Game 1, move 10 : Herd 4-1

[diane]

how brave are we feeling? 

[stog]

Spoiler

we need to vote for cube methinks if Linus doesn't whack us (and last time probably too)

[close]

[Julia_H]

Spoiler

Yes, I thought we were going to have a cube vote?

Well, given the dice are on the table now, I'm going to vote for the pick and pass. We're still well down in the race, we need to make up ground. 8/7 18/14 is the best of the non-hits, but probably gives us a little more than a single winning shot before the game boils down to a race, and still exposes a few jokers - White is just as likely to roll that nine as he is to hit us from the bar after 6/5*/1.

And then we think about the cube on any reply except being hit.

[close]

[NIHILIST]

Spoiler

Pretty craven IMHO. If you can't make the play that makes you a 2-1 favorite at 0-0 to 5, take up jacks or hopscotch as your new game. Even if you pick and pass he beats us outright with 5-5. After 6-5*-1, if he fans do we then have a cube ? Does he still have a take ?

My play is 18-14, 6-5*.

Course I've always preferred money play over tourney play, and in money play, with the Jacoby Rule, the loose hit is mandatory here

[close]

Bob

[ah_clem]

Spoiler

Pick-and-pass.  25/36 times he'll remain on the bar while we make up for our deficit in the pipcount.  If he dances twice, we're really in good shape, although I think it's a cash if he dances just once.

Yes, we risk 4 fly shots from the bar, but I think it's worth it.  Otherwise he just runs and we're not nearly close to 25/36 to win.

[close]

[ah_clem]

About the cube:

Spoiler

I'm fairly sure we did not have a cube before this roll and that any vote would not have resulted in a double.  Had he danced it would have been a different story.

But assuming the pick-and-pass prevails here, we should pause for a cube vote unless Linus hits one of the fly shots.

[close]

[ah_clem]

Spoiler

Pretty craven IMHO. If you can't make the play that makes you a 2-1 favorite at 0-0 to 5, take up jacks or hopscotch as your new game. Even if you pick and pass he beats us outright with 5-5. After 6-5*-1, if he fans do we then have a cube ? Does he still have a take ?

Bob

My opinion is that we have a cash after a fan.  The race should be about even, then he's only 30% to enter and then ~50% to win the roughly even race.  That seems to give him about 15% winning chances after a dance. 

If this analysis is correct, then the pick-and-pass makes us a 2-1 favorite and leaving a loose shot accomplishes nothing other than draining our equity.

Of course, I could be wrong about the cash after a dance, and a slotted 5 might be the difference between a cash and a take.  But I'll be quite happy if he takes after pick-and-pass/dance.

[close]

[KDP]

Spoiler

i hit and split 18-14 6-5* if he fans, double pass

[close]

[NIHILIST]

Now, if only dorbel would weigh in.

Bob

[diane]

About the cube:

Spoiler

I'm fairly sure we did not have a cube before this roll and that any vote would not have resulted in a double.  Had he danced it would have been a different story.

But assuming the pick-and-pass prevails here, we should pause for a cube vote unless Linus hits one of the fly shots.

[close]

That was pretty much how I felt about it..particularly after the last vote. I hadn't seen any request from anyone to have a vote for a cube, and we are so close to the last position really, I didn't think it worth stopping. I am poised though - and probably would have forced another vote on you next roll, even if you hadnt all asked this time 

[ah_clem]

ROLLOUT

Spoiler

Pick-and-pass is correct, but there are a few slotting plays that are not too far behind.  18/14, 6/5* is a .056 error, and the worst of the four possible reasonable hitting plays.

Cube action after this play looms large in affecting the correct checker play, and it's worth looking at the cube action after each play followed by a fan.  I had thought that we had a clear cash after pick-and-pass/dance, but this is not the case.  It's more like a narrow cube and clear take.  That said, it's a very efficient cube with ~73% GWC, and when you can get a take at that win rate it's almost as good as a cash. (within about 2% MWC)

After the herd's second choice (18/14 6/5*) it is a cash.  But all 11 entering rolls are a disaster for us if we slot the 5 where only 4 are with the pick-and-pass; the other 7 leave us roughly even.  Why give up those 7 extra shots for a small  gain?

