The Opening Roll

Discussion:

The Opening Roll

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Arthur

2005-04-16 17:37:08 UTC

Assuming you get the opening roll and play it to it's best advantage,
can there ever be a situation where you're the underdog, after having
gotten the opening roll? This doesn't take into account your opponent
rolling yet.

Arthur

grapelli

2005-04-16 19:16:51 UTC

Permalink

According to an earlier thread, an opening roll of 52 is the best
candidate.

http://www.bkgm.com/rgb/rgb.cgi?view+1154

But I don't think these settings are very robust. Maybe try rolling out
52 yourself, while waiting for an answer ;)

***@fibs

Gregg Cattanach

2005-04-18 13:36:48 UTC

Permalink

Post by grapelli
According to an earlier thread, an opening roll of 52 is the best
candidate.
http://www.bkgm.com/rgb/rgb.cgi?view+1154
But I don't think these settings are very robust. Maybe try rolling
out 52 yourself, while waiting for an answer ;)

My numbers show that you are a small underdog opening 41 (24/23 13/9). With
opening 52 (24/22 13/8) you are a small favorite. This based on +20,000
full rollouts.

--
Gregg C.

Tom Keith

2005-04-17 16:52:43 UTC

Permalink

According to rollouts I've done with GnuBG (cubeless, 0-ply play),
the worst opening roll is 2-1 with a cubeless equity of +0.0026.
That means any time you win the opening roll you have an
advantage, though sometimes a very small one.

In match play at double match point, rolling 4-1 gives a
slightly negative equity (.4986 chance of winning).

See rollouts below. A similar chart, with slightly different
rankings, appears here:
http://www.bkgm.com/openings.html#rolls_ranked

Tom

Roll 3-1: Rollout 8/5 6/5 Eq.: +0.1603
0.5526 0.1658 0.0074 - 0.4474 0.1129 0.0053 CL +0.1603
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 4-2: Rollout 8/4 6/4 Eq.: +0.1181
0.5371 0.1629 0.0076 - 0.4629 0.1210 0.0055 CL +0.1181
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 6-1: Rollout 13/7 8/7 Eq.: +0.1023
0.5352 0.1476 0.0063 - 0.4648 0.1172 0.0049 CL +0.1023
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 6-5: Rollout 24/13 Eq.: +0.0611
0.5318 0.1156 0.0056 - 0.4682 0.1199 0.0038 CL +0.0611
[0.0003 0.0003 0.0001 - 0.0003 0.0003 0.0001 CL 0.0009]
Roll 5-3: Rollout 8/3 6/3 Eq.: +0.0611
0.5168 0.1561 0.0079 - 0.4832 0.1306 0.0060 CL +0.0611
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 5-4: Rollout 24/20 13/8 Eq.: +0.0211
0.5072 0.1307 0.0061 - 0.4928 0.1254 0.0048 CL +0.0211
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 4-3: Rollout 13/10 13/9 Eq.: +0.0137
0.4996 0.1489 0.0065 - 0.5004 0.1336 0.0074 CL +0.0137
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0011]
Roll 6-4: Rollout 8/2 6/2 Eq.: +0.0119
0.4996 0.1509 0.0076 - 0.5004 0.1396 0.0062 CL +0.0119
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 6-2: Rollout 24/18 13/11 Eq.: +0.0108
0.5084 0.1235 0.0055 - 0.4916 0.1297 0.0053 CL +0.0108
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 5-1: Rollout 24/23 13/8 Eq.: +0.0100
0.5022 0.1310 0.0055 - 0.4978 0.1262 0.0047 CL +0.0100
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 6-3: Rollout 24/18 13/10 Eq.: +0.0094
0.5061 0.1267 0.0058 - 0.4939 0.1299 0.0054 CL +0.0094
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 5-2: Rollout 24/22 13/8 Eq.: +0.0075
0.5023 0.1292 0.0055 - 0.4977 0.1273 0.0045 CL +0.0075
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 4-1: Rollout 24/23 13/9 Eq.: +0.0044
0.4986 0.1382 0.0057 - 0.5014 0.1308 0.0059 CL +0.0044
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 3-2: Rollout 24/21 13/11 Eq.: +0.0038
0.5015 0.1292 0.0060 - 0.4985 0.1286 0.0057 CL +0.0038
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 2-1: Rollout 24/23 13/11 Eq.: +0.0026
0.4996 0.1318 0.0055 - 0.5004 0.1282 0.0057 CL +0.0026
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]

Post by Arthur
Assuming you get the opening roll and play it to it's best advantage,
can there ever be a situation where you're the underdog, after having
gotten the opening roll? This doesn't take into account your opponent
rolling yet.
Arthur

S.B.

