Rollouts: Replies to opening moves

[Alexander Nitschke]

I’m 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 isn’t 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)