I don't have a good explanation why 7/3 6/5* does so well.  it seems weird to play boldly and slot the 5 while simultaneously removing a builder - the best i can come up with is that a double-hit makes Linus TG while a simple hit on the 5 is a cash.  Not sure about that though.



XGID=-BBBBaCAA---------Bdbbcc--:0:0:1:41:0:0:0:5:10

X:Player 1   O:Player 2
Score is X:0 O:0 5 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
|                X |   | O  O  O  O  O    |
|                X |   | O  O  O  O  O    |
|                  |   | O        O  O    |
|                  |   | O                |
|                  |   |                  |
|                  |BAR|                  |
|                  |   |                  |
|                  |   |                  |
|                  |   | X                |
|                  |   | X     X  X  X  X |
|             X  X |   | X  O  X  X  X  X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 89  O: 77 X-O: 0-0/5
Cube: 1
X to play 41

    1. Rollout¹    6/5* 5/1                     eq:+0.307
      Player:   59.07% (G:0.84% B:0.01%)
      Opponent: 40.93% (G:6.53% B:0.10%)
      Confidence: ±0.005 (+0.302..+0.311) - [93.5%]
      Duration: 2 minutes 01 second

    2. Rollout¹    7/3 6/5*                     eq:+0.301 (-0.006)
      Player:   57.99% (G:1.09% B:0.02%)
      Opponent: 42.01% (G:16.66% B:0.19%)
      Confidence: ±0.006 (+0.295..+0.307) - [6.5%]
      Duration: 2 minutes 06 seconds

    3. Rollout¹    8/4 6/5*                     eq:+0.281 (-0.026)
      Player:   57.30% (G:1.06% B:0.01%)
      Opponent: 42.70% (G:15.39% B:0.16%)
      Confidence: ±0.005 (+0.275..+0.286) - [0.0%]
      Duration: 2 minutes 00 second

    4. Rollout¹    18/14 6/5*                   eq:+0.251 (-0.056)
      Player:   63.62% (G:1.80% B:0.02%)
      Opponent: 36.38% (G:20.28% B:1.54%)
      Confidence: ±0.003 (+0.247..+0.254) - [0.0%]
      Duration: 1 minute 02 seconds


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


eXtreme Gammon Version: 2.10, MET: Kazaross XG2



/////// cube action after a fan ///////////////////////
XGID=aCBBB-BAA---------Bdbbcc--:0:0:1:00:0:0:0:5:10

X:Player 1   O:Player 2
Score is X:0 O:0 5 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
|                X |   | O  O  O  O  O    |
|                X |   | O  O  O  O  O    |
|                  |   | O        O  O    |
|                  |   | O                |
|                  |   |                  |
|                  |BAR|                  |
|                  | O |                  |
|                  |   |                  |
|                  |   |                X |
|                  |   | X     X  X  X  X |
|             X  X |   | X     X  X  X  X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 84  O: 82 X-O: 0-0/5
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
  Player Winning Chances:   72.76% (G:0.99% B:0.02%)
  Opponent Winning Chances: 27.24% (G:2.38% B:0.08%)
Double/Take
  Player Winning Chances:   73.41% (G:0.87% B:0.02%)
  Opponent Winning Chances: 26.59% (G:2.41% B:0.08%)

Cubeless Equities: No Double=+0.442, Double=+0.856

Cubeful Equities:
       No double:     +0.710 (-0.003) (55.49%)
       Double/Take:   +0.714   (55.52%)
       Double/Pass:   +1.000 (+0.286)  (57.73%)
   

