Open your mind - Backgammon Forum - Discuss Backgammon Strategy, Clubs and Books

everyone is allowed to contribute
present your problem at least 24 hours after the rollout of the previous problem
present the rollout after 48 hours with a maximum of 72 hours

rollout condition in my case:
Truncated cubeful rollout (depth 10) with var.redn.
147 games, Mersenne Twister dice gen. with seed 770449777 and quasi-random dice
Stop when std.errs. are small enough: ratio 0,1 (min. 144 games)
Play: world class 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0,16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

Quote

03-07-2015 , 07:00 PM

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

White - Pips 77

Black - Pips 97

Black to Play 3-1
Unlimited game, no Jacoby, no beavers
XGID=-BBBBaBA--Ba----A--bbcAcc-:2:-1:1:31:0:0:0:0:10

Anybody up for losing a gammon?

Mike

Quote

03-08-2015 , 12:52 AM

yogiman

adept

Join Date: Jun 2012 Posts: 784

16/12 offers a little duplication, but also 3 blots. Comparing 16/13 and 7/4, I think that in this final stage and with an open 5-point that killing a checker is no sin (ignoring the cube). If white doesn't hit, black has a better defensive opportunity.

Anybody up for losing a gammon?

Ofcourse, 6/5*/2. If white doesn't enter (about 55%) the tables are almost turned. If he does enter, half of black 5's don't hit. If white does hit, black still has some chance to enter.

Quote

03-08-2015 , 09:47 AM

uberkuber

veteran

Join Date: Jul 2009 Posts: 3,032

10/7 4/3 also offers some duplication.

Quote

03-08-2015 , 10:40 AM

yogiman

adept

Join Date: Jun 2012 Posts: 784

When I say -open your mind-, I don't mean -open your board-. Open your mind, weigh the options wisely and decide.

And a little correction. The chance not to enter with a 4-board is 2/3 for the one dice and 2/3 for the other dice, and 2/3 x 2/3 = 4/9. That is 45% instead of 55%.

Quote

03-08-2015 , 12:56 PM

bleep69

grinder

Join Date: Sep 2008 Posts: 483

This reminds me a little of the final position on the other thread, with the seemingly suicidal move of opening up the board while white was on the bar.

My initial thought was 10/7 4/3, but the pip counts is horribly against us, so I ruled the safer play out. The next move I considered was 6/5* 6/3, which also duplicated 5's. Getting hit probably puts white in a too good to double scenario, and we look nicely set up to be gammoned. I looked at shifting some of the mid-board pips around, and other than 16/2 (duplicating 1's) nothing grabbed me, so after a long rambling internal discourse I ended up opting for 6/5* 6/3.

Quote

03-09-2015 , 08:33 AM

peachpie

centurion

Join Date: Aug 2014 Posts: 182

There are several ways to leave some duplication on white's pending double shot. But hitting is obviously much better than leaving any double shot.

So the only question is how to play the three. 6/3 or 5/2? I am probably gammoned if I get hit in any case. So I will diversify a little with 5/2.

Quote

03-09-2015 , 11:12 AM

peachpie

centurion

Join Date: Aug 2014 Posts: 182

Quote:

equity difference with the obvious move is greater than 0.8

Yikes! Did you mean 0.08?

Also, I suppose there must be an "obvious" move to qualify, which DQs Taper's submission in my opinion.

Quote

03-09-2015 , 03:43 PM

yogiman

adept

Join Date: Jun 2012 Posts: 784

Yes, yes. you are qualified to post, peachpie.

Quote

03-10-2015 , 04:59 AM

#10

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

Quote:

Originally Posted by peachpie

Also, I suppose there must be an "obvious" move to qualify, which DQs Taper's submission in my opinion.

Sometimes "obvious" is in the eye of the beholder. For many, busting the board in order to hit loose is still an alien concept. In any event, I thought it would be nice to start off this thread with a position that was not too hard.

Hope to see some positions from you.

Mike

Quote

03-10-2015 , 05:12 AM

#11

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

White - Pips 77

Black - Pips 97

Black to Play 3-1
Unlimited game, no Jacoby, no beavers
XGID=-BBBBaBA--Ba----A--bbcAcc-:2:-1:1:31:0:0:0:0:10

Black is trailing by 20 pips in Position 1. White has a 5-point board. There is no safe play. Hitting White, and hoping for a dance (or at least a miss of the return shot) on White’s part, is Black’s best chance to turn things around. When it does not work out, he was favored to lose anyway. If Black does not hit, his chances of winning are only around 31%, of which 6% are gammon victories. When he hits, his win rate jumps to 46%, and, with a second White blot at risk, his gammon rate goes up to 9%.

