BGonline.org Forums

Bearoff, take or dropp?

Posted By: Daniel Murphy
Date: Wednesday, 30 May 2007, at 6:36 a.m.

In Response To: Bearoff, take or dropp? (M Oscarson)

You win if White rolls 4-1. Give yourself 2/36 wins.

You win if you roll a doublet -- if you get to roll. White has 4/36 winning doublets and 4-1 we've already counted, so give yourself 1/6 of 30/36 = 5/36 more wins. You're up to 7/36 wins, and our magic number is 9/36.

So ... you win if White fails to roll 11 pips -- the right 11 pips -- in two rolls. At this point you either have to have memorized something useful, or do a lot of quick calculation, or realize that even though you've already counted about 1/6 of these sequences -- the ones you've won with a doublet or when White rolled 4-1 -- they're surely worth at least 2/36 more wins for you. For starters, 1/4 of all rolls are 5 pips or less, so at least 1/4 * 1/4 = 1/16 (and actually quite a bit more) of all two-roll sequences are 10 pips or less. 1/16 = 6.25%, which is more than 2 rolls in 36. Of course we shouldn't count the first 4-1, and we shouldn't count 1/6 of the 6.25% twice, but still -- you've surely got more than 9/36 wins.

And you have redouble vig if White rolls 1-1 2-1 or 3-1.

So ... take.

In another forum, Achim wrote: "All positions with 11 pips are a redouble/take," referring to bearoffs where Roller has 11 pips and Opponent has 3 (or 4) checkers on the acepoint. That's true if all checkers are in the homeboard. That's probably a good thing to note and remember.

If roller has one checker it has to be on the 11 point, and that's Double/Pass:

The score (after 0 games) is: White 0, Blue 0. White on roll

White	11
Blue	4
Position ID: DwAAAIAAAAAAAA Match ID: BAEGAAAAAAAA

Cube decision
Rollout cubeless equity		+0.5357
Cubeful equities:
1.	Double, pass	+1.0000
2.	Double, take	+1.0478	+0.0478
3.	No double	+0.6425	-0.3575
Proper cube action:		Redouble, pass
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player White owns 16-cube 0.7679 0.0000 0.0000 - 0.2321 0.0000 0.0000 +0.5357 +0.6425 Standard error 0.0001 0.0000 0.0000 - 0.0001 0.0000 0.0000 0.0001 0.0011 Player Blue owns 32-cube 0.7679 0.0000 0.0000 - 0.2321 0.0000 0.0000 +1.0715 +1.0478 Standard error 0.0001 0.0000 0.0000 - 0.0001 0.0000 0.0000 0.0003 0.0021
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 1064740658 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.12
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

If Roller has two checkers they have to be on the 6 and 5 points, and that's double/take:

The score (after 0 games) is: White 0, Blue 0. White on roll.

White	11
Blue	4
Position ID: DwAAAAoAAAAAAA Match ID: BAEGAAAAAAAA

Cube decision
2-ply cubeless equity		+0.5126
	0.7563 0.0000 0.0000 - 0.2437 0.0000 0.0000
Cubeful equities:
1.	Double, take	+0.9814
2.	Double, pass	+1.0000	+0.0186
3.	No double	+0.6039	-0.3776
Proper cube action:		Redouble, take

If roller has 3 checkers left, they're all Double/Takes. Achim's website discussion of such positions is at https://www.acepoint.de/index.php?id=101

Messages In This Thread

• Bearoff, take or dropp?
  M Oscarson -- Tuesday, 29 May 2007, at 3:47 p.m.
  • Bearoff, take or dropp?
    Keene -- Tuesday, 29 May 2007, at 3:58 p.m.
    • Bearoff, take or dropp?
      Marty Storer -- Tuesday, 29 May 2007, at 6:24 p.m.
  • Bearoff, take or dropp?
    Chuck Bower -- Tuesday, 29 May 2007, at 4:37 p.m.
    • Bearoff, take or dropp?
      Matt Cohn-Geier -- Tuesday, 29 May 2007, at 6:28 p.m.
  • Bearoff, take or dropp?
    Daniel Murphy -- Wednesday, 30 May 2007, at 6:36 a.m.