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Pay now?

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BlueDice

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Apr 22, 2017, 5:25:48 PM4/22/17
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XGID=-DDB-B--A-a----B-a-cbbbbb-:0:0:1:63:0:0:0:0:10

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 |
| X | | O O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X X |
| | | X X |
| | | X X X X |
| O X | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 66 O: 71 X-O: 0-0
Cube: 1
X to play 63
--
BD

Michael

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Apr 22, 2017, 5:51:31 PM4/22/17
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I think he has to because he can't afford any more wastage while having so many crossovers.
15/12 15/9

Michael

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Apr 22, 2017, 6:07:20 PM4/22/17
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Will she Double if we pay now??

Tim Chow

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Apr 23, 2017, 2:37:34 PM4/23/17
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X is pretty likely to have to pay later anyway if he doesn't pay now, and
paying later reduces both his racing vig and his chance of winning by hitting
a shot (since he has to tear up his board). I would pay now.

There is a question as to how to pay now. The obvious play is to minimize
shots by playing 15/12 15/9, but playing 15/6 has a couple of advantages:
(1) if O rolls 31, 21, or 11, then X gets another shot; (2) O's 5's are
already quite good racing rolls for her. I would try 15/6.

---
Tim Chow

BlueDice

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Apr 24, 2017, 4:06:21 AM4/24/17
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The bot says 'pay later/pay never'.
To try to make sense of this I moved the checkers around. After X plays 8/2 5/2 she has 40% winning chances. If we then give O an average roll to move his straggler past X's outfield point then X's equity goes up to 45%. I think that the bot sees the risk of getting hit as more expensive than burning race equity in the home board.

Rollout
=======
1. Rollout¹ 8/2 5/2 eq:-0.318
Player: 39.72% (G:0.02% B:0.00%)
Opponent: 60.28% (G:2.40% B:0.06%)
Confidence: ±0.009 (-0.327..-0.310) - [100.0%]
Duration: 33.8 seconds

2. Rollout¹ 15/12 15/9 eq:-0.386 (-0.068)
Player: 35.35% (G:0.00% B:0.00%)
Opponent: 64.65% (G:2.92% B:0.02%)
Confidence: ±0.009 (-0.395..-0.377) - [0.0%]
Duration: 9.2 seconds

3. Rollout¹ 15/6 eq:-0.486 (-0.167)
Player: 33.35% (G:0.03% B:0.00%)
Opponent: 66.65% (G:2.72% B:0.05%)
Confidence: ±0.009 (-0.495..-0.477) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller


eXtreme Gammon Version: 2.10
--
BD

Michael

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Apr 24, 2017, 5:31:32 AM4/24/17
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On Monday, April 24, 2017 at 11:06:21 AM UTC+3, BlueDice wrote:
>
>
> Rollout
> =======
> 1. Rollout¹ 8/2 5/2 eq:-0.318
> Player: 39.72% (G:0.02% B:0.00%)

WOW! Quite honestly I thought X was in the range of 55-60% GWC.
I am wondering, did anyone estimate it to be that low??

Tim Chow

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Apr 24, 2017, 7:24:16 PM4/24/17
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On Monday, April 24, 2017 at 4:06:21 AM UTC-4, BlueDice wrote:
> If we then give O an average roll to move his straggler past X's outfield
> point

Ah, this is what I missed. It wasn't clear to me that O would move past X's
outfield point with an average roll.

---
Tim Chow

Michael

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Apr 25, 2017, 11:25:30 AM4/25/17
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GNU Backgammon Position ID: 7zcBGADbthMQAA
Match ID : MIEOAAAAAAAE
+12-11-10--9--8--7-------6--5--4--3--2--1-+ O: O
| X O | | O O O O O O | 0 points
| X | | O O O O O O | Rolled 53
| | | O |
| | | |
| | | |
^| |BAR| | (Cube: 1)
| | | 6 |
| | | X X |
| | | X X |
| | | X X X |
| O | | X X X X | 0 points
+13-14-15-16-17-18------19-20-21-22-23-24-+ X: X
Pip counts : O 71, X 57

1. Rollout 8/5 6/1 Eq.: +0.28017
58.556 2.513 0.033 - 41.444 0.011 0.000 CL +0.19646 CF +0.28017

2. Rollout 8/3 6/3 Eq.: +0.27055 ( -0.00962)
58.606 2.148 0.030 - 41.394 0.020 0.000 CL +0.19371 CF +0.27055

3. Rollout 15/7 Eq.: +0.13476 ( -0.14542)
54.333 0.000 0.000 - 45.667 0.000 0.000 CL +0.08666 CF +0.13476

Michael

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Apr 25, 2017, 11:34:51 AM4/25/17
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I forgot to add comments: as per rollout above she won't let X jump from 40% to 45% by running with an average roll, she would rather stay there.

