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Leave a blot during bearoff?

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08-06-2011 , 08:04 PM

ajmargarine

Carpal \'Tunnel

Join Date: Jun 2005 Posts: 21,228

Assume cash game, no cube. I trail pip count 49-36. Is there some trick here to know what's best in this spot? As in, how do I know when to leave a blot and when to play safe. Top 3 moves in spoiler.

Spoiler:

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08-07-2011 , 04:46 AM

ClassicalGuitar23

grinder

Join Date: Jul 2009 Posts: 546

yea two off.

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08-07-2011 , 10:43 AM

RealNick

journeyman

Join Date: Apr 2010 Posts: 217

How do you plan to win this game? Answer that and the best play is obvious.

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08-07-2011 , 02:39 PM

uberkuber

veteran

Join Date: Jul 2009 Posts: 3,032

Quote:

Originally Posted by RealNick

How do you plan to win this game? Answer that and the best play is obvious.

Once you know the answer, the best play might be obvious, but the answer itself might not be obvious.

I would try to win a race and, therefore, I would play safe with 6/3 6/2. If White enters right away, he's a favorite in the race. If he dances once, then I think Black becomes a slight favorite, but it looks close. If he dances twice or more, then Black becomes a substantial favorite. White has 25/36 (~69%) of dancing at least once, so I would go for the race.

Now I'm gonna look at the spoiler...

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08-07-2011 , 02:43 PM

uberkuber

veteran

Join Date: Jul 2009 Posts: 3,032

[Spoiler read + disgusted look on my face]

Well, I guess I overestimated Black's chances in the race when White dances only once. Or I simply underestimated the other game plan, which is to contain White as long as possible and hope not getting hit.

I knew the answer to the game plan wasn't obvious, at least for me!

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08-07-2011 , 05:31 PM

ajmargarine

Carpal \'Tunnel

Join Date: Jun 2005 Posts: 21,228

How do I plan to win this game? Well, the obvious answer is to bearoff before he does.

So, does that make 4/off 3/off best in and of itself? No, because there's a line in there somewhere. If pip count were 49-49, 6/3 6/2 is better and we still plan to win the game the same way, bearing off before he does.

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08-07-2011 , 08:52 PM

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

Before he rolled this 43, XG Roller++ had Black as a 53% favorite to win at DMP. Had his spares been positioned optimally, on the 4, 5 and 6 points, XG would have rated him even higher, as a 62% favorite. After Black plays 6/3, 6/2, things change a bit. When White dances, Black falls lower, becoming a 51% favorite, but when White enters, say with a 63, Black plummets to only 13% winning chances!

So, you can see Black could hardly be worse off being hit. When Black rips off two checkers on this turn, his overall odds are better. After White fans, his winning percentage rises to 56%, and even when White hits, say with a 63, Blacks chances are still 11.5%. More directly, we can ask XG what Black's chances are after this turn, when White is on roll. According to the following rollout, Black's best play is to pull just one checker. This beats ripping two because it is easier for Black to clean up the blot next time. After pulling two, Black is often in danger whenever he rolls a five or six next time.

Black's winning percentage when White has 7 checkers off:

41.0% after ripping 0: 6/3, 6/2
44.1% after ripping 1: 6/3, 4/off
43.8% after ripping 2: 4/off, 3/off

So, how many checkers must remain for White before Black is best advised to play safe? With just one more White checker on his one point, it is a near tossup. My 10K rollout still gives a 1% edge to pulling one. With two additional White checkers in play, it is not close. Black should then play safe, 6/3, 6/2.

Black's winning percentage when White has 6 checkers off:

49.6% after ripping 0: 6/3, 6/2
50.7% after ripping 1: 6/3, 4/off
50.5% after ripping 2: 4/off, 3/off

Black's winning percentage when White has 5 checkers off:

60.3% after ripping 0: 6/3, 6/2
57.5% after ripping 1: 6/3, 4/off
57.6% after ripping 2: 4/off, 3/off

Code:

XGID=aCCBCBB----------------eb-:0:0:1:43:0:0:0:1:10

    1. Rollout¹    6/3 4/Off                    eq:-0.118
      Player:   44.11% (G:0.00% B:0.00%)
      Opponent: 55.89% (G:0.00% B:0.00%)
      Confidence: ±0.001 (-0.118..-0.117) - [100.0%]
      Duration: 4.9 seconds