2005-04-18 21:41:21 UTC

Permalink

I check that with my older version of Snowie 3.2.

I used 3ply, hugh search space and 100% speed.

The worst opening moves seems to be:

2-1 or 1-2, after 24/23 13/11 you have 49,8% MWC
4-1 or 1-4, after 24/23 13/9 you have 49,5% MWC

All other moves are over 50% MWC.

Best regards

S.B.

Carla

2005-04-19 11:10:17 UTC

Permalink

Very interesting thank you.

Which leads to the following questions:
1) In a post-Crawford game, and if the leader gets to play the opening
roll,
which opening rolls should lead to a free pass ?

2) In a post-Crawford game, and if the trailer gets to play the opening
roll,
which replies to opening rolls should lead to a free pass ?

Any link about this subject ?

Thank you very much,
Carla

Post by Tom Keith
According to rollouts I've done with GnuBG (cubeless, 0-ply play),
the worst opening roll is 2-1 with a cubeless equity of +0.0026.
That means any time you win the opening roll you have an
advantage, though sometimes a very small one.
In match play at double match point, rolling 4-1 gives a
slightly negative equity (.4986 chance of winning).
See rollouts below. A similar chart, with slightly different
http://www.bkgm.com/openings.html#rolls_ranked
Tom
Roll 3-1: Rollout 8/5 6/5 Eq.: +0.1603
0.5526 0.1658 0.0074 - 0.4474 0.1129 0.0053 CL +0.1603
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 4-2: Rollout 8/4 6/4 Eq.: +0.1181
0.5371 0.1629 0.0076 - 0.4629 0.1210 0.0055 CL +0.1181
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 6-1: Rollout 13/7 8/7 Eq.: +0.1023
0.5352 0.1476 0.0063 - 0.4648 0.1172 0.0049 CL +0.1023
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 6-5: Rollout 24/13 Eq.: +0.0611
0.5318 0.1156 0.0056 - 0.4682 0.1199 0.0038 CL +0.0611
[0.0003 0.0003 0.0001 - 0.0003 0.0003 0.0001 CL 0.0009]
Roll 5-3: Rollout 8/3 6/3 Eq.: +0.0611
0.5168 0.1561 0.0079 - 0.4832 0.1306 0.0060 CL +0.0611
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 5-4: Rollout 24/20 13/8 Eq.: +0.0211
0.5072 0.1307 0.0061 - 0.4928 0.1254 0.0048 CL +0.0211
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 4-3: Rollout 13/10 13/9 Eq.: +0.0137
0.4996 0.1489 0.0065 - 0.5004 0.1336 0.0074 CL +0.0137
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0011]
Roll 6-4: Rollout 8/2 6/2 Eq.: +0.0119
0.4996 0.1509 0.0076 - 0.5004 0.1396 0.0062 CL +0.0119
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 6-2: Rollout 24/18 13/11 Eq.: +0.0108
0.5084 0.1235 0.0055 - 0.4916 0.1297 0.0053 CL +0.0108
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 5-1: Rollout 24/23 13/8 Eq.: +0.0100
0.5022 0.1310 0.0055 - 0.4978 0.1262 0.0047 CL +0.0100
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 6-3: Rollout 24/18 13/10 Eq.: +0.0094
0.5061 0.1267 0.0058 - 0.4939 0.1299 0.0054 CL +0.0094
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 5-2: Rollout 24/22 13/8 Eq.: +0.0075
0.5023 0.1292 0.0055 - 0.4977 0.1273 0.0045 CL +0.0075
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 4-1: Rollout 24/23 13/9 Eq.: +0.0044
0.4986 0.1382 0.0057 - 0.5014 0.1308 0.0059 CL +0.0044
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 3-2: Rollout 24/21 13/11 Eq.: +0.0038
0.5015 0.1292 0.0060 - 0.4985 0.1286 0.0057 CL +0.0038
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]
Roll 2-1: Rollout 24/23 13/11 Eq.: +0.0026
0.4996 0.1318 0.0055 - 0.5004 0.1282 0.0057 CL +0.0026
[0.0004 0.0003 0.0001 - 0.0004 0.0003 0.0001 CL 0.0010]

Post by Arthur
Assuming you get the opening roll and play it to it's best

advantage,

Post by Tom Keith

Post by Arthur
can there ever be a situation where you're the underdog, after having
gotten the opening roll? This doesn't take into account your opponent
rolling yet.
Arthur

Hank Youngerman

2005-04-19 12:49:22 UTC

Permalink

Years ago I asked Kent Goulding the first question, and his answer was
that he always takes. Certainly if the trailer needs 4 or more you
should take, as the marginal possible gain from dropping is less than
the value of retaining the free drop. I believe that David Montgomery
wrote an article in Inside Backgammon some years ago on this subject
and concluded that you should pass only after 2-1. This was
pre-Snowie however.