Best Cube action: Double / Take

Rollout:
  1296 Games rolled with Variance Reduction.
  Moves: 3-ply, cube decisions: XG Roller
  Confidence No Double: ± 0.005 (+0.706..+0.715)
  Confidence Double:    ± 0.007 (+0.707..+0.721)

  Double Decision confidence: 79.5%
  Take Decision confidence: 100.0%

  Duration: 2 minutes 22 seconds

eXtreme Gammon Version: 2.10, MET: Kazaross XG2



///////////// cube action after a fan 2 ////////////////////////


XGID=aBBBBABAA-----A---Adbbcc--:0:0:1:00:0:0:0:5:10

X:Player 1   O:Player 2
Score is X:0 O:0 5 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
|    X           X |   | O  O  O  O  O    |
|                  |   | O  O  O  O  O    |
|                  |   | O        O  O    |
|                  |   | O                |
|                  |   |                  |
|                  |BAR|                  |
|                  | O |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   | X     X  X  X  X |
|             X  X |   | X  X  X  X  X  X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 84  O: 82 X-O: 0-0/5
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
  Player Winning Chances:   86.66% (G:2.42% B:0.03%)
  Opponent Winning Chances: 13.34% (G:1.40% B:0.03%)
Double/Take
  Player Winning Chances:   87.55% (G:1.98% B:0.03%)
  Opponent Winning Chances: 12.45% (G:1.64% B:0.08%)

Cubeless Equities: No Double=+0.743, Double=+1.445

Cubeful Equities:
       No double:     +0.853 (-0.147) (56.60%)
       Double/Take:   +1.389 (+0.389)  (60.74%)
       Double/Pass:   +1.000 (57.73%)

Best Cube action: Double / Pass

Rollout:
  1296 Games rolled with Variance Reduction.
  Moves: 3-ply, cube decisions: XG Roller
  Confidence No Double: ± 0.002 (+0.851..+0.856)
  Confidence Double:    ± 0.005 (+1.384..+1.394)

  Double Decision confidence: 100.0%
  Take Decision confidence: 100.0%

  Duration: 1 minute 29 seconds

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

[close]

[ah_clem]

more rollout

Spoiler

I was curious about whether slotting might be right for money/Jacoby, and XGR++ says it is by a comfortable margin.  The Jacoby rule makes the difference - after slotting, we lose a lot of gammons when hit but those don't count with Jacoby turned on.  Without Jacoby, the pick-and-pass is correct.






XGID=-BBBBaCAA---------Bdbbcc--:0:0:1:41:0:0:1:0:10

X:Player 1   O:Player 2
Score is X:0 O:0. Unlimited Game, Jacoby
+13-14-15-16-17-18------19-20-21-22-23-24-+
|                X |   | O  O  O  O  O    |
|                X |   | O  O  O  O  O    |
|                  |   | O        O  O    |
|                  |   | O                |
|                  |   |                  |
|                  |BAR|                  |
|                  |   |                  |
|                  |   |                  |
|                  |   | X                |
|                  |   | X     X  X  X  X |
|             X  X |   | X  O  X  X  X  X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 89  O: 77 X-O: 0-0
Cube: 1
X to play 41

    1. XG Roller++ 18/14 6/5*                   eq:+0.401
      Player:   63.79% (G:1.71% B:0.03%)
      Opponent: 36.21% (G:19.53% B:1.42%)

    2. XG Roller++ 7/3 6/5*                     eq:+0.390 (-0.011)
      Player:   57.80% (G:1.29% B:0.02%)
      Opponent: 42.20% (G:16.55% B:0.21%)

    3. XG Roller++ 8/4 6/5*                     eq:+0.390 (-0.011)
      Player:   57.44% (G:1.28% B:0.02%)
      Opponent: 42.56% (G:15.78% B:0.23%)