    2. Rollout¹    4/Off 3/Off                  eq:-0.125 (-0.007)
      Player:   43.77% (G:0.00% B:0.00%)
      Opponent: 56.23% (G:0.00% B:0.00%)
      Confidence: ±0.001 (-0.126..-0.124) - [0.0%]
      Duration: 22.3 seconds

    3. Rollout¹    6/3 6/2                      eq:-0.178 (-0.061)
      Player:   41.08% (G:0.00% B:0.00%)
      Opponent: 58.92% (G:0.00% B:0.00%)
      Confidence: ±0.001 (-0.179..-0.178) - [0.0%]
      Duration: 0.9 second


¹  5184 Games rolled with Variance Reduction.
   Moves: 3-ply, cube decisions: XG Roller


eXtreme Gammon Version: 2.00, MET: Kazaross XG2

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08-07-2011 , 09:29 PM

ajmargarine

Carpal \'Tunnel

Join Date: Jun 2005 Posts: 21,228

wow mike, thanks alot. Checkers off more important than straightup pip count....

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08-07-2011 , 09:58 PM

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

Quote:

Originally Posted by ajmargarine

wow mike, thanks alot. Checkers off more important than straightup pip count....

Yes. That's because White is closer to an "N-rolls" position than he is to a "count-the-pips" position.

See this must-read article by Walter Trice:

Effective Pip Count
by Walter Trice
http://www.bkgm.com/articles/EffectivePipCount/

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08-08-2011 , 08:56 AM

#10

RealNick

journeyman

Join Date: Apr 2010 Posts: 217

Quote:

Originally Posted by Taper_Mike

Code:

XGID=aCCBCBB----------------eb-:0:0:1:43:0:0:0:1:10

    1. Rollout¹    6/3 4/Off                    eq:-0.118
      Player:   44.11% (G:0.00% B:0.00%)
      Opponent: 55.89% (G:0.00% B:0.00%)
      Confidence: ±0.001 (-0.118..-0.117) - [100.0%]
      Duration: 4.9 seconds

    2. Rollout¹    4/Off 3/Off                  eq:-0.125 (-0.007)
      Player:   43.77% (G:0.00% B:0.00%)
      Opponent: 56.23% (G:0.00% B:0.00%)
      Confidence: ±0.001 (-0.126..-0.124) - [0.0%]
      Duration: 22.3 seconds

    3. Rollout¹    6/3 6/2                      eq:-0.178 (-0.061)
      Player:   41.08% (G:0.00% B:0.00%)
      Opponent: 58.92% (G:0.00% B:0.00%)
      Confidence: ±0.001 (-0.179..-0.178) - [0.0%]
      Duration: 0.9 second


¹  5184 Games rolled with Variance Reduction.
   Moves: 3-ply, cube decisions: XG Roller


eXtreme Gammon Version: 2.00, MET: Kazaross XG2

Mike,

This roll out is not for the position originally posted, the correct play is two pips off for that position.

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08-08-2011 , 09:58 AM

#11

Robertie

old hand

Join Date: May 2004 Posts: 1,954

The position type here is what we call the "Post-Ace-Point Game". White bore off some checkers, then got hit (in this case probably from a deuce-point game, but that doesn't matter) then got closed out. Now Black has to decide how aggressively to play the bearoff. His choices are:

4/off 3/off (two off + shot + inner gap) or

4/off 6/3 (one off + shot) or

6/3 6/2 (none off)

For some thoughts on how to evaluate these positions, look at the solution to Problem 39.

Note that the Trice article referenced earlier, while excellent (actually brilliant, since no one knew how to equate pips to rolls until Walter figured it out in the 1990s) doesn't apply. His formulas are for races only.

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08-08-2011 , 10:09 AM

#12

OmahaDonk

Pooh-Bah

Join Date: Apr 2011 Posts: 4,933

1) 4/off 3/off

2) 4/off 6/3

If we are going to leave white a place to hit us, shouldn't we bear off in the process? Is it reasonable to say that choice 1 is almost dominant to choice 2?

Follow up questions after we play choice 1:

What are the odds we can close the board on the next roll if white misses? Also, would we want to close the board or keep bearing off aggressively (within reason)?

