1 away Crawford
you should very clearly play 8/4(2) 6/2*(2).

51  13/8 24/23        *-.067 *-.069 *-.071  47.6 12.0  .4  52.4 14.1  .7  .010
51  24/18              -.098  -.111  -.103  47.2 10.7  .5  52.8 15.4  .7  .011   1.6%
51  6/1* 24/23         -.101  -.115  -.127  45.5 11.2  .3  54.5 14.5  .7  .010    .0%

52  13/8 24/22        *-.065 *-.075 *-.089  47.5 10.7  .4  52.5 14.4  .6  .010
52  6/1* 24/22         -.088  -.093  -.125  45.5 10.9  .4  54.5 14.1  .6  .010    .5%
52  13/8 13/11         -.097  -.097  -.100  46.4 12.1  .6  53.6 14.9  .8  .010  21.8%
52  6/1* 13/11         -.112  -.118  -.121  46.0 12.1  .5  54.0 16.2  .7  .011   1.6%
52  13/6               -.125  -.127  -.147  44.7 11.7  .5  55.3 15.7  .7  .010    .0%

It isnt that good to hit on the ace point as I thought.

53  8/3 6/3           *-.031 *-.033 *-.034  48.6 13.7  .8  51.4 14.3  .6  .010
53  13/8 24/21         -.050  -.044  -.053  47.9 11.7  .6  52.1 13.0  .5  .009   7.9%

54  13/8 24/20        *-.050 *-.067 *-.075  47.5 11.8  .5  52.5 14.2  .6  .010
54  13/8 13/9          -.089  -.086  -.127  45.3 11.8  .6  54.7 15.0  .7  .010    .0%
54  24/15              -.068  -.089  -.085  47.9 10.7  .4  52.1 15.0  .4  .010  24.0%
54  13/8 6/2*          -.098  -.101  -.110  46.2 11.4  .6  53.8 14.7  .7  .009    .5%
54  6/1* 24/20         -.088  -.107  -.102  46.4 11.5  .3  53.6 14.4  .4  .010   2.8%
54  6/1* 13/9          -.101  -.109  -.136  45.2 12.2  .7  54.8 15.7 1.1  .010    .0%

In this situation you must get your back checkers going. 13/8 13/9 is
clearly inferior.

55  8/3(2) 6/1*(2)     *.164  *.133  *.098  51.5 19.6  .6  48.5 12.8  .6  .011
55  13/8(2) 6/1*(2)     .121   .112   .087  52.2 17.2  .6  47.8 12.8  .5  .010  23.0%
55  13/3(2)             .066   .078   .067  51.6 16.2  .7  48.4 12.9  .5  .010   1.9%

This is a really big surprise: The most ugly 13/8(2) 6/1*(2) is darn
close to the more natural 8/3(2) 6/1*(2). In double match point this is
even the best move!

61  13/7 8/7          *-.005 *-.010 *-.010  50.2 12.8  .5  49.8 14.1  .7  .010

62  24/18 13/11       *-.076 *-.083 *-.075  48.0 11.3  .5  52.0 14.8  .6  .010
62  24/16              -.087  -.098  -.113  46.9 10.5  .6  53.1 15.7  .6  .010    .4%
62  8/2* 24/22         -.120  -.122  -.158  44.2 11.0  .5  55.8 15.0  .8  .010    .0%
62  24/18 24/22        -.115  -.131  -.121  46.7 11.2  .6  53.3 16.7  .5  .010    .1%

I expected a close result, but 24/18 13/11 is the clear winner.

63  24/18 13/10        -.071 *-.086  -.090  47.5 11.2  .4  52.5 14.8  .8  .010  36.2%
63  24/15             *-.068  -.089 *-.085  47.9 10.7  .4  52.1 15.0  .4  .010
63  24/18 24/21        -.112  -.107  -.088  47.5 11.1  .3  52.5 14.8  .5  .010  41.6%

Here the results are really close, you can choose either move.

64  24/14*             *.140  *.136  *.129  55.1 13.7  .7  44.9 11.2  .5  .011

65  24/13             *-.002 *-.018 *-.058  49.3  9.6  .3  50.7 14.0  .3  .009

66  24/18(2) 13/7(2)   *.363  *.352  *.374  63.9 16.3  .6  36.1  7.1  .2
.009

As a side effect of these opening reply rollouts I am able to calculate
equities for the opening moves with 18144 games played on level 6, and
so with an incredible low standard deviation. The calculated equity is
even more precise than a normal level 6 rollout, because I take the best
replies to the openings based on above rollouts rather than the replies
of level 6 in a normal level 6 rollout.

