You might get a shot next turn

[Tim Chow]

XGID=--ABC-CAb----C--a-Bbbbcba-:0:0:1:53:0:0:1:0:10
X:Player 1 O:Player 2

Score is X:0 O:0. Money session, Jacoby
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O X | | O O O O O O |
| X X | | O O O O O |
| X | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |
| O | | X X X |
| O X | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pipcount X: 120 O: 87 X-O: 0-0
Cube : 1
X to play 53

---
Tim Chow

[Freeven]

13/5 is the play that jumps out at me. It's safe and slots a point I'll
want/need if I hit a shot. I guess the question is whether having two
inner board blots is desirable when O is looking to break his outside
point. Looking for alternatives, 7/2 plays nicely, but I don't like the
3s I'm left with. I'll stick with my initial reaction and play 13/5, but
I suspect I'm missing something.

[Bradley K. Sherman]

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

> X:120 O:87, Cube:1, X to play 53

Must hit, and have a board to win:
6/1,4/1

--bks

[badgolferman]

My play would be 7/2, 6/1.

[badgolferman]

I meant 7/2, 4/1.

[Walt]

On 5/7/2013 6:46 PM, Tim Chow wrote:

How? 22 forces a shot next roll, but i don't see any others.

So, if we're going to get a shot, it won't come for a roll or two. I'll
slot the 5 so as to have some chance at containment in case we do.

13/5

--
//Walt

[peps...@gmail.com]

On Wednesday, May 8, 2013 2:36:39 PM UTC+1, Walt wrote:
> On 5/7/2013 6:46 PM, Tim Chow wrote:
>
> > XGID=--ABC-CAb----C--a-Bbbbcba-:0:0:1:53:0:0:1:0:10
>
> > X:Player 1 O:Player 2
>
> >
>
> > Score is X:0 O:0. Money session, Jacoby
>
> > +13-14-15-16-17-18------19-20-21-22-23-24-+
>
> > | X O X | | O O O O O O |
>
> > | X X | | O O O O O |
>
> > | X | | O |
>
> > | | | |
>
> > | | | |
>
> > | |BAR| |
>
> > | | | |
>
> > | | | |
>
> > | | | X X |
>
> > | O | | X X X |
>
> > | O X | | X X X X |
>
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
>
> > Pipcount X: 120 O: 87 X-O: 0-0
>
> > Cube : 1
>
> > X to play 53
>
>
>
> How? 22 forces a shot next roll, but i don't see any others.
>

...
1) You should also see 11 which forces a shot next roll.
2) Tim presumably means that if you leave two blots in your inner board, your opponent will take advantage of the opportunity to pay now.

Because 13/5 simply lets the opponent off the midpoint with impunity, I think it's a really terrible play.

I'm renewing my membership of the Bad Golfing Fan Club and will also play 7/2 4/1.

Paul Epstein

[peps...@gmail.com]

Sorry, I didn't mean the "midpoint". Also, 13/5 may well be best, because if O runs from the 17 point, even though X can't usually gain much by hitting a shot on the next roll, X can cover up a blot on the next roll and give O clean up problems.

I'm not changing my mind but I'm changing my confidence level 7/2 4/1.

Paul Epstein

[Freeven]

On 5/8/2013 9:50 AM, peps...@gmail.com wrote:
> On Wednesday, May 8, 2013 2:36:39 PM UTC+1, Walt wrote:
>> On 5/7/2013 6:46 PM, Tim Chow wrote:
>>
>>> XGID=--ABC-CAb----C--a-Bbbbcba-:0:0:1:53:0:0:1:0:10
>>
>>> X:Player 1 O:Player 2
>>
>>>
>>
>>> Score is X:0 O:0. Money session, Jacoby
>>
>>> +13-14-15-16-17-18------19-20-21-22-23-24-+
>>
>>> | X O X | | O O O O O O |
>>
>>> | X X | | O O O O O |
>>
>>> | X | | O |
>>
>>> | | | |
>>
>>> | | | |
>>
>>> | |BAR| |
>>
>>> | | | |
>>
>>> | | | |
>>
>>> | | | X X |
>>
>>> | O | | X X X |
>>
>>> | O X | | X X X X |
>>
>>> +12-11-10--9--8--7-------6--5--4--3--2--1-+
>>
>>> Pipcount X: 120 O: 87 X-O: 0-0
>>
>>> Cube : 1
>>
>>> X to play 53
>>
>>
>>
>> How? 22 forces a shot next roll, but i don't see any others.
>>
> ...