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08-08-2011 , 11:28 AM

#13

ajmargarine

Carpal \'Tunnel

Join Date: Jun 2005 Posts: 21,228

Quote:

Originally Posted by Robertie

For some thoughts on how to evaluate these positions, look at the solution to Problem 39.

Week 39 problem
Week 39 solution

According to the criteria laid out from week 39, it is best to play safe, 6/3 6/2?!?

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08-09-2011 , 01:13 PM

#14

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

Quote:

Originally Posted by RealNick

Mike,

This roll out is not for the position originally posted, the correct play is two pips off for that position.

Thanks for the correction, Nick. I'm not sure how all those checkers of the opponent landed on the wrong points. The problem may be the same thing that causes 747s to occassionally make unscheduled landings on the sides of mountains: pilot error.

Anyway, here are the correct positions and equities. The safe play still kicks in when the opponent has 5 checkers off. When she has 6 or 7 checkers off, ripping two is correct.

To Ajmargarine: In your original post, you sought a formula involving pip-count. When I mentioned the article by Walter Trice, I was suggesting that you count rolls rather that pips. His article explains why. Counting crossovers, as Bill Robertie points out, is a better way to go. It may be that counting half-rolls, where the board is divided into groups of 4 points each, could yield even more accurate results. But that is just a conjecture!

Position 1 Opponent has 7 checkers off. This is the original position posted by Ajmargarine.

Code:

XGID=aCCBCBB---------------b-e-:0:0:1:43:0:0:3:0:10

 
    1. Rollout¹    4/Off 3/Off                  eq:+0.029
      Player:   49.01% (G:0.00% B:0.00%)
      Opponent: 50.99% (G:0.00% B:0.00%)
      Confidence: ±0.008 (+0.022..+0.037) - [100.0%]
      Duration: 8.1 seconds
 
    2. Rollout¹    6/3 4/Off                    eq:-0.015 (-0.045)
      Player:   45.34% (G:0.00% B:0.00%)
      Opponent: 54.66% (G:0.00% B:0.00%)
      Confidence: ±0.007 (-0.022..-0.008) - [0.0%]
      Duration: 2.2 seconds
 
    3. Rollout¹    6/3 6/2                      eq:-0.131 (-0.160)
      Player:   42.53% (G:0.00% B:0.00%)
      Opponent: 57.47% (G:0.00% B:0.00%)
      Confidence: ±0.008 (-0.138..-0.123) - [0.0%]
      Duration: 1.0 second
 
    4. Rollout¹    5/2 4/Off                    eq:-0.137 (-0.167)
      Player:   41.86% (G:0.00% B:0.00%)
      Opponent: 58.14% (G:0.00% B:0.00%)
      Confidence: ±0.007 (-0.144..-0.131) - [0.0%]
      Duration: 4.2 seconds
 
 
¹  1296 Games rolled with Variance Reduction.
   Moves: 3-ply, cube decisions: XG Roller
 
 
eXtreme Gammon Version: 2.00

Position 2 Opponent has 6 checkers off.

Code:

XGID=aCCBCBB---------------b-f-:0:0:1:43:0:0:3:0:10
 
    1. Rollout¹    4/Off 3/Off                  eq:+0.223
      Player:   56.09% (G:0.00% B:0.00%)
      Opponent: 43.91% (G:0.00% B:0.00%)
      Confidence: ±0.006 (+0.217..+0.229) - [100.0%]
      Duration: 6.8 seconds
 
    2. Rollout¹    6/3 4/Off                    eq:+0.132 (-0.091)
      Player:   52.02% (G:0.00% B:0.00%)
      Opponent: 47.98% (G:0.00% B:0.00%)
      Confidence: ±0.004 (+0.128..+0.135) - [0.0%]
      Duration: 1.9 seconds
 
    3. Rollout¹    6/3 6/2                      eq:+0.113 (-0.110)
      Player:   51.88% (G:0.00% B:0.00%)
      Opponent: 48.12% (G:0.00% B:0.00%)
      Confidence: ±0.006 (+0.107..+0.119) - [0.0%]
      Duration: 0.6 second
 
    4. Rollout¹    5/2 4/Off                    eq:+0.043 (-0.180)
      Player:   48.66% (G:0.00% B:0.00%)
      Opponent: 51.34% (G:0.00% B:0.00%)
      Confidence: ±0.006 (+0.037..+0.049) - [0.0%]
      Duration: 3.4 seconds
 
 
¹  1296 Games rolled with Variance Reduction.
   Moves: 3-ply, cube decisions: XG Roller
 
 
eXtreme Gammon Version: 2.00

Position 3 Opponent has 5 checkers off.

