Discussion:
Bearing in, no contact
(too old to reply)
Tim Chow
2018-02-10 19:44:14 UTC
Permalink
XGID=-BCCBB--A---A----A-dbbc-b-:1:1:1:55:0:0:0:0:10

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 O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X | +---+
| | | X X X X X | | 2 |
| X X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 72 O: 53 X-O: 0-0
Cube: 2, X own cube
X to play 55

---
Tim Chow
Paul
2018-02-10 20:39:43 UTC
Permalink
Post by Tim Chow
XGID=-BCCBB--A---A----A-dbbc-b-:1:1:1:55:0:0:0:0:10
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 O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X | +---+
| | | X X X X X | | 2 |
| X X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 72 O: 53 X-O: 0-0
Cube: 2, X own cube
X to play 55
On the train once, I actually saw a guy pouring
beer from a can onto the floor (true story).

That's exactly the type of person who would
use one of the fives to play 7/2 -- it's wasteful!
It's true that there is some wastage in playing 12/7(2)
but it is less wasteful than the alternatives.

17/7 12/7 8/3.

Paul
BlueDice
2018-02-10 22:40:08 UTC
Permalink
Post by Tim Chow
XGID=-BCCBB--A---A----A-dbbc-b-:1:1:1:55:0:0:0:0:10
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 O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X | +---+
| | | X X X X X | | 2 |
| X X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 72 O: 53 X-O: 0-0
Cube: 2, X own cube
X to play 55
---
Tim Chow
17/2 8/3 maximising crossovers
We have to roll well to win and if we roll a six next time we now get one checker off (66, 3 off) leaving an even ammount of checkers remaining, improving our chances of winning the race.
--
BD
Michael
2018-02-12 11:22:41 UTC
Permalink
Post by Tim Chow
XGID=-BCCBB--A---A----A-dbbc-b-:1:1:1:55:0:0:0:0:10
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 O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X | +---+
| | | X X X X X | | 2 |
| X X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 72 O: 53 X-O: 0-0
Cube: 2, X own cube
X to play 55
---
Tim Chow
I anti-Walted. My initial thought was in favor of Paul's move.
After reading BD's post I changed my mind. :-)
Yep that's it -to minimize cross overs.
Paul
2018-02-12 20:37:11 UTC
Permalink
Post by Michael
Post by Tim Chow
XGID=-BCCBB--A---A----A-dbbc-b-:1:1:1:55:0:0:0:0:10
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 O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X | +---+
| | | X X X X X | | 2 |
| X X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 72 O: 53 X-O: 0-0
Cube: 2, X own cube
X to play 55
---
Tim Chow
I anti-Walted. My initial thought was in favor of Paul's move.
After reading BD's post I changed my mind. :-)
Yep that's it -to minimize cross overs.
You should probably have stuck with your first instinct of following me.
BD's play works great if the next roll is a 6 but obviously that probably
won't happen and my play works better if the next roll doesn't contain a 6.

Efficiency is a far more important general consideration than crossovers,
so we should avoid such deep burial.
In some positions which are either desperate or gammon avoiders, the
crossover count is paramount. But this position is a close race.
We don't need to roll particularly well to win. We're only slightly behind.

Paul
Michael
2018-02-13 02:31:40 UTC
Permalink
Post by Paul
Post by Michael
Post by Tim Chow
XGID=-BCCBB--A---A----A-dbbc-b-:1:1:1:55:0:0:0:0:10
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 O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X | +---+
| | | X X X X X | | 2 |
| X X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 72 O: 53 X-O: 0-0
Cube: 2, X own cube
X to play 55
---
Tim Chow
I anti-Walted. My initial thought was in favor of Paul's move.
After reading BD's post I changed my mind. :-)
Yep that's it -to minimize cross overs.
You should probably have stuck with your first instinct of following me.
BD's play works great if the next roll is a 6 but obviously that probably
won't happen and my play works better if the next roll doesn't contain a 6.
Efficiency is a far more important general consideration than crossovers,
so we should avoid such deep burial.
In some positions which are either desperate or gammon avoiders, the
crossover count is paramount. But this position is a close race.
We don't need to roll particularly well to win. We're only slightly behind.
Paul
For the sake of discussion how many rolls do you think our efficiency's worth?
You can find out by using
Axel Reichert's method in doing an approximate EPC count (**)
http://www.bkgm.com/articles/Reichert/insights-with-isight.pdf
(page 28)
or just use my Races program setting O as Player A.
Notice EPC/8.2= number of rolls

(**) @ Tim: It usually does well in estimating EPCs and the relative difference between the two. By his other part in estimating GWC% often deviates a lot.
Michael
2018-02-13 02:32:55 UTC
Permalink
By his other part-->but his other part
Tim Chow
2018-02-13 00:15:49 UTC
Permalink
XGID=-BCCBB--A---A----A-dbbc-b-:1:1:1:55:0:0:0:0:10

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 O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X | +---+
| | | X X X X X | | 2 |
| X X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 72 O: 53 X-O: 0-0
Cube: 2, X own cube
X to play 55

BlueDice's analysis is exactly right. This lucky roll improves our racing
chances a lot but we're still an underdog. By playing 17/2 8/3 we give
ourselves the chance of saving a roll by rolling a 6 next turn.