> 2) Tim presumably means that if you leave two blots in your inner board, your opponent will take advantage of the opportunity to pay now.
>
> Because 13/5 simply lets the opponent off the midpoint with impunity, I think it's a really terrible play.

O isn't on the midpoint, so I think you mean 8pt. If so, I disagree with
your assessment.

X needs to both hit and contain a shot to win. He'll have trouble
containing anything with an open 5pt, and if he doesn't slot it now, he
may never make it.

It's true that X doesn't particularly want two inner board blots when he
hits. But O takes quite a risk if he breaks the 8pt now. He's already
got an exposed blot, and he'll usually be leaving multiple blots and a
lot of direct shots. There's a fair chance X can hit and cover at least
one of his inner board blots -- or possibly double hit. If X hits and is
unable to tidy up his inner blots, so be it. O misses them about half
the time, after which X will have taken the initiative. If O does hit
back, X has some return shots of his own. If X fails to hit at all, O
still has a lot of clean up to do, so X may very well make his 5pt and
have another chance next turn. And of course if O doesn't break the 8pt
now, X will be happy for the chance to make his 5pt and crank the
pressure up on O for next time. Admittedly, X takes considerable risk in
this approach, but when you're an underdog, it's often right to take
some risks to turn things around.

[peps...@gmail.com]

This analysis seems correct to me. It's also similar to what I said as an afterthought:

QUOTE OF PREVIOUS POST

Sorry, I didn't mean the "midpoint". Also, 13/5 may well be best, because if O runs from the 17 point, even though X can't usually gain much by hitting a shot on the next roll, X can cover up a blot on the next roll and give O clean up problems.

END QUOTE

Having said all that, I'm not changing my vote.

Paul

[crf]

I slot the 5. If I tempt O to break now, I'll want the best chance of making the 5 and those extras to contain. Lots of numbers (every one?) makes a point, so I can probably make another point if I can hit, where making a deep point I'm stripped and maybe even duplicating 5s if O is forced to break.

[Tim Chow]

As Freeven said, it will be difficult to win this game without making
the 5pt, so that provides a strong motivation to slot it now.
However, the counterargument is that O is looking for an opportunity
to run off her back anchor in comparative safety. Does leaving two
blots in our board, rather than making another point, let O off the
hook too easily?

This is a difficult question and I've found that even XG 3-ply
(version 1 at least) gets somewhat confused about it. First of all,
let's suppose that X plays 13/5. With what (non-doublet) rolls should
O choose to break her back point? Answer: 65 64 63 62 53 and perhaps
even 32! Even though O is not forced to leave shot with these rolls,
it's better to pay now than to pay later, since paying later means
shredding her board and probably having to leave a similar number of
shots next turn anyway when X's board will be stronger.

Now what if X makes a point, say with 6/1 4/1? This is where XG 3-ply
and XGR+ disagree sometimes. It seems that for many, but not all, of
the same rolls, O should still pay now. Therefore, X definitely
should consider the possibility that he will get a shot next turn and
make his current play accordingly. This might seem to be an argument
for making another home-board point, but actually, if X plays 13/5 and
O breaks her back point, then all of X's 5's hit and cover a home-
board point, so it is no cakewalk for O.

According to the rollout below, 13/5 is best by a huge margin. The
fact that XG 3-ply is misplaying O's response after X makes a point
suggests that the true margin may be even larger. I would be curious
to see what XG version 2 thinks of O's decision next turn after 6/1
4/1 or some other point-making play, and whether an XG2 rollout gives
a different verdict.