The advantage to not hitting is that Black will lose fewer gammons, but that does not mean none. He is still losing a gammon in 15% of the games. The hitting plays loses an additional 10% gammons, but gets back the 3% mentioned above when Black wins a gammon. Black is trading a net of 7% gammon losses in order to pick up an additional 15% wins.

The key to this sort of play is to remember that the gammon price in an unlimited game is only 0.5. Each single loss that is converted into a gammon loss costs an extra 1 point, while each loss that is converted into a single win is worth an extra 2 points. Because hitting converts 15% of all games from losses into wins, Black could afford to lose an additional net of 30% gammons, and still break even! When you understand this, all those blots don’t seem so scary.

Not hitting is a quadruple whopper. The best play duplicates White’s 5 by lifting the remaining checker from the 6pt after hitting.

5k XG2 Rollout

Code:

XGID=-BBBBaBA--Ba----A--bbcAcc-:2:-1:1:31:0:0:0:0:10

X:Player 1   O:Player 2
Score is X:0 O:0. Unlimited Game
Pip count  X: 97  O: 77 X-O: 0-0
Cube: 4, O own cube
X to play 31

    1. Rollout¹    6/3 6/5*              eq:-0.3505
      Player:   45.60% (G:9.09% B:0.22%)
      Opponent: 54.40% (G:24.58% B:1.34%)
      Confidence: ±0.0052 (-0.3556..-0.3453) - [100.0%]

    2. Rollout²    6/5* 5/2              eq:-0.3890 (-0.0385)
      Player:   44.78% (G:9.49% B:0.21%)
      Opponent: 55.22% (G:27.79% B:1.42%)
      Confidence: ±0.0030 (-0.3920..-0.3860) - [0.0%]

    3. Rollout²    16/13 6/5*            eq:-0.5292 (-0.1787)
      Player:   42.16% (G:11.97% B:0.27%)
      Opponent: 57.84% (G:36.72% B:2.77%)
      Confidence: ±0.0048 (-0.5340..-0.5244) - [0.0%]

    4. Rollout²    7/4 6/5*              eq:-0.5519 (-0.2014)
      Player:   39.19% (G:9.08% B:0.22%)
      Opponent: 60.81% (G:32.89% B:1.50%)
      Confidence: ±0.0026 (-0.5545..-0.5493) - [0.0%]

    5. Rollout²    10/7 6/5*             eq:-0.6729 (-0.3224)
      Player:   41.11% (G:11.87% B:0.28%)
      Opponent: 58.89% (G:38.69% B:4.00%)
      Confidence: ±0.0045 (-0.6773..-0.6684) - [0.0%]

    6. Rollout²    16/13 7/6             eq:-0.7628 (-0.4123)
      Player:   31.28% (G:6.03% B:0.24%)
      Opponent: 68.72% (G:14.77% B:0.14%)
      Confidence: ±0.0046 (-0.7674..-0.7582) - [0.0%]

¹  1296 Games rolled with Variance Reduction.
   Dice Seed: 60019417
   Moves: 3-ply, cube decisions: XG Roller

²  5184 Games rolled with Variance Reduction.
   Dice Seed: 60019417
   Moves: 3-ply, cube decisions: XG Roller

Rollout by Taper_Mike
2015-Mar-07
eXtreme Gammon Version: 2.10.199.2658
Flashcard PositionID 000978.xgp

Mike

Quote

03-10-2015 , 07:53 AM

#12

peachpie

centurion

Join Date: Aug 2014 Posts: 182

I see that there is a nontrivial edge for playing 6/3 with the 3. I wonder why that is.

Quote

03-10-2015 , 08:21 AM

#13

Robertie

old hand

Join Date: May 2004 Posts: 1,954

Quote:

Originally Posted by peachpie

I see that there is a nontrivial edge for playing 6/3 with the 3. I wonder why that is.

After playing 6/5* 6/3, White hits from the bar with all 5s plus 61 = 13 shots.

After 6/5*/2, White hits with all 6s plus 51, 52, and 55 = 16 shots.

There's considerable duplication after 6/3, and it makes a big difference.

Quote

03-10-2015 , 11:31 AM

#14

peachpie

centurion

Join Date: Aug 2014 Posts: 182

Quote:

Originally Posted by Robertie

I suppose I could have figured that out if I had actually counted the shots. -1 for laziness.

Quote

03-10-2015 , 06:10 PM

#15

uberkuber

veteran

Join Date: Jul 2009 Posts: 3,032

Quote:

Originally Posted by peachpie

I suppose I could have figured that out if I had actually counted the shots. -1 for laziness.

I'd say -4 since the cube is on 4.

Quote

03-11-2015 , 11:12 AM

#16

yogiman

adept

Join Date: Jun 2012 Posts: 784

Position ID: jHcHBFDanBAAPQ Match ID: UQkGAAAAAAAE

White - Pips 139

Black - Pips 173
Black to Play 4-1
Created with www.BGdiagram.com

Quote

03-11-2015 , 05:02 PM

#17

peachpie

centurion

Join Date: Aug 2014 Posts: 182

Aha, I like this one. At first glance, it seems obvious to cover the 2 point. Is that really right?