The second question involves 15 possible openings and 21 replies, not
all played the same way, so a minimum of 315 cases. Your question,
alas, is oversimplified.

Post by Carla
Very interesting thank you.
1) In a post-Crawford game, and if the leader gets to play the opening
roll,
which opening rolls should lead to a free pass ?
2) In a post-Crawford game, and if the trailer gets to play the opening
roll,
which replies to opening rolls should lead to a free pass ?
Any link about this subject ?
Thank you very much,
Carla

Post by Arthur
Assuming you get the opening roll and play it to it's best

advantage,

Post by Tom Keith

Post by Arthur
can there ever be a situation where you're the underdog, after

having

Post by Tom Keith

Post by Arthur
gotten the opening roll? This doesn't take into account your

opponent

Post by Tom Keith

Post by Arthur
rolling yet.
Arthur

Carla

2005-04-19 14:40:12 UTC

Permalink

Thanks for your answer Hank.

I was hoping for a link to a site where these questions would have
been addressed, especially the second one.

What about using the equities listed in the following article :
http://www.bkgm.com/openings/replies.html#rollouts_of_replies
and pass when the equity of the (GS ?) best move is negative ?

Carla

Post by Hank Youngerman
Years ago I asked Kent Goulding the first question, and his answer was
that he always takes. Certainly if the trailer needs 4 or more you
should take, as the marginal possible gain from dropping is less than
the value of retaining the free drop. I believe that David Montgomery
wrote an article in Inside Backgammon some years ago on this subject
and concluded that you should pass only after 2-1. This was
pre-Snowie however.
The second question involves 15 possible openings and 21 replies, not
all played the same way, so a minimum of 315 cases. Your question,
alas, is oversimplified.

Post by Arthur
Assuming you get the opening roll and play it to it's best

advantage,

Post by Tom Keith

Post by Arthur
can there ever be a situation where you're the underdog, after

having

Post by Tom Keith

Post by Arthur
gotten the opening roll? This doesn't take into account your

opponent

Post by Tom Keith

Post by Arthur
rolling yet.
Arthur

Tom Keith

2005-04-19 20:12:25 UTC

Permalink

Post by Carla
I was hoping for a link to a site where these questions would have
been addressed, ...

Hi Carla,

You can find some answers previously posted to the newgroup here:
http://www.bkgm.com/rgb/rgb.cgi?menu+matchplay
[Scroll down to the last three articles.]

Post by Carla
especially the second one.
http://www.bkgm.com/openings/replies.html#rollouts_of_replies
and pass when the equity of the (GS ?) best move is negative ?

Yes, you can use the information in these charts. When Trailer
doubles at a score of -1/-2 PC, Leader will want to drop if his
probability of winning is less than 50%. Just find the appropriate
play and check the probability of winning. (Don't look at the
EQUITY values because they factor in gammons, which won't be
counting once the cube has been turned.)

Suppose Trailer opens 2-1: 24/23, 13/11.
[http://www.bkgm.com/openings/r21-yxnl-frame.html]

Then if Leader replies 6-2: 24/18, 13/11, and T doubles, L
should DROP because his probability of winning is only .480.

Or if Leader replies 5-5: 13/8(2), 6/1(2)*, and T doubles, L
should TAKE because his probability of winning is .521. (Notice
that L chooses the best DMP play, not the best money play.)

Or, if Leader replies 6-1: 13/7, 8/7, and T doubles, L has an
optional take because his probability of winning is exactly .500
[as far as the chart goes].

Tom

Carla

2005-04-21 16:09:48 UTC

Permalink

Many thanks to Tom and Gregg for your helpful answers.
I will be reading them thoroughly.