Finally, some comments about playing against human opponents. The
main consideration, I think, is that many humans playing O's side will
*not* voluntarily break the back point next roll, though they might be
more willing to break if X leaves two blots. Slotting the 5pt is so
much better, though, that I think it will come out clearly ahead
regardless of typical human misplays of O's side.

=======
Rollout
=======

1. Rollout: 13/5 eq:-0.305
Player : 39.81% (G:6.23% B:0.22%)
Opponent: 60.19% (G:11.61% B:0.45%)
Confidence: ±0.014 (-0.319<E<-0.291)

2. Rollout: 6/1 4/1 eq:-0.399 (-0.094)
Player : 36.95% (G:4.90% B:0.12%)
Opponent: 63.05% (G:11.12% B:0.32%)
Confidence: ±0.013 (-0.412<E<-0.386)

3. Rollout: 7/2 6/3 eq:-0.402 (-0.097)
Player : 35.97% (G:4.16% B:0.12%)
Opponent: 64.03% (G:8.03% B:0.14%)
Confidence: ±0.013 (-0.415<E<-0.389)

4. Rollout: 7/2 4/1 eq:-0.404 (-0.098)
Player : 37.13% (G:4.98% B:0.14%)
Opponent: 62.87% (G:11.22% B:0.29%)
Confidence: ±0.014 (-0.418<E<-0.390)

1296 Games rolled with Variance Reduction.
Dice Seed: 2
Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.21

---
Tim Chow

[Freeven]

On 5/9/2013 1:48 PM, Tim Chow wrote:
>I would be curious
> to see what XG version 2 thinks of O's decision next turn after 6/1
> 4/1 or some other point-making play, and whether an XG2 rollout gives
> a different verdict.

I'll plug these into XG2 and report back. The rollout shouldn't take
long since the plays aren't that close.

[Freeven]

On 5/9/2013 1:48 PM, Tim Chow wrote:

> According to the rollout below, 13/5 is best by a huge margin. The
> fact that XG 3-ply is misplaying O's response after X makes a point
> suggests that the true margin may be even larger. I would be curious
> to see what XG version 2 thinks of O's decision next turn after 6/1
> 4/1 or some other point-making play, and whether an XG2 rollout gives
> a different verdict.

According to XG2 XGR++:

If X makes a point -- for example with 41: 7/2, 31: 6/2, or 61: 7/1 2/1
(Aside: XGR++ doesn't like making the 1pt with 61) -- O should only come
off the 17pt if he can do so with doubles or with an 8 (22, 62, 53),
played 17/9 (making the 9pt).

Here's an XG2 rollout of the original position, which tightens things up
a bit over the XG1 rollout:

XGID=--ABC-CAb----C--a-Bbbbcba-:0:0:1:53:0:0:1:0:10

Score is X:0 O:0. Unlimited Game, Jacoby
+24-23-22-21-20-19------18-17-16-15-14-13-+
| O O O O O O | | X O X |
| O O O O O | | X X |
| O | | X |
| | | |
| | | |
| |BAR| |

| | | |
| | | |
| X X | | |
| X X X | | O |

| X X X X | | X O |
+-1--2--3--4--5--6-------7--8--9-10-11-12-+
Pip count X: 120 O: 87 X-O: 0-0

Cube: 1
X to play 53

1. Rollout� 13/5 eq:-0.318
Player: 39.70% (G:7.03% B:0.24%)
Opponent: 60.30% (G:10.19% B:0.17%)
Confidence: �0.010 (-0.328..-0.308) - [100.0%]
Duration: 15 minutes 02 seconds

2. Rollout� 7/2 6/3 eq:-0.379 (-0.061)
Player: 35.93% (G:4.65% B:0.13%)
Opponent: 64.07% (G:8.10% B:0.12%)
Confidence: �0.013 (-0.392..-0.366) - [0.0%]
Duration: 11 minutes 24 seconds

