It makes more difference than you think

[Tim Chow]

XGID=-HCB--A--A---------cbcaba-:1:-1:1:21:0:0:0:0:10

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-+
| | | O O O O O O | +---+
| | | O O O O | | 2 |
| | | O O | +---+
| | | |
| | | |
| |BAR| |
| | | 8 |
| | | 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: 35 O: 48 X-O: 0-0
Cube: 2, O own cube
X to play 21

---
Tim Chow

[Bradley K. Sherman]

Tim Chow <tchow...@yahoo.com> wrote:
>Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | | | O O O O O O | +---+
> | | | O O O O | | 2 |
> | | | O O | +---+
> | | | |
> | | | |
> | |BAR| |
> | | | 8 |
> | | | X |
> | | | X X |
> | | | X X X |
> | X | | X X X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+

> X:35 O:48, X to play 21

Might have played 9/6 OTB, but forced to think, I'll try:
9/8,6/4

--bks

[badgolferman]

Normally I would get my man in with 9/6, but gnubg always dings me for
that, instead preferring to move the man on the 6-point up. I think
I'll still play 9/6 though.

[Walt]

X has an odd number of checkers to bear off, so missing once is does not
burn a roll. Missing twice does.

I'd play 9/8 6/4 to eliminate the gaps on the 4 & 5 and almost guarantee
ripping off two every roll once the runner is borne in.

OTB, there's a good chance I'd play 9/6 without thinking about it.

//Walt

[check...@yahoo.com]

I bet it doesn't.

9/8 6/4 is clear.

[66 55 44 22] take three men off putting us in a possible six roll position depending on how well we roll the rest of the way. With a bonehead play like 9/6 [33 22 11] also take three off but leave a worse overall structure to hope that it remain a six roll. (that effect is only with 22 after 9/8 6/4)

After 9/6 we don't even get a man off with 54. That doesn't happen with any roll after 9/8 6/4.

I won't go through all the sequences but it is much more likely, as mentioned by others, that we miss twice as 9/6. We can miss once and not waste a roll but twice is a tragedy.

Stick

[Tim Chow]

On Monday, December 9, 2013 8:03:32 AM UTC-5, check...@yahoo.com wrote:
> I bet it doesn't.

So what are your quantitative estimates of the equity differences between the top three plays?

Assuming you haven't already looked at the bot by the time you read this.

---
Tim Chow

[check...@yahoo.com]

I've already looked but I had a similar problem come up this past week. Wish I would have saved it because it would have made a perfect companion problem for yours. Mentally, I only categorize small (0.00-.040), medium (.040-.080), and large (anything over .080). This was easily in the large category. I didn't do any exact estimates because all that mattered to me is the little backgammon man on my shoulder saying "Man, how awful is 9/6!?"

Stick

[Tim Chow]

Stick, as usual, is much better at playing backgammon than at second-guessing me. I blundered here because I was on auto-pilot, but even my auto-pilot knows not to play 9/6. Instead, I hastily played 9/7 6/5. In retrospect, it's obvious that 9/8 6/4 is better because it's more important to fill in the gap on the 4pt than to shift the outside checker closer by a pip. The "difference" I was referring to in the subject line was the equity difference between 9/7 6/5 and 9/8 6/4, which is larger than I expected.

1. Rollout¹ 9/8 6/4 eq:-0.762
Player: 27.33% (G:0.00% B:0.00%)
Opponent: 72.67% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.766..-0.759) - [16.7%]

2. Rollout¹ 9/7 6/5 eq:-0.850 (-0.088)
Player: 25.47% (G:0.00% B:0.00%)
Opponent: 74.53% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.853..-0.847) - [16.7%]

3. Rollout¹ 6/3 eq:-0.887 (-0.125)
Player: 24.67% (G:0.00% B:0.00%)
Opponent: 75.33% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.890..-0.884) - [16.7%]

4. Rollout¹ 6/4 3/2 eq:-0.890 (-0.128)
Player: 24.61% (G:0.00% B:0.00%)
Opponent: 75.39% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.893..-0.887) - [16.7%]

5. Rollout¹ 6/4 2/1 eq:-0.917 (-0.155)
Player: 24.05% (G:0.00% B:0.00%)
Opponent: 75.95% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.920..-0.914) - [16.7%]

6. Rollout¹ 9/6 eq:-0.963 (-0.201)
Player: 23.02% (G:0.00% B:0.00%)
Opponent: 76.98% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.966..-0.960) - [16.7%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: 4-ply

eXtreme Gammon Version: 2.10

---
Tim Chow

[Bradley K. Sherman]

Tim Chow <tchow...@yahoo.com> wrote:
> ...

>Stick, as usual, is much better at playing backgammon than at
>second-guessing me. I blundered here because I was on auto-pilot, but
>even my auto-pilot knows not to play 9/6. Instead, I hastily played 9/7
>6/5. In retrospect, it's obvious that 9/8 6/4 is better because it's

> ...

There is a class of non-contact problems about when to
twiddle innerboard checkers as opposed to bearing in
checkers, and when to bear a checker deeper into the
board in preference to bearing a different checker
into the 6 or 5 point. In the spirit of Stick's
comment I would like to see positions where it's a
definite blunder to choose one over another, even if
the problem is constructed.

--bks

[Tim Chow]

On Monday, December 9, 2013 7:10:06 PM UTC-5, Bradley K. Sherman wrote:
> There is a class of non-contact problems about when to
> twiddle innerboard checkers as opposed to bearing in
> checkers, and when to bear a checker deeper into the
> board in preference to bearing a different checker
> into the 6 or 5 point. In the spirit of Stick's
> comment I would like to see positions where it's a
> definite blunder to choose one over another, even if
> the problem is constructed.

I've discussed some examples in the past but I can't seem to find them.

In any case, it's not hard to construct examples of your own. If you're in an "ordinary" race as opposed to racing off the gammon, then the standard mistake is to think, "I have to bear in all my checkers first before I can bear off, so I should aim to bear in all my checkers as fast as possible, and only then start thinking about bearing off." But in fact, it does no good to bear in faster by half a roll if it means that you'll miss more often later. So just create a position with some checkers on the 6pt, a checker on the 7pt, and a gap on the 5pt. Then pick a roll involving an ace. It will almost always be right to play 6/5 rather than 7/6 with the ace. This is the paradigmatic example but it's easy to create other examples where bearing in creates a poor distribution with serious danger of later misses while the better play fills in a gap.

When you're racing off the gammon, a different set of issues come into play. Usually it's right to bear all your checkers in as efficiently as possible since you don't have to worry about misses later; the game will be over by then. However, even here there are exceptions. Sometimes your opponent has only two rolls left and you have to maximize your chances of getting off the gammon next turn. This can lead to some surprising plays. See problem 4 (by Bill Davis) here:

http://www.edcollins.com/backgammon/backprobs.htm

More commonly occurring but also less well-known is the principle that if your board is mostly filled in except for a gap on your 1pt and/or 2pt, and you're scrambling your last checker around, then you may want to use an ace or a deuce to fill in the gap rather than shuffle your outside checker closer. This can happen while saving the gammon, because often on your next roll you'll use your larger die to bear in and your smaller die to bear off, and you don't want to miss with your smaller die. It can also happen in a straight race when you have a comfortable lead and the most likely way you'll lose is if you roll an ace during the bearoff and miss.

---
Tim Chow

[Bradley K. Sherman]

Tim Chow <tchow...@yahoo.com> wrote:
> ...

>surprising plays. See problem 4 (by Bill Davis) here:
>http://www.edcollins.com/backgammon/backprobs.htm

> ...

Excellent!

--bks