all or nothing

[badgolferman]

GNU Backgammon Position ID: sw8AALLbTgAUAA
Match ID : AhngAAAAAAAE
+12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg
| O | | O O O O O | 0 points
| | | O O O O O |
| | | O O |
| | | |
| | | |
^| |BAR| |
| | | X | X
| | | X | X
| | | X | X
| | | X X X | X Cube offered at 8
| | X | O O X X X | X 0 points
+13-14-15-16-17-18------19-20-21-22-23-24-+ X: badgolferman

Pips X=53 O=96 7-point match

My head says pass but my heart says take. I am often torn by these
type of positions where I think I should have won the game and now I
may have to concede. I'd rather be beaten than submit.

[Walt]

What's your takepoint? If you pass, you'll be at 7a 3a for 23.5% MWC.
If you take, you are playing this game for the match so your takepoint
is 23.5%.

The relevant reference position is closed out on the bar with 5 checkers
off. That's 22% to win. Here, you are not closed out yet, but your
remaining checker distribution is not "fast" (ie it will take more rolls
than the reference position to bear off) I'm going to make a big
assumption that these roughly cancel each other. If that's correct,
then it is a close pass.


I'm not entirelys sure since I can't say with any certainty that the 22%
from the reference position accurately reflects the winning percentages
here. I'd take against a better opponent, hoping to get lucky, and pass
against an inferior one hoping to bring more skill factor to bear.

I think it's a technical pass - X's slow board is definitely a factor,
and the chances of X entering and escaping are small since X's poor
board means O can hit with impunity. The double seems absolutely clear
FWIW.

D/P.

//Walt

[Bradley K. Sherman]

badgolferman <REMOVETHISb...@gmail.com> wrote:
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg
> | O | | O O O O O | 0 points
> | | | O O O O O |
> | | | O O |
> | | | |
> | | | |
>^| |BAR| |
> | | | X | X
> | | | X | X
> | | | X | X
> | | | X X X | X Cube offered at 8
> | | X | O O X X X | X 0 points
> +13-14-15-16-17-18------19-20-21-22-23-24-+ X: badgolferman
>Pips X=53 O=96 7-point match

Drop.

--bks

[Freeven]

Nice analysis. I often flounder on these types of decisions because I
haven't put in time to learn relevant reference positions -- something
that is on my study list. You conclude that this is a technical pass,
which looks reasonable to my eye. But I note that X wins a few gammons
here, whereas he doesn't in your reference position. I'm wondering if
that is enough to tip a close decision the other way. Did you not
consider the gammons, or do you think they are rare enough not to matter?

[Walt]

On 5/17/2013 3:31 PM, Freeven wrote:
> On 5/17/2013 7:39 AM, Walt wrote:
>> On 5/17/2013 7:19 AM, badgolferman wrote:
>>> GNU Backgammon Position ID: sw8AALLbTgAUAA
>>> Match ID : AhngAAAAAAAE
>>> +12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg
>>> | O | | O O O O O | 0 points
>>> | | | O O O O O |
>>> | | | O O |
>>> | | | |
>>> | | | |
>>> ^| |BAR| |
>>> | | | X | X
>>> | | | X | X
>>> | | | X | X
>>> | | | X X X | X Cube offered at 8
>>> | | X | O O X X X | X 0 points
>>> +13-14-15-16-17-18------19-20-21-22-23-24-+ X: badgolferman

>>
>

> Nice analysis. I often flounder on these types of decisions because I
> haven't put in time to learn relevant reference positions -- something
> that is on my study list.

I haven't learned a lot of reference positions either, but here's the
link for closed out with N checkers off;
http://www.gammonlife.com/writers/07tardieuart1.htm

> You conclude that this is a technical pass,
> which looks reasonable to my eye. But I note that X wins a few gammons
> here, whereas he doesn't in your reference position. I'm wondering if
> that is enough to tip a close decision the other way. Did you not
> consider the gammons, or do you think they are rare enough not to matter?

I didn't consider gammons, because with the cube at 8 in a match to 7 I
thought they were not terribly relevant. And even if gammons did count,
I think they are too rare to bother.