3. Rollout� 7/2 4/1 eq:-0.386 (-0.067)
Player: 37.39% (G:5.97% B:0.16%)
Opponent: 62.61% (G:12.75% B:0.34%)
Confidence: �0.014 (-0.400..-0.372) - [0.0%]
Duration: 8 minutes 45 seconds

4. Rollout� 6/1 4/1 eq:-0.403 (-0.085)
Player: 37.12% (G:5.87% B:0.14%)
Opponent: 62.88% (G:12.34% B:0.42%)
Confidence: �0.012 (-0.416..-0.391) - [0.0%]
Duration: 14 minutes 34 seconds


� 1296 Games rolled with Variance Reduction.
Dice Seed: 4
Moves: 3-ply, cube decisions: XG Roller


eXtreme Gammon Version: 2.10

[Tim Chow]

On May 9, 6:59 pm, Freeven <no...@nowhere.com> wrote:
> According to XG2 XGR++:
>
> If X makes a point -- for example with 41: 7/2, 31: 6/2, or 61: 7/1 2/1
> (Aside: XGR++ doesn't like making the 1pt with 61) -- O should only come
> off the 17pt if he can do so with doubles or with an 8 (22, 62, 53),
> played 17/9 (making the 9pt).

Thanks, Freeven. Does XG 3-ply concur with XGR++? For the purposes
of assessing the reliability of the rollout, what counts is how XG 3-
ply plays the checkers, since that's what your rollout settings are
using.

> The rollout shouldn't take long since the plays aren't that close.

This is a general comment about rollouts. I recommend paying more
attention to the actual value of the standard deviation than to the
confidence percentages. So for example in your rollout, we see that
the equity of 13/5 is -0.318 ± 0.010. The value "0.010" is more
important to look at than the "100%" confidence probability, because
in most cases we care not only about *whether play #1 could have
achieved its #1 ranking by chance*, but also *how big the equity
differences are*. The "0.010" gives you some sense of how much the
equity estimate might fluctuate if you were to keep rolling the thing
out, and so usually you want that value to be small. I see lots of
people stopping when they reach 100% and then drawing some conclusion
about the sizes of the equity differences between the plays; this is a
conceptual error. The "100%" is NOT saying that the bot is 100%
confident that the equity difference between the top two plays (in
this example) is 0.061. It just tells you that there's a very small
probability that the #1 play attained its #1 ranking just by chance,
which is a nice thing to know, but is a pretty minimal fact.

Conversely, some people seem obsessed with rolling things out until
they get 100% confidence, even when the confidence intervals are down
to ± 0.001. This may be amusing but is of zero practical value. You
already have as good an estimate as you're going to get of the
equities. The message of the rollout is that the equities are
extremely close, and it's irrelevant for any practical purpose to know
which one the bot judges to be a tiny bit ahead of the other.

So when deciding how many trials to run, the key question is how long
will it take to drive the standard deviation down to a satisfactorily
small value, NOT how far apart the top two plays are in equity.

---
Tim Chow

[Freeven]

On 5/9/2013 7:53 PM, Tim Chow wrote:
> On May 9, 6:59 pm, Freeven <no...@nowhere.com> wrote:
>> According to XG2 XGR++:
>>
>> If X makes a point -- for example with 41: 7/2, 31: 6/2, or 61: 7/1 2/1
>> (Aside: XGR++ doesn't like making the 1pt with 61) -- O should only come
>> off the 17pt if he can do so with doubles or with an 8 (22, 62, 53),
>> played 17/9 (making the 9pt).
>
> Thanks, Freeven. Does XG 3-ply concur with XGR++? For the purposes
> of assessing the reliability of the rollout, what counts is how XG 3-
> ply plays the checkers, since that's what your rollout settings are
> using.
>

My mistake; the original results I reported were 4-ply. I'm still
getting the hang of XG's Dice Distribution feature. 3-ply does concur.