And Backgammon Galore site is such a great resource !!!
I should always check it before posting any question ;-)

Carla

Gregg Cattanach

2005-04-19 23:18:51 UTC

Permalink

Post by Carla
Very interesting thank you.
1) In a post-Crawford game, and if the leader gets to play the opening
roll,
which opening rolls should lead to a free pass ?
2) In a post-Crawford game, and if the trailer gets to play the
opening roll,
which replies to opening rolls should lead to a free pass ?

The second question is a lot harder as there are a lot more variations. My
rule of thumb is that I need to hit something, make a point or roll doubles
in order to take the cube. Otherwise I'll use the free pass.

I did a study a while ago of the first question. My results here:

Rollout Rollout Rollout
Play Snowie 2-ply GnuBG 0-ply GnuBG 2-ply
-------------- ----------- ----------- -----------
21 13/11 6/5 Take 50.5% Take 51.0%
21 24/23 13/11 Take 50.3% Pass 49.5% **
31 8/5 6/5 Take 55.4% NR
32 24/21 13/11 Take 50.1% Take 50.5%
32 13/8 Pass 48.2% Pass 48.8%
32 13/11 13/10 Pass 49.5% Pass 49.7%
41 24/23 13/9 Pass 49.6% Pass 49.7%
41 13/9 6/5 Pass 49.7% Pass 49.7%
42 8/4 6/4 Take 53.6% NR
43 24/21 13/9 Pass 49.9% Take 50.2% ** Take 50.2%
43 24/20 13/10 Pass 49.7% Pass 49.7%
43 13/10 13/9 Pass 49.6% Take 50.3% ** Pass 49.7%
51 24/23 13/8 Take 50.2% Take 50.0%
51 13/8 6/5 Pass 49.3% Pass 49.1%
52 24/22 13/8 Take 50.6% Pass 49.7% ** Pass 49.9%
52 13/11 13/8 Pass 49.3% Pass 49.9%
53 8/3 6/3 Take 51.6% NR
54 24/20 13/8 Take 50.6% Take 50.5%
54 13/9 13/8 Pass 49.6% Pass 49.8%
61 13/7 8/7 Take 53.4% NR
62 24/18 13/11 Take 50.8% Take 51.0%
62 24/16 Take 50.3% Take 51.0%
62 13/5 Pass 49.2% Pass 49.4%
63 24/18 13/10 Take 50.7% Take 51.2%
63 24/15 Take 50.6% Take 50.0%
64 24/18 13/8 Take 50.6% Take 50.4%
64 24/14 Pass 49.9% Take 50.4% ** Take 50.4%
64 8/2 6/2 Pass 49.8% Pass 49.2%
65 24/13 Take 52.5% NR

864 games, 1296 games full, 1296 games full,
2-ply, precise, 0-ply checkers, 2-ply checkers,
full 2-ply cube 2-ply cube

Recently, I had a couple matches analyzed where Snowie indicated that even
though I won the opening roll I was supposed to take the free drop (at
1-away, 2-away post-Crawford). I decided to roll all these out and see if
there really were some plays where this would be right.

I assumed that if I made a point on the first roll (other than 64) then I'm
a favorite and should take, these I didn't roll out. The rest I did with
Snowie. Then I did them all with Gnu 0-ply. On most of the plays that the
two bots disagreed I did another rollout with Gnu 2-ply.

The Gnu rollouts are probably a bit better as they are moving the checkers
as the DMP game that it really is.

Conclusions:

You should always split with your opening roll, including all 6x rolls.
Exception: slot with 21. 24/21 13/9 looks to be the best split with 43.

It looks like with 52 and 41 you should drop, the rest you should take.

Percentages are the single games won by the 1-away player that won the
opening roll. ** is where Snowie and Gnu disagreed.

--
Gregg C.

g***@yahoo.com

2005-04-21 13:29:26 UTC

Permalink

It might be statistically wrong, but I play an opening 43 as 24/20
13/10, as it allows me to later make my opponent's 5-point, which has
an immense psychological effect on my opponent.

Gregg Cattanach

2005-04-21 14:10:29 UTC

Permalink

Post by g***@yahoo.com
It might be statistically wrong, but I play an opening 43 as 24/20
13/10, as it allows me to later make my opponent's 5-point, which has
an immense psychological effect on my opponent.

It *may* allow you to make his 20 point if you don't get attacked there and
lose the battle. The reasons that 24/21 13/9 is slightly better is that if
you do get attacked, he's attacking on a less important point than if you'd
played 24/20. Also, the builder on the 9 point creates a lot more point
making numbers that the builder on the 10.

--
Gregg C.

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