    4. XG Roller++ 6/5* 5/1                     eq:+0.351 (-0.050)
      Player:   59.43% (G:0.83% B:0.01%)
      Opponent: 40.57% (G:6.73% B:0.14%)

eXtreme Gammon Version: 2.10


/////////////////no Jacoby //////////////////////////

XGID=-BBBBaCAA---------Bdbbcc--:0:0:1:41:0:0:0:0:10

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    |
|                X |   | O  O  O  O  O    |
|                  |   | O        O  O    |
|                  |   | O                |
|                  |   |                  |
|                  |BAR|                  |
|                  |   |                  |
|                  |   |                  |
|                  |   | X                |
|                  |   | X     X  X  X  X |
|             X  X |   | X  O  X  X  X  X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 89  O: 77 X-O: 0-0
Cube: 1
X to play 41

    1. XG Roller++ 6/5* 5/1                     eq:+0.323
      Player:   59.28% (G:0.81% B:0.01%)
      Opponent: 40.72% (G:6.45% B:0.11%)

    2. XG Roller++ 8/4 6/5*                     eq:+0.290 (-0.033)
      Player:   57.21% (G:1.30% B:0.02%)
      Opponent: 42.79% (G:15.30% B:0.18%)

    3. XG Roller++ 7/3 6/5*                     eq:+0.276 (-0.048)
      Player:   57.93% (G:1.32% B:0.02%)
      Opponent: 42.07% (G:16.98% B:0.25%)

    4. XG Roller++ 18/14 6/5*                   eq:+0.231 (-0.092)
      Player:   63.64% (G:1.73% B:0.03%)
      Opponent: 36.36% (G:20.35% B:1.67%)

    5. 1-ply       18/14 8/7                    eq:-0.249 (-0.572)
      Player:   42.93% (G:0.94% B:0.01%)
      Opponent: 57.07% (G:4.23% B:0.06%)


eXtreme Gammon Version: 2.10

[close]

[Zorba]

Re: efficient cube / rollout results

Spoiler

I don't find that the cube after pick'n'pass/dance is very efficient, nor almost as good as a cash. Usually, it's called a 100% efficient cube when it's a borderline take/pass decision, i.e. your equity after double/take is close to 1 (in a gammonless game for money, that usually occurs around 78.5% winning chances, as 21.5% is often the takepoint when factoring in recube vigorish at an average 70% liveliness cube).

Here, it's not the take that is borderline, it's the double that is borderline. The take is obvious at a little over 0.7, far from 1.0. When your equity after double/take is 0.7, it's not a very efficient cube usually, and not nearly as good as cashing (1.0). Another way to look at it is that ~73% game winning chances are still pretty far from the 78.5% maximum efficiency point.

In other words, this is doubling when you're not near the top/end of the doubling window.

That said, after the alternative play of slotting 18/14 6/5*, followed by a miss, the cube isn't very efficient either, but this time on the other side of the doubling window. It's now a very big pass (almost +1.4), so you sort of overshot the mark by a lot at 87% GWC. This is a double quite far beyond the top/end of the doubling window and not very efficient either.

Which of those two doubles would be more efficient? One way to calculate that would be (cubeful equity after correct cube action / cubeless equity before doubling). This shows how much correct usage of the cube adds to your equity percentage wise, compared to playing without the cube.

Using XG's numbers, you'd get for the cube after pick'n'pass/dance: (0.714/0.442) ~= 1.615 so the double/take adds 61.5%, compared to your cubeless equity.

For the 18/14 6/5* loose hit/dance: (1.000/0.743) ~= 1.346 so the double/pass adds 34.6% over the cubeless equity.

Simulations of backgammon games put the average cube efficiency calculated this way around the 66.7% mark, so that would put the first cube at a little below average efficiency. The second cube is very inefficient.

I think that last fact is also why 7/3 6/5* or 8/4 6/5* do better than 18/14 6/5* which is indeed very counterintuitive. If we get hit, the 18/14 play opening up two extra blots leads to many extra gammon losses and even 1.5% extra backgammon losses. If we don't get hit, it's a cash either way.

[close]