How to run with 66

Discussion:

How to run with 66

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Tim Chow

2017-11-03 23:28:08 UTC

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Paul

2017-11-04 08:00:11 UTC

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Post by Tim Chow
XGID=--BACBC--b--bB-----cBbcc--:0:0:1:66:0:0:0:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O X O O O |
| X | | O X O O O |
| | | O O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |
| O O | | X X X X |
| O O | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 113 O: 99 X-O: 0-0
Cube: 1
X to play 66

X has a significant pip lead.
(If we subtract 4 for being on-roll
as is standard, X has a lead of 6 points).
So the clearest path to win is to race home
by never leaving any shots. 20/8(2) is
quite likely to accomplish this.
O will break the midpoint soon, and
then X can win the race in 2 ways:
1) O may have to break contact.
2) 7 rolls work to get past O -- 65 +
all doubles that are not 44. So wait
for one of those good rolls.

Someone did say "Ahead in the race, race."
So I'm going with 20/8 (2).

However, I doubt that Tim would have thought
the position worth posting if such a
pedestrian and natural play were correct
so a QF case could be made for 20/14(2) 13/7(2)
which does work well under some sequences where
O is forced to leave a shot or to waste lots
of pips to avoid leaving shots.

However, sometimes Tim posts with the obvious
play being correct, and the solution is something like

"Here, I didn't play the obvious X. I played the
strange-seeming Y because I thought A and B and C and D would
all happen. If A and B and C and D happen, Y is correct so
that is why I played the bizarre Y. However, the rollout
confirms that the obvious and natural X, which everyone chose,
is indeed correct."

However, I consider it more likely that we have the more usual QF.

My answer is in two parts:
1) What is the correct play according to my own personal backgammon
understanding, and what would I play OTB?
The answer is 20/8(2).

2)Suppose that my overriding concern was to get this quiz solution
correct, and I allowed all forms of reasoning including Tim's posting
history etc. What do I actually believe is likely to be the correct
answer?
The answer is 13/7(2) 20/14(2).

In sum, I expect 13/7(2) 20/14(2) to be correct.
However, this is a backgammon quiz, not a question on
the life of Tim. Therefore I should only be
applauded if 20/8(2) is correct which is definitely
what I do play in these very normal situations.

Paul

Michael

2017-11-04 23:01:03 UTC

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20/8x2.After these 66s and an average roll by O the pip count will be 90 Vs 91 giving him around 60% GWC. He doesn't need the maximum possible contact.
Otoh O blots 4/36 with the other move compared with 2/36 with this move and if that happens it's a sure Double. But that's just only for one exchange over the many needed to end the game.
Can it possibly influence things that much? I doubt.

20/8x2 is my move

Paul

2017-11-04 23:31:28 UTC

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Post by Michael

Anyone who's not Stick or a friend-of-Stick would play
the only sane move of 20/8(2) but Quentin Francis has
moved into our community, and I think we should
accept him and agree that the solution is 13/7(2) 20/14(2).
The extra 5.5% blotting probability is highly significant.
Well spotted.

After the correct 20/14(2) 13/7(2) all of O's non-doubles
with aces or twos play inefficiently with inner-board shuffling.
That's also a very important advantage of the correct play.
It's true that the increased contact can later on cause inefficiencies
for X too, but it's a good principle to cater to the immediate
future. In the immediate future, X won't have efficiency problems with
the correct play. The correct play puts X in the good position of
two checkers holding four which is certainly value for money.

It's a good problem. I wonder how bad the standard 20/8(2) is?
It's a mistake for sure.

Paul

Paul

2017-11-04 23:35:58 UTC

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Post by Paul

Post by Michael

Anyone who's not Stick or a friend-of-Stick would play
the only sane move of 20/8(2) but Quentin Francis has
moved into our community, and I think we should
accept him and agree that the solution is 13/7(2) 20/14(2).
The extra 5.5% blotting probability is highly significant.
Well spotted.
After the correct 20/14(2) 13/7(2) all of O's non-doubles
with aces or twos play inefficiently with inner-board shuffling.
That's also a very important advantage of the correct play.
It's true that the increased contact can later on cause inefficiencies
for X too, but it's a good principle to cater to the immediate
future. In the immediate future, X won't have efficiency problems with
the correct play. The correct play puts X in the good position of
two checkers holding four which is certainly value for money.
It's a good problem. I wonder how bad the standard 20/8(2) is?
It's a mistake for sure.
Paul

Re the extra 2/36 blotting, it's actually a lot more than 2/36.
O often has to shuffle in the inner table and then the extra blotting
roll rears its ugly head (cliche alert) again and again.
"Ugly head" might be unfair -- the head might be thought to be either
beautiful or ugly, depending on whether X or O has your sympathies.

