Is this a Beaver - Backgammon Forum - Discuss Backgammon Strategy, Clubs and Books

Two Plus Two Forums Sports and Games Chess and Other Board Games Backgammon Forum hosted by Bill Robertie.

Is this a Beaver

Post Reply Subscribe

...

06-28-2013 , 12:28 PM

TerryPin

stranger

Join Date: Jun 2013 Posts: 8

After reading the posts here I felt that I needed to buy XG, and I am really glad that I did, although I needed to buy a new computer as well because my old centrino 900Mz was taking minutes to play each move at World Class level. Now I have an i5 which sizzles!

I was playing both sides with XG in tutor mode when I got to this position:

XGID=aBC-DAB--B-A-----a-bcbbbb-:0:0:-1:00:0:0:3:0:10

(hope that I have done the image and ID correct)

XG said that I should have doubled as black. I hit the cube and thought that it must be a take for white but when I accepted the double XG said I was making a mistake. OK, it must be a pass then, but no, this was a mistake also! I clicked on analyse and it said Beaver!

With both sides on world class analysis, how could XG recommend a double/beaver?

I guess it must be some rare and conflicting algorithms, but I am still not sure if it is an initial double or not, and if the beaver is correct. What do you think?

Terrapin

Quote

06-28-2013 , 09:06 PM

Robertie

old hand

Join Date: May 2004 Posts: 1,954

There are a few positions which are both correct doubles and correct beavers. It's called the "Kauder Paradox", and was postulated about 35 years ago.

Positions that satisfy the Kauder Paradox usually fit these conditions:

1) Cube in the middle, Jacoby rule in effect.

2) Black on roll wins 30%-35% of the time. (Black has a single direct shot to win.)

3) When Black wins, he mostly wins a gammon.

4) When Black misses his immediate shot, he gets doubled out.

In your position, these conditions are mostly satisfied. Black has 13 numbers to hit on the 20-point and win with his closed board. If he dances, White doubles him out. If he enters without hitting, it's a little unclear.

The problem is that hitting doesn't guarantee a gammon. Black still has to pick up the blot on the 15-point, and he's only a slight favorite to do that. Even if he hits both blots, he's only about 75% to win a gammon -- not enough.

I couldn't duplicate your result in my version of XG2. I did both an XGR++ analysis and a rollout and got no double/beaver in both cases. Not sure what happened, but no double/beaver should be the right evaluation.

Quote

06-29-2013 , 06:34 AM

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

I am able to get the Double/Beaver recommendation, but only on low analysis settings.

Follow these steps to duplicate my results:

Copy the XGID from your message.
Paste it into XG.
Perform a 2-ply analysis. You do this by clicking the icon on the bottom, far left side of the Move Panel. It looks like a row of checkers where the left two are colored red.

Voilà!

The same problem occurs with a 3-ply or 4-ply analysis, but not with XG Roller, XG Roller+, or XG Roller++.

The likely problem is that the strength used by Tutor mode is weaker than the strength used for analysis. You should check your settings.

Select Options, Settings... to open the “Options and Settings” dialog box.
Open the Mode tab.
Verify that the level for Hints is XG Roller+. If need be, change it.
Verify that the level for Tutor is XG Roller+. If need be, change it.
Open the Analyze tab.
Verify that the Analysis Mode is “World Class.” If need be, change it.
Click OK to save your changes, and close the dialog box.

With luck, that should solve your problem.

Quote

06-29-2013 , 02:11 PM

TerryPin

stranger

Join Date: Jun 2013 Posts: 8

Thanks to both of you. The "Kauder Paradox" is something that I've never come across but is good to know that it can happen.

It looks like I am on those settings but I'll keep an eye on it and check them if I get any more problems. It is curious that with the above analysis levels (assuming I have them set OK), sometimes I make a move that is accepted then when I review it, it has become second or third choice. I assume that XG continues to analyse moves in the background while it allows the game to proceed in a timely fashion.

Quote

06-29-2013 , 08:44 PM

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

White - Pips 70

Black - Pips 80
Black on roll. Cube action?

I’m not sure what is happening, but the train’s put its brakes on.

Today, XG declares your position to be a Kauder Paradox.

Here is the 31k rollout. In addition to the rollout, analyses at 2-ply, 3-ply, XGR+, and XGR++ all have it as double/beaver. Only XGR continues to report no-double/beaver.

