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Hit or take off two? Actual statistics

Posted By: Daniel Murphy
Date: Wednesday, 4 July 2012, at 1:58 p.m.

In Response To: Hit or take off two? (Daniel Murphy)

(1) If Blue just wanted to bear off in the fewest possible rolls, he'd take two checkers off:

Rolls to bear off (if not hit)
	2 rolls	3 rolls	4 rolls
5/off 5/4*	22.6%	65.8%	11.5%
5/off 1/off	27.4%	72.3%	0.258%

That's for a noncontact position. In the problem position, of course, Blue is hit 11/36 of the time after 5/off 1/off, but even more often -- 14/36 -- after 5/off 5/4*.

(2) However, hitting sets Opponent back 4 pips (needing at least 20 pips, instead of at least 16 pips, to get off the gammon), and a crossover (needing 5 not 4). That's huge:

Chance of rolling at least 16 pips in 2 rolls:	44.8%.	In 3 rolls:	94.4%
Chance of rolling at least 20 pips in 2 rolls:	20.2%.	In 3 rolls:	74.1%

(3) Another way to look at it is to focus on crossovers instead of pips. If Blue doesn't hit, and White doesn't hit, White can bear off a checker in two rolls without rolling a doublet. These nondoublet sequences would work:

1st roll	2nd roll
65	65 64 63 62 61 54 53 52 51 43 42 41
64	65 64 63 62 61 54 53 52 51
63 or 54	65 64 63 62 61

That's 124/1296 = 9.6% sequences that get White off the gammon in 2 rolls.

But if Blue hits, and White doesn't hit, White can't bear off a checker in two rolls without rolling a doublet (and 22 and 11 never work) in at least one of his two rolls.

---

For bearoff in X rolls data: use Gnubg "evaluation" feature for any mutual bearoff with all remaining checkers in their respective home boards.

For pips rolled in X rolls: http://www.bkgm.com/rgb/rgb.cgi?view+1119

Messages In This Thread

• Hit or take off two?
  Minerva -- Tuesday, 3 July 2012, at 12:45 p.m.
  • Hit or take off two?
    Giuliano Pietoso -- Tuesday, 3 July 2012, at 3:36 p.m.
    • Hit or take off two?
      benf -- Tuesday, 3 July 2012, at 4:23 p.m.
      • Hit or take off two?
        Casper van der Tak -- Tuesday, 3 July 2012, at 5:41 p.m.
        • Hit or take off two?
          benf -- Tuesday, 3 July 2012, at 6:16 p.m.
          • Hit or take off two?
            Casper van der Tak -- Tuesday, 3 July 2012, at 6:39 p.m.
  • Hit or take off two?
    Keene -- Tuesday, 3 July 2012, at 4:59 p.m.
  • Hit or take off two?
    Timothy Chow -- Tuesday, 3 July 2012, at 5:27 p.m.
  • Hit or take off two?
    ah_clem -- Tuesday, 3 July 2012, at 5:37 p.m.
    • Hit or take off two?
      Timothy Chow -- Wednesday, 4 July 2012, at 2:19 a.m.
  • Hit or take off two?
    Daniel Murphy -- Wednesday, 4 July 2012, at 5:39 a.m.
    • Hit or take off two? Actual statistics
      Daniel Murphy -- Wednesday, 4 July 2012, at 1:58 p.m.
  • Hit or take off two? ROLLOUT
    ah_clem -- Friday, 6 July 2012, at 8:12 p.m.