Michael

2017-11-05 08:33:52 UTC

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"Beautiful" analysis Paul.
O will be in urgent need to roll something that won't include an ace or a 2 ( 11 and 22 excluded). The forced to blot rolls get repeated ~50% of the times for each exchange.
Waiting for the rollouts to tell us the degree of error...

Paul

2017-11-05 09:37:40 UTC

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Post by Michael
"Beautiful" analysis Paul.
O will be in urgent need to roll something that won't include an ace or a 2 ( 11 and 22 excluded). The forced to blot rolls get repeated ~50% of the times for each exchange.
Waiting for the rollouts to tell us the degree of error...

Many thanks. I'm betting that the degree of error is somewhat slight --
less than 0.05 or so. The "surprise" will be that 20/14(2) 13/7(2) is correct, not that alternative plays are blunders.

My problem is that I can't do these problems using anything but QF.
We identified many sequences where the correct play works well.
But minimising contact with a significant racing lead also makes sense,
and there are equally a huge number of sequences where X would regret
not minimising contact.

Paul

BlueDice

2017-11-05 18:25:30 UTC

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20/8(2)
We are 10 pips ahead after this roll (an effective 6 pip lead)
I will go with the better racing play although the QF suggests something other than the 'obvious' play,
--
BD

Tim Chow

2017-11-05 20:09:56 UTC

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XGID=--BACBC--b--bB-----cBbcc--:0:0:1:66:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O X O O O |
| X | | O X O O O |
| | | O O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |
| O O | | X X X X |
| O O | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 113 O: 99 X-O: 0-0
Cube: 1
X to play 66

Generally speaking if one is ahead in the race then one should aim for less
contact, which means clearing the rear point with 20/8(2). However, if the
race is still fairly close, and your two rear points are close together,
then it is worth checking to see if there are any immediate sequences that
favor keeping more contact. Michael and Paul have mentioned some immediate
blotting rolls for O, and another thing to note is that an unblocked 55 for
O gains more for her than an unblocked 44 does.

The rollout does favor 20/14(2) 13/7(2) but, as Paul predicted, not by a huge
margin. In the variant, I have given O five extra pips in the race and the
rollout indicates a dead heat.

1. Rollout¹ 20/14(2) 13/7(2) eq:+0.413
Player: 63.02% (G:2.85% B:0.06%)
Opponent: 36.98% (G:0.66% B:0.02%)
Confidence: ±0.008 (+0.405..+0.421) - [100.0%]

2. Rollout¹ 20/8(2) eq:+0.380 (-0.033)
Player: 62.87% (G:1.26% B:0.02%)
Opponent: 37.13% (G:0.48% B:0.01%)
Confidence: ±0.008 (+0.372..+0.388) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.208.pre-release

-------
Variant
-------

XGID=--BACBC--b--bB-----dBcbb--:0:0:1:66:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O X O O O |
| X | | O X O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |
| O O | | X X X X |
| O O | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 113 O: 104 X-O: 0-0
Cube: 1
X to play 66

1. Rollout¹ 20/8(2) eq:+0.532
Player: 67.29% (G:0.95% B:0.03%)
Opponent: 32.71% (G:0.52% B:0.02%)
Confidence: ±0.009 (+0.523..+0.541) - [93.1%]

2. Rollout¹ 20/14(2) 13/7(2) eq:+0.523 (-0.009)
Player: 66.05% (G:3.08% B:0.10%)
Opponent: 33.95% (G:0.85% B:0.03%)
Confidence: ±0.008 (+0.515..+0.531) - [6.9%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.208.pre-release

---
Tim Chow