Rollout result for  21 (13/11 24/23) with best replies:       .002
Rollout result for  21 (13/11 24/23) with replies of level 6: .005

Using the best replies gains an equity of .003 compared to level 6 play.
The equity of .002 now may be underestimating for the opener because
only the replies are corrected but not the replies to the replies and so
on.

-- Alexander (acey_deucey@FIBS)
```

### Opening Rolls

At different match scores  (Louis Nardy Pillards, July 2002)
Average advantage of winning opening roll  (Chuck Bower, Oct 1998)
Choosing a strategy  (Daniel Murphy, June 2001)
Early game rule of thumb  (Rich Munitz, Feb 2009)
Factors to consider  (Kit Woolsey, July 1994)
How computers play  (Kit Woolsey, Mar 1995)
Magriel's Chapter 5  (Hayden Alfano+, May 2006)
Mloner vs Jellyfish  (Kit Woolsey, Dec 1995)
Nactating a whole game  (Nack Ballard+, Jan 2011)
Nactation  (Jim Stutz+, June 2010)
Nactation overview  (Nack Ballard, Oct 2009)
Nactation--Why use it?  (leobueno+, Jan 2011)
Opening 1's: Split or slot?  (Douglas Zare, Dec 2003)
Opening 21: Rollout  (Stick, Mar 2006)
Opening 21: Split or slot?  (Dick Adams+, Dec 2003)
Opening 32: Rollout  (Stick, Feb 2006)
Opening 43: In GOL online match  (Raccoon+, Feb 2004)
Opening 43: Pros and cons  (Stick+, Jan 2006)
Opening 43: Which split is better?  (Peter Backgren+, Aug 2000)
Opening 43: Which split is better?  (Michael J. Zehr+, Mar 1996)
Opening 51: Rollout  (Stick, Feb 2006)
Opening 52: Merits of splitting  (Peter Bell, Apr 1995)
Opening 53: Magriel's recommendation  (George Parker+, July 1997)
Opening 53: Split to 21?  (Alex Zamanian, Aug 2000)
Opening 53: Why make the three point?  (Kit Woolsey+, Feb 1996)
Opening 6's: Slot the bar point?  (Chuck Bower+, Feb 2000)
Opening 6's: Slot the bar point?  (David Montgomery, June 1995)
Opening 62: Could running be best?  (Gary Wong, Sept 1997)
Opening 62: Split, run, or slot?  (Chuck Bower, May 1997)
Opening 63: Middle Eastern split?  (Mark+, Apr 2002)
Opening 63: Slot the four point?  (Dennis Cartwright+, Mar 2002)
Opening 64: Make the two point?  (William Hill+, Jan 1998)
Opening 64: Make the two point?  (Darse Billings, Feb 1995)
Opening 64: Rollout  (Peter Grotrian, Jan 2006)
Opening 64: Split to 20?  (Peter Bell, June 1995)
Opening 64: Three choices  (Brian Sheppard, July 1997)
Opening 65: Becker on lover's leap  (Jeffrey Spiegler+, Aug 1991)
Opening 65: Computer rankings  (Chuck Bower, Jan 1997)
Opening rolls ranked  (Arthur+, Apr 2005)
Rollouts of opening 21 and replies  (Alexander Nitschke, Oct 1997)
Rollouts of openings  (Tom Keith+, Jan 2006)
Rollouts: Expert Backgammon  (Tom Fahland, Aug 1994)
Rollouts: Jellyfish 3.0  (Midas+, Sept 1997)
Rollouts: Jellyfish 3.0 level 6  (Chuck Bower, Feb 1999)
Rollouts: Snowie 4.1  (Rene Cerutti, Apr 2004)
Slotting the four point  (Joe Loria+, Oct 1999)
Snowie's openers and replies  (rcerutti, Feb 1999)
Splitting versus building  (Dave Slayton+, Aug 2000)
Splitting versus slotting  (Daniel Murphy, Apr 2001)
Splitting versus slotting  (Daniel Murphy, Sept 1997)
Trice's rankings  (Marty Storer, Feb 1992)

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