Walt

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Apr 25, 2017, 2:41:26 PM4/25/17
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X is ahead in the race, but not so much when you account for wastage.
The chicken play makes for even more wastage.

Paying now means leaving 12 shots and O basically wins all of them if
she hits and about half if she doesn't. With a win percentage in the
60s and 12 market losers X will be eating an unapetizing cube if he runs
off the fifteen, with no immediate recube if she misses.

I'll pay later. At least the cube stays in the center.

8/2 5/3

--
//Walt

Walt

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Apr 25, 2017, 2:45:07 PM4/25/17
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On 4/23/2017 2:37 PM, Tim Chow wrote:
> On Saturday, April 22, 2017 at 5:25:48 PM UTC-4, BlueDice wrote:
>> XGID=-DDB-B--A-a----B-a-cbbbbb-:0:0:1:63:0:0:0:0:10
>>
>> 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 |
>> | X | | O O O O O O |
>> | | | O |
>> | | | |
>> | | | |
>> | |BAR| |
>> | | | |
>> | | | X X |
>> | | | X X |
>> | | | X X X X |
>> | O X | | X X X X |
>> +12-11-10--9--8--7-------6--5--4--3--2--1-+
>> Pip count X: 66 O: 71 X-O: 0-0
>> Cube: 1
>> X to play 63
>
> X is pretty likely to have to pay later anyway if he doesn't pay now

I'm not seeing that. Seems to me that O will break contact and race
after the chicken play. Maybe I'm wrong, but as O I wouldn't hang around
on the ten point.

Now, if O had an anchor on the ten...


--
//Walt

Tim Chow

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Apr 25, 2017, 7:59:45 PM4/25/17
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On Tuesday, April 25, 2017 at 11:34:51 AM UTC-4, Michael wrote:
> I forgot to add comments: as per rollout above she won't let X jump from
> 40% to 45% by running with an average roll, she would rather stay there.

O.K., that makes more sense to me; it's what I originally thought.

So, paying later doesn't necessarily mean not paying at all. I think that
means the logic is this: Getting hit now is as bad as it gets, so even a
modest chance of not having to pay at all is worth the wasted pips.

---
Tim Chow

Michael

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Apr 26, 2017, 5:03:56 AM4/26/17
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Correct,I got this totally wrong by thinking was the favorite to win, so I didn't even look that deep

BlueDice

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Apr 28, 2017, 5:55:27 AM4/28/17
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On Tuesday, April 25, 2017 at 4:34:51 PM UTC+1, Michael wrote:
> I forgot to add comments: as per rollout above she won't let X jump from 40% to 45% by running with an average roll, she would rather stay there.


Interesting...
O stays put after rolling 63 but runs home 15/5 after rolling 64
--
BD

Michael

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Apr 28, 2017, 11:11:12 AM4/28/17
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I agree. Notice the rollout was for 53.
Herebelow the rollout for 64 just 2 pips more lowers X's chances down to 37%. In the past Tim told me races are known to be such super sensitive thingies.. ;-)

I am wondering how the guys at Stick's forum would go on finding the correct solution to this...
It was a great quiz anyway.

1. Rollout 15/5 Eq.: +0.40888
63.119 0.000 0.000 - 36.881 0.000 0.000 CL +0.26238 CF +0.40888

2. Rollout 15/9 8/4 Eq.: +0.40171 ( -0.00717)
62.806 0.000 0.000 - 37.194 0.000 0.000 CL +0.25611 CF +0.40171

3. Rollout 8/2 6/2 Eq.: +0.33082 ( -0.07806)
59.195 4.063 0.087 - 40.805 0.032 0.000 CL +0.22508 CF +0.33082

BlueDice

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Apr 28, 2017, 1:36:59 PM4/28/17
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I followed your lead and posted this on Stick's forum:
http://www.bgonline.org/forums/webbbs_config.pl?read=199992
--
BD

Tim Chow

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Apr 28, 2017, 7:30:50 PM4/28/17
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On Friday, April 28, 2017 at 11:11:12 AM UTC-4, Michael wrote:
> Herebelow the rollout for 64 just 2 pips more lowers X's chances down to 37%.

I looked at this position with the bot and found that if, in the original
position, we change X's roll to 64, then the bot pays now 15/11 15/9. So
it really is a very delicate decision.

---
Tim Chow
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