//Walt




--
//Walt

[Freeven]

On 5/17/2013 3:50 PM, Walt wrote:

> I didn't consider gammons, because with the cube at 8 in a match to 7 I
> thought they were not terribly relevant. And even if gammons did count,
> I think they are too rare to bother.
>
> //Walt
>

Oops. Silly oversight on my part. Thanks.

"Not terribly relevant." I like that. :)

[Tim Chow]

On May 17, 7:39 am, Walt <walt_ask...@yahoo.com> wrote:
> What's your takepoint?  If you pass, you'll be at 7a 3a for 23.5% MWC.
> If you take, you are playing this game for the match so your takepoint
> is 23.5%.
>
> The relevant reference position is closed out on the bar with 5 checkers
> off.  That's 22% to win.  Here, you are not closed out yet, but your
> remaining checker distribution is not "fast" (ie it will take more rolls
> than the reference position to bear off)  I'm going to make a big
> assumption that these roughly cancel each other.  If that's correct,
> then it is a close pass.
>
> I'm not entirelys sure since I can't say with any certainty that the 22%
> from the reference position accurately reflects the winning percentages
> here.  I'd take against a better opponent, hoping to get lucky, and pass
> against an inferior one hoping to bring more skill factor to bear.
>
> I think it's a technical pass - X's slow board is definitely a factor,
> and the chances of X entering and escaping are small since X's poor
> board means O can hit with impunity.  The double seems absolutely clear
> FWIW.

I basically agree with this analysis except that my guess is that the
pass is pretty clear, for two reasons: (1) 22% is already noticeably
less than 23.5%, and (2) I think X's slow board is worse than O's lack
of a closeout (not completely sure about this but that's my guess). X
could even get a second checker sent back, though admittedly that's
not too likely.

---
Tim Chow

[badgolferman]

As I said earlier this was a really close decision for me and if
playing for real would probably have dropped. But the bot won't be
able to hold it over my head later so I decided to play on. The
rollout says the plays are equal in equity although to my untrained eye
the numbers seem to favor a drop so maybe someone can explain it for
me. By the way, I lost by 1 pip!


Cube analysis
Rollout cubeless equity +0.515 (Money: +0.496)

Cubeful equities:
1. Double, take +1.000
2. Double, pass +1.000 ( +0.000)
3. No double +0.949 ( -0.051)
Proper cube action: Redouble, take

Rollout details:
Player gnubg owns 4-cube:
0.764 0.000 0.000 - 0.236 0.027 0.006 CL +0.515 CF +0.949
[0.001 0.000 0.000 - 0.001 0.001 0.002 CL 0.001 CF 0.002]
Player badgolferman owns 8-cube:
0.762 0.000 0.000 - 0.238 0.048 0.010 CL +1.000 CF +1.000
[0.001 0.000 0.000 - 0.001 0.002 0.002 CL 0.005 CF 0.005]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 682886349 and
quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

[peps...@gmail.com]

You are correct that the plays are equal in equity according to the rollout -- an exactly marginal decision. This is a big surprise to myself and probably a big surprise to Tim too -- we thought it was a clear pass.

With regard to the take/drop decision, the correct decision is the one that maximises the probability of winning the match. If you drop, you're at 7 away vs 3 away. There are tables (called match equity tables) which are supposed to give you the probability of winning at this match score, which is the same as 4-0 in a match to 7. Deriving these match equity tables is not a completely solved problem, and the numbers will vary slightly.

Suppose the probability of the underdog winning at that match score is 23.8%. That would mean that 23.8% is the probability of the underdog winning after a drop. This is slightly different from Walt's number of 23.5%. However, these figures do vary because we don't yet know how to calculate them exactly.

In the rollout of the position after the take, you can see that the underdog won 23.8% of the time -- observe the 0.238 number. After a take, winning or losing the game is equivalent to winning or losing the match. So, after a take, the probability of the underdog winning is 23.8%.

Taking or dropping both give the same match-winning probabilities and they are both therefore equally good plays according to the rollout.

You asked for an explanation, and I have tried to provide one. Please could you confirm that you understand, or ask further questions if there is still an explanatory gap.