Code:

XGID=aCCBCBB---------------b-g-:0:0:1:43:0:0:3:0:10
 
    1. Rollout¹    6/3 6/2                      eq:+0.481
      Player:   62.81% (G:0.00% B:0.00%)
      Opponent: 37.19% (G:0.00% B:0.00%)
      Confidence: ±0.009 (+0.472..+0.490) - [100.0%]
      Duration: 0.8 second
 
    2. Rollout¹    4/Off 3/Off                  eq:+0.455 (-0.026)
      Player:   63.08% (G:0.00% B:0.00%)
      Opponent: 36.92% (G:0.00% B:0.00%)
      Confidence: ±0.009 (+0.447..+0.464) - [0.0%]
      Duration: 6.5 seconds
 
    3. Rollout¹    6/3 4/Off                    eq:+0.394 (-0.087)
      Player:   58.98% (G:0.00% B:0.00%)
      Opponent: 41.02% (G:0.00% B:0.00%)
      Confidence: ±0.006 (+0.388..+0.400) - [0.0%]
      Duration: 1.7 seconds
 
    4. Rollout¹    5/2 4/Off                    eq:+0.203 (-0.278)
      Player:   56.03% (G:0.00% B:0.00%)
      Opponent: 43.97% (G:0.00% B:0.00%)
      Confidence: ±0.007 (+0.196..+0.210) - [0.0%]
      Duration: 3.9 seconds
 
 
¹  1296 Games rolled with Variance Reduction.
   Moves: 3-ply, cube decisions: XG Roller
 
 
eXtreme Gammon Version: 2.00

Quote

08-09-2011 , 01:41 PM

#15

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

Quote:

Originally Posted by Robertie

...For some thoughts on how to evaluate these positions, look at the solution to Problem 39.

Thanks, Bill, for reminding us to check Problem of the Week #39.

Counting crossovers gives:

Player (on bottom): 15
Opponent (on top): 7 + 5 = 12

Trailing by three, we must check the other criteria:

(1) Trail by 3 -> tend to play safe
(2) Opponent has no home-board blots -> tend to play safe
(3) Ripping two leaves an odd number of checkers -> tend to play safe
(4) No speed board -> tend to bear off.

By a close vote of 3 to 1, safe play wins.

Darn! The formula is wrong for Ajmargarine's position.

I don't think this anecdotal result detracts, however, from its value. It just proves that one size does not fit all.

Quote

08-09-2011 , 04:42 PM

#16

plm

newbie

Join Date: Sep 2009 Posts: 44

Quote:

Originally Posted by Taper_Mike

Thanks, Bill, for reminding us to check Problem of the Week #39.

[...]
Darn! The formula is wrong for Ajmargarine's position.

I don't think this anecdotal result detracts, however, from its value. It just proves that one size does not fit all.

In the current problem, among the hitting numbers after 4/off 3/off, 3-1, 3-2 and to a lesser extent 3-3 play differently than equivalent numbers do in PoW #39.

Quote

08-09-2011 , 05:24 PM

#17

Robertie

old hand

Join Date: May 2004 Posts: 1,954

In POW 39, the choice was between

(two off + blot) or

(one off + safe).

Here the choice is between

(two off + blot) or

(none off + safe).

The aggressive play has much more going for it since it gets two more checkers off than the safe play, making it clearly dominant since the crossover count is putting us in the gray zone (trailing by 3 or 4 crossovers.)

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08-13-2011 , 05:53 PM

#18

GrantHoffman

centurion

Join Date: Aug 2011 Posts: 113

The factor that seems to be being overlooked here is taking 2 off can cause blotting in Whites board - suppose Black takes 2 checkers off and White rolls 32(1 blot) or 31 (leaving 2 blots) - this is what tips the rules towards taking 2 off

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