I don't know of an easy way to compute the EPC for this position but I
believe that 17/2 8/3 actually wastes fewer pips than either alternative.
This might seem surprising because we're accustomed to thinking that it's
only by burying a checker deep in one's board that we waste pips. But
checkers on our 7pt or 8pt are also wasteful. One way to think about it
is that such checkers are likely to be buried deeply later.

1. Rollout¹ 17/2 8/3 eq:-0.464
Player: 23.43% (G:0.00% B:0.00%)
Opponent: 76.57% (G:0.00% B:0.00%)
Confidence: ±0.002 (-0.466..-0.461) - [100.0%]

2. Rollout¹ 17/2 12/7 eq:-0.514 (-0.051)
Player: 21.39% (G:0.00% B:0.00%)
Opponent: 78.61% (G:0.00% B:0.00%)
Confidence: ±0.002 (-0.516..-0.513) - [0.0%]

3. Rollout¹ 17/7 12/7 8/3 eq:-0.516 (-0.053)
Player: 21.36% (G:0.00% B:0.00%)
Opponent: 78.64% (G:0.00% B:0.00%)
Confidence: ±0.002 (-0.518..-0.514) - [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

---
Tim Chow
Paul
2018-02-14 21:42:46 UTC
Permalink
Post by Tim Chow
XGID=-BCCBB--A---A----A-dbbc-b-:1:1:1:55:0:0:0:0:10
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 O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X | +---+
| | | X X X X X | | 2 |
| X X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 72 O: 53 X-O: 0-0
Cube: 2, X own cube
X to play 55
BlueDice's analysis is exactly right. This lucky roll improves our racing
chances a lot but we're still an underdog. By playing 17/2 8/3 we give
ourselves the chance of saving a roll by rolling a 6 next turn.
Yes, the play is right, yes this is BlueDice's analysis. But, given what you
say later, I think the analysis is exactly _wrong_ even though the play is
right. Standard bearoff play is to minimize EPC. However, in some
major-underdog situations, EPC is sacrificed in order to cater to high numbers.
The fact that we're still an underdog is correct, but completely irrelevant,
because the optimal play is just the EPC play, as is normal.
You seem to be wrongly putting the position into the category of "Maximise
opportunity for luck" where the problem has got nothing to do with that
but is just a standard EPC computation.

Paul
Tim Chow
2018-02-15 02:53:03 UTC
Permalink
Post by Paul
The fact that we're still an underdog is correct, but completely irrelevant
Yes, I think you're right about that.

---
Tim Chow
Michael
2018-02-15 09:40:45 UTC
Permalink
Post by Paul
However, in some
major-underdog situations, EPC is sacrificed in order to cater to high numbers.
Paul
I think this can only happen in the last few rolls?
Paul
2018-02-15 21:08:36 UTC
Permalink
Post by Michael
Post by Paul
However, in some
major-underdog situations, EPC is sacrificed in order to cater to high numbers.
Paul
I think this can only happen in the last few rolls?
Yes, but you're actually agreeing with me.
The Tim/BD analysis had the flavour of "X is
behind, so has to make the high rolls play well."

But, although that leads to the correct play,
it's the wrong way of thinking about it.
The idea (as in standard bearoff problems) is to
play as efficiently as possible.

The reason the winning play is the winning play isn't
so much "It lets sixes play well" but is simply more
efficient over all.

So my idea of avoiding waste was the right idea,
even though the execution was wrong.

Paul
Tim Chow
2018-02-16 00:32:01 UTC
Permalink
Post by Paul
The reason the winning play is the winning play isn't
so much "It lets sixes play well" but is simply more
efficient over all.
I thought about this a little more. You're correct that sometimes, if one is
way behind, one has to cater to one's high numbers at the expense of EPC, but
that that's not the case here. So you're right that X being an underdog is
not really relevant.

However, "it lets sixes play well" is a different matter. Making sure that
your numbers play well is a general principle (diversification) that can help
you figure out what play minimizes EPC.

---
Tim Chow

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