Mike

Code:

XGID=-BBBBCB-A-----a-b--bad-cbA:0:0:1:00:0:0:3:0:10

X:Player 2   O:Player 1
Score is X:0 O:0. Unlimited Game, Jacoby Beaver

Pip count  X: 80  O: 70 X-O: 0-0
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
  Player Winning Chances:   50.60% (G:14.71% B:0.23%)
  Opponent Winning Chances: 49.40% (G:0.74% B:0.01%)
Double/Take
  Player Winning Chances:   50.43% (G:17.49% B:0.31%)
  Opponent Winning Chances: 49.57% (G:0.75% B:0.01%)

Cubeless Equities: No Double=+0.1539, Double=+0.3580

Cubeful Equities:
       No double:     -0.1806 (-0.0133)
       Double/Beaver: -0.1672
       Double/Pass:   +1.0000 (+1.1672)

Best Cube action: Double / Beaver

Rollout:
  31104 Games rolled with Variance Reduction.
  Dice Seed: 29924256
  Moves: 3-ply, cube decisions: XG Roller
  Confidence No Double: ±0.0006 (-0.1811..-0.1800)
  Confidence Double:    ±0.0023 (-0.1695..-0.1649)

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

  Duration: 7 minutes 45 seconds

Rollout by Taper_Mike
2013-Jun-29
eXtreme Gammon Version: 2.10.199.2658
Kauder Paradox
http://forumserver.twoplustwo.com/138/backgammon/beaver-1346782/

Quote

06-29-2013 , 10:36 PM

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

The whistle is screaming!

Now, I have this 4-ply rollout confirming a Kauder Paradox. It uses a large search interval.

Barring some mistake on my part, this looks like the real thing.

Mike

Code:

XGID=-BBBBCB-A-----a-b--bad-cbA:0:0:1:00:0:0:3:0:10

X:Player 1   O:Player 2
Score is X:0 O:0. Unlimited Game, Jacoby Beaver
Pip count  X: 80  O: 70 X-O: 0-0
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
  Player Winning Chances:   50.44% (G:14.57% B:0.22%)
  Opponent Winning Chances: 49.56% (G:0.75% B:0.01%)
Double/Take
  Player Winning Chances:   50.33% (G:17.61% B:0.31%)
  Opponent Winning Chances: 49.67% (G:0.73% B:0.01%)

Cubeless Equities: No Double=+0.1492, Double=+0.3566

Cubeful Equities:
       No double:     -0.1823 (-0.0125)
       Double/Beaver: -0.1697
       Double/Pass:   +1.0000 (+1.1697)

Best Cube action: Double / Beaver

Rollout:
  31104 Games rolled with Variance Reduction.
  Dice Seed: 29924256
  Moves and cube decisions: 4-ply
  Search interval: Large
  Confidence No Double: ±0.0005 (-0.1828..-0.1818)
  Confidence Double:    ±0.0021 (-0.1718..-0.1677)

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

  Duration: 59 minutes 45 seconds

Rollout by Taper_Mike
2013-Jun-29
eXtreme Gammon Version: 2.10.199.2658
Flashcard PositionID 000830 4-ply.xgp
Kauder Paradox
http://forumserver.twoplustwo.com/138/backgammon/beaver-1346782/

Quote

06-30-2013 , 03:01 AM

TomCowley

Pooh-Bah

Join Date: Sep 2004 Posts: 5,649

Is there any way to get XG to analyze a raccoon decision (with a capped cube)? I should be able to make a double-beaver-raccoon position as long as the cube is capped at 8, but I can't make it evaluate the raccoon, and I'm not sure it's taking the raccoon into account for the beaver decision.

Quote

06-30-2013 , 05:23 AM

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

Quote:

Originally Posted by TomCowley

I don't know if this will help, but I noticed that XG did not display beaver equities during either of the two rollouts above. Even when I clicked the rollout progress bar to open the "Analysis Queue & Rollout" dialog box, beaver was not one of things being "analyzed."

Only when the rollouts were finished did the word beaver appear.

I think you will find that is how the raccoon analysis behaves as well.

Late addition: I just found this thread at BgOnline where Xavier, the programmer of XG, states, "Beavers are totally ignored in Rollouts. So it will miss the rare Kauder paradox positions."

I have not read the thread yet, but in case you want to, it is here:

XG rollout Money No Jacoby / Beaver

Tom, are you able to verify that TerryPin has indeed found a Kauder Paradox position?

Mike

Quote

Post Reply Subscribe

...