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Bearoff Recube Action

Posted By: Daniel Murphy
Date: Sunday, 1 April 2012, at 10:23 p.m.

In Response To: Bearoff Recube Action (RobertFontaine)

1. White's take point is equal to his equity at 5-away 1-away Crawford, which is about 16%.

2. White's GWC in a pure two-roll position is about 14%.

3. White's GWC in the problem position has to be much better (that is, surely more than 2% better) than a pure 2-roll position because although White is off in two rolls at most, Blue has many various small ways to fail to bear off in two rolls:

"OTB"	if you have time to think, or think fast
2-1 followed by 19/36 of Blue's rolls.	2 * 19 = 38
3-1 or 1-1 followed by 9/36 of Blue's rolls.	3 * 9 = 27
4-1 followed by any ace.	2 * 11 = 22
3-2 followed by 3-2 3-1 2-1 or 1-1.	2 * 7 = 14
5-1 4-2 or 5-2 followed by 2-1.	6 * 2 = 12

From the right hand portion of the table above, 12 + 22 + 14 + 27 + 38 = 113. 113/1296 = 8.7%. 8.7% times 31/36 (since Blue would lose anyway if White rolls one of his good doublets) = 7.5% extra GWC for White. That is probably too much for OTB thinking, and quite possibly slightly incorrect, but also not necessary to do completely. You're only looking for ~2% more GWC for White. Ignoring White's interim roll, every thirteen two-roll sequences that you find for Blue that fail to bear off in two rolls represent 13/1296 = 1% additional winning chances for White. So if you start with Blue's smallest rolls, you can see that 2-1 followed by 19/36 misses is 38/1296, or about 3% (still ignoring White's roll), and 1-1 or 3-1 followed by 9/36 misses is another 27/1296, or about 2% ... and stop whenever you like.

So White has a take and of course Blue has a double since, OTB, you might judge without too much difficulty that (a) although White must have a take, Blue shouldn't be too far from White's take point and (b) most two-roll sequences are huge market losers -- the 4 good doublets, and nearly everything else except 2-1, I believe, provided White doesn't bear off in 1 roll.

---

I did not mention any extra winning chances due White because Blue has two doublets that do not win in one roll. That's because there aren't any. Blue has two nonworking doublets, but White has one, and that combination is costly to White. Note the progression of side-on-roll's winning chances from a pure 2-roll position when not all initial doublet immediately win:

6/36 + 30/36 * 30/36 = 86.11% <- a pure 2-roll position has 86.11% GWC.

5/36 + 31/36 * 30/36 = 85.65% <- lacking 1 doublet

4/36 + 32/36 * 30/36 = 85.18% <- lacking 2 doublets

So each nonworking doublet for the side-on-roll costs about 0.5% GWC. But in the problem position White one missing doublet outweighs Blue's two:

4/36 + 32/36 * 31/36 = 87.65%

Messages In This Thread

• Bearoff Recube Action
  RobertFontaine -- Sunday, 1 April 2012, at 8:08 p.m.
  • Bearoff Recube Action
    Daniel Murphy -- Sunday, 1 April 2012, at 10:23 p.m.
    • Well done! *NM*
      Taper_Mike -- Tuesday, 3 April 2012, at 1:21 p.m.