On consideration, the two point is not so important in this position. Black has so many checkers back that one or two more wont matter much and might even improve his timing. And, the best use of the spare on the 6 point is to make the 5 point later on.

Now I look at that miserable stack back on the other ace point. I think the most urgent goal in this position is to make a better position for the back men, and work on recirculation. I choose 24/20 24/23.

Quote

03-11-2015 , 07:59 PM

#18

uberkuber

veteran

Join Date: Jul 2009 Posts: 3,032

24/20 2/1*. With 2 men on the bar, that's our opportunity to anchor if possible.

Quote

03-12-2015 , 08:18 AM

#19

peachpie

centurion

Join Date: Aug 2014 Posts: 182

Quote:

Originally Posted by uberkuber

24/20 2/1*. With 2 men on the bar, that's our opportunity to anchor if possible.

Yeah, I like that better. Switching is a persistent blind spot for me.

Quote

03-12-2015 , 10:10 AM

#20

Robertie

old hand

Join Date: May 2004 Posts: 1,954

I like 24/20 2/1*. Right now everything is secondary to getting off the 24-point and making the 20-point. Once Black does that, his game is solid and he can think about going forward.

Quote

03-12-2015 , 10:40 AM

#21

yogiman

adept

Join Date: Jun 2012 Posts: 784

Code:

 1. 24/20 2/1*                   Eq.:  -0,002 
       0,458 0,166 0,008 - 0,542 0,237 0,033 CL  -0,180 CF  -0,002 
     
    2. 24/23 6/2                    Eq.:  -0,166 ( -0,164) 
       0,401 0,136 0,008 - 0,599 0,243 0,023 CL  -0,321 CF  -0,166 
     
    3. 24/23 24/20                  Eq.:  -0,226 ( -0,224) 
       0,401 0,119 0,007 - 0,599 0,273 0,036 CL  -0,380 CF  -0,226

In the case of black having a lot more flexibility by moving two checkers on his 1 point to the 13 point, then covering will be no wrong decision.

White - Pips 139

Black - Pips 149
Black to Play 4-1
Created with www.BGdiagram.com

Code:

    1. 12/11 6/2                    Eq.:  +0,495
       0,557 0,253 0,015 - 0,443 0,142 0,011 CL  +0,230 CF  +0,495
     
    2. 24/20 2/1*                   Eq.:  +0,480 ( -0,015)
       0,568 0,261 0,014 - 0,432 0,143 0,012 CL  +0,256 CF  +0,480
     
    3. 24/23 6/2                    Eq.:  +0,400 ( -0,095)
       0,539 0,232 0,015 - 0,461 0,128 0,007 CL  +0,190 CF  +0,400

Quote

03-12-2015 , 11:40 AM

#22

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

Grunch. I have not read the solution or the posts of others.

Well, we certainly have an obvious play here. Actually, there is more than one. To a beginner, making the 2pt might be as obvious as it gets. To a more advanced player, unstacking the 24pt is the obvious best use of the 4. Like beauty, obvious is sometimes in the eye of the beholder.

I don’t see Black winning very often from here if he keeps 4 checkers on the 24pt, so I start by playing 24/20. For the ace, I like hitting better than making the 23pt. Black does not have enough timing to hold two anchors, and the 23pt is primed. Making it will not help him as much as making the 20pt or 21pt would.

By hitting, Black gets a bit of a win-win. Barring doublets, White cannot attack in his home board. If hit, Black will usually have a triple shot to make a high anchor. If missed, Black will have a direct shot to make his 1pt.

Mike

Quote

03-13-2015 , 03:35 PM

#23

yogiman

adept

Join Date: Jun 2012 Posts: 784

Position ID: uL0DAAcbm8EDIA Match ID: cIkNAAAAAAAE

White - Pips 130

Black - Pips 120
Black to Play 3-3
Created with www.BGdiagram.com

Quote

03-13-2015 , 04:36 PM

#24

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

If Black makes his bar point, then the low numbers White cannot use to run are just the numbers that will let him extend his prime. If Black makes the 10pt instead, then many of White’s 6s are going straight to his 1pt.

13/10(4)

This is a double-edged sword. This play also blocks Black’s 6s. He may end up being the one who has to kill a checker when he rolls a 6.

One other problem with making the bar point is that Black would then hold 7 points. That’s the dreaded TMP (too many points)! He would have to break somewhere on the following turn, and might find that some of his options are awkward.

Mike

Quote

03-13-2015 , 08:54 PM

#25

uberkuber

veteran

Join Date: Jul 2009 Posts: 3,032

Agreed with 13/10 (4).

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