Thank you,

Paul Epstein

[Tim Chow]

On May 19, 6:13 am, pepste...@gmail.com wrote:
> This is a big surprise to myself and probably a big surprise
> to Tim too -- we thought it was a clear pass.

It is a surprise to me. Maybe not a *big* surprise because I knew I
wasn't sure about the relative importance of the non-closeout and X's
slow bearoff. It looks like the non-closeout is the more important
factor, which is the opposite of what I expected.

---
Tim Chow

[Tim Chow]

On May 18, 7:45 pm, "badgolferman" <REMOVETHISbadgolfer...@gmail.com>
wrote:

> As I said earlier this was a really close decision for me and if
> playing for real would probably have dropped.  But the bot won't be
> able to hold it over my head later so I decided to play on.  The
> rollout says the plays are equal in equity although to my untrained eye
> the numbers seem to favor a drop so maybe someone can explain it for
> me.  By the way, I lost by 1 pip!

If we assume that in general the bot is stronger than you are, and
that you're not likely to make many mistakes in the remainder of the
present game after taking the cube, even if the game turns around,
then taking is a good decision. The bot is basing the take/drop
decision on its estimate of how often you will be able to win the
match after dropping, and that will be an overestimate if you're not
as strong as the bot is.

---
Tim Chow

[badgolferman]

Player gnubg owns 4-cube:
0.764 0.000 0.000 - 0.236 0.027 0.006 CL +0.515 CF +0.949
[0.001 0.000 0.000 - 0.001 0.001 0.002 CL 0.001 CF 0.002]
Player badgolferman owns 8-cube:
0.762 0.000 0.000 - 0.238 0.048 0.010 CL +1.000 CF +1.000
[0.001 0.000 0.000 - 0.001 0.002 0.002 CL 0.005 CF 0.005]

Thank you for trying to explain the statistics to this math challenged
hacker. Adding up the golf scorecard is significantly easier since it
doesn't have decimal points, just numbers like 6,7,8....

So in this case you are telling me if the cube is accepted at 8 then
the probability of winning is 23.8% as evidenced by the 0.238 number.
However if the cube is rejected the winning probability is 23.6% or
0.236. Is that correct?

What do the numbers that come after the winning probability mean?

[badgolferman]

Tim Chow wrote:

>On May 19, 6:13�am, pepste...@gmail.com wrote:
>> This is a big surprise to myself and probably a big surprise
>> to Tim too -- we thought it was a clear pass.
>

>It is a surprise to me. Maybe not a big surprise because I knew I

>wasn't sure about the relative importance of the non-closeout and X's
>slow bearoff. It looks like the non-closeout is the more important
>factor, which is the opposite of what I expected.

What is a slow bearoff -- scattered checkers that don't cover the lower
points?

[Walt]

This is a close one. Note that XG uses Neil Kazaross's MET which places
the takepoint at 23.79%; I had quoted the takepoint as 23.5% which is
from the g11 MET.

4-ply analysis gives X 24.4% GWC, and declares it a take by .021.

XGR++ gives X 23.5% GWC and declares it a pass by .011.

XG Rollout gives X 23.16% GWC and declares it a pass by .024.


I'm inclined to believe this is a pass, but note how sensitive it is to
which MET you use.



/////////////4-ply analysis////////////////////////////////

XGID=-B-BEaa----------a-cbbcb-A:2:-1:-1:00:0:0:0:7:10

X:Player 1 O:Player 2
Score is X:0 O:0 7 pt.(s) match.
+12-11-10--9--8--7-------6--5--4--3--2--1-+
| O | | O O O O O | +---+
| | | O O O O O | | 4 |
| | | O O | +---+
| | | |
| | X | |

| |BAR| |
| | | X |
| | | X |
| | | X |
| | | X X X |

| | | O O X X X |

+13-14-15-16-17-18------19-20-21-22-23-24-+
Pip count X: 53 O: 96 X-O: 0-0/7
Cube: 4, O own cube
O on roll, cube action

Analyzed in 4-ply
Player Winning Chances: 75.62% (G:0.00% B:0.00%)
Opponent Winning Chances: 24.38% (G:2.18% B:0.03%)

Cubeless Equities: No Double=+0.492, Double=+0.979

Cubeful Equities:
No redouble: +0.936 (-0.043)
Redouble/Take: +0.979
Redouble/Pass: +1.000 (+0.021)

Best Cube action: Redouble / Take


///////////////XGR++/////////////////////////////////////


Analyzed in XG Roller++
Player Winning Chances: 76.02% (G:0.00% B:0.00%)
Opponent Winning Chances: 23.98% (G:2.15% B:0.06%)

Cubeless Equities: No Double=+0.501, Double=+1.011

Cubeful Equities:
No redouble: +0.949 (-0.051)
Redouble/Take: +1.011 (+0.011)
Redouble/Pass: +1.000

Best Cube action: Redouble / Pass

eXtreme Gammon Version: 2.10, MET: Kazaross XG2



/////////////////////rollout//////////////////////////////////////

Analyzed in Rollout
No redouble
Player Winning Chances: 76.41% (G:0.00% B:0.00%)
Opponent Winning Chances: 23.59% (G:2.28% B:0.07%)
Redouble/Take
Player Winning Chances: 76.84% (G:0.00% B:0.00%)
Opponent Winning Chances: 23.16% (G:3.74% B:0.23%)

Cubeless Equities: No Double=+0.508, Double=+1.024

Cubeful Equities:
No redouble: +0.954 (-0.046)
Redouble/Take: +1.024 (+0.024)
Redouble/Pass: +1.000

Best Cube action: Redouble / Pass

Rollout:
1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.003 (+0.951..+0.958)
Confidence Double: ± 0.006 (+1.018..+1.030)

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

Duration: 1 minute 27 seconds

eXtreme Gammon Version: 2.10, MET: Kazaross XG2


--
//Walt

[Tim Chow]

On May 20, 7:47 am, "badgolferman" <REMOVETHISbadgolfer...@gmail.com>
wrote:

> So in this case you are telling me if the cube is accepted at 8 then
> the probability of winning is 23.8% as evidenced by the 0.238 number.

Yes, that is correct.

> However if the cube is rejected the winning probability is 23.6% or
> 0.236.  Is that correct?

No. The match winning probability if the cube is rejected cannot be
directly read off these statistics. You have to look that up
separately from a "match equity table" (MET).

What 0.236 tells you is the estimated game winning probability if the
bot *does not double* and if the game were played out without the
cube. The "without the cube" proviso is in my opinion rather
artificial, but the backgammon community has gotten used to it and
doesn't seem to want to change it.

> What do the numbers that come after the winning probability mean?

The number right after the winning probability is estimated
probability of winning a gammon (again, if there were no doubling
cube) and the number after that is the estimated probability of
winning a backgammon (with no doubling cube). The number after "CL"
is the cubeless equity which I recommend ignoring entirely.

---
Tim Chow

[Tim Chow]

On May 20, 7:49 am, "badgolferman" <REMOVETHISbadgolfer...@gmail.com>
wrote:

> What is a slow bearoff -- scattered checkers that don't cover the lower
> points?

Yes.

---
Tim Chow

[peps...@gmail.com]

On Monday, May 20, 2013 4:13:14 PM UTC+1, Walt wrote:
...

> I'm inclined to believe this is a pass, but note how sensitive it is to
>
> which MET you use.

...

Thanks for interesting positions, rollouts, and analysis, but occasionally you say something that puzzles me.

Here, I happen to be puzzled as to why you "believe this is a pass."

If you mean that, instinctively, the pass looks like the better play if you had to play the position, then I definitely agree with you.

However, the analysis says that the position is ultra-marginal. It is extremely unlikely (literally less probable than 1 in a trillion) that the position is really exactly marginal. Either taking or passing is correct but we don't know which. With such a marginal situation demonstrated, I'm really puzzled as to how someone can "be inclined to believe" one side.

To see why I'm puzzled, it's analogous to the following situation. You're trying to estimate if a bar of chocolate weighs more or less than 100g. So you measure it according to three scales. One scale measures it at 100.001g , the other one at 100.002g, and the other one at 99.999g.

I would not say that I'm inclined to believe that the chocolate weighs more than 100g but maybe you would.

Paul Epstein