Here, any 3 that is not answered with a 61 is surely a massive market loser
This happens with probability 14/36 * 17/18 = 119/324. This is nearly
37%. So I'm sure that _considering_ doubling is correct.
One objection to doubling might be that I don't have a particularly big
edge. I'm doing great if I get my 3, but I'm an underdog to make it,
and maybe I'm doing badly enough if I miss to make it a hold.
I thought this might be the case and that's why my double was by no
means confident. The mystery (to me) is that the equity figures
don't make sense. If there's not much to double about, why does D/T
still give me 0.437??
As the title says, big advantage + massive volatility = ND/T here.
What's going on? How can I find my way to a hold in similar positions
in future?

XGID=a-BBABBA---------bAbbdBBd-:1:1:1:00:0:0:3:0:10
X:Daniel O:eXtremeGammon

Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O X | | O O O X X O |
| O | | O O O X X O |
| | | O O |
| | | O O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | | +---+
| | | X X X X | | 2 |
| X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 151 O: 83 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

Analyzed in XG Roller+
Player Winning Chances: 66.93% (G:15.89% B:0.53%)
Opponent Winning Chances: 33.07% (G:15.79% B:0.73%)

Cubeless Equities: No Double=+0.338, Double=+0.678

Cubeful Equities:
No redouble: +0.613
Redouble/Take: +0.437 (-0.176)
Redouble/Pass: +1.000 (+0.387)

Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 23.8%

eXtreme Gammon Version: 2.10

On 5/15/2022 5:02 AM, peps...@gmail.com wrote:
> Here, any 3 that is not answered with a 61 is surely a massive market loser
> This happens with probability 14/36 * 17/18 = 119/324. This is nearly
> 37%. So I'm sure that _considering_ doubling is correct.

Well, if X rolls 31 then he might not lose his market, and even if X
rolls 21 then O can probably take after 11 or 31 as well as 61. But
that doesn't change your main point.

> One objection to doubling might be that I don't have a particularly big
> edge. I'm doing great if I get my 3, but I'm an underdog to make it,
> and maybe I'm doing badly enough if I miss to make it a hold.

I believe this reasoning is sound.

> I thought this might be the case and that's why my double was by no
> means confident. The mystery (to me) is that the equity figures
> don't make sense. If there's not much to double about, why does D/T
> still give me 0.437??

Redoubling as a backgamer is a little different from your typical
redoubling decision. After a bad exchange, you typically have higher
chances of getting gammoned than in a "typical" advantageous position.

More generally, rules of thumb about the relationship between the
equity and the cube action don't always hold for backgame positions.
Dirk Schiemann discusses this point briefly in his book "Theory of
Backgammon," though I think he only explicitly considers cube actions
in which the backgamee is on roll, rather than post-hit backgamer
cube actions.

---
Tim Chow

Oh, another thing is that if you roll it out, the size of the
error seems to be smaller than what XGR+ thinks. I didn't feel
like doing a full rollout, but the short rollout below should
give you some idea.

XGID=a-BBABBA---------bAbbdBBd-:1:1:1:00:0:0:3:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O X | | O O O X X O |
| O | | O O O X X O |
| | | O O |
| | | O O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | | +---+
| | | X X X X | | 2 |
| X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 151 O: 83 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble
Player Winning Chances: 67.02% (G:16.14% B:0.55%)
Opponent Winning Chances: 32.98% (G:15.76% B:0.66%)
Redouble/Take
Player Winning Chances: 68.41% (G:17.19% B:0.77%)
Opponent Winning Chances: 31.59% (G:15.83% B:0.64%)

Cubeful Equities:
No redouble: +0.634
Redouble/Take: +0.555 (-0.080)
Redouble/Pass: +1.000 (+0.366)

Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 15.2%

Rollout:
400 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 4-ply, cube decisions: XG Roller+
Search interval: Large
Confidence No Double: ± 0.013 (+0.621..+0.648)
Confidence Double: ± 0.031 (+0.524..+0.586)

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

On Sunday, May 15, 2022 at 8:33:11 PM UTC+1, Tim Chow wrote:
> On 5/15/2022 5:02 AM, peps...@gmail.com wrote:
> > Here, any 3 that is not answered with a 61 is surely a massive market loser
> > This happens with probability 14/36 * 17/18 = 119/324. This is nearly
> > 37%. So I'm sure that _considering_ doubling is correct.
> Well, if X rolls 31 then he might not lose his market, and even if X
> rolls 21 then O can probably take after 11 or 31 as well as 61. But
> that doesn't change your main point.
> > One objection to doubling might be that I don't have a particularly big
> > edge. I'm doing great if I get my 3, but I'm an underdog to make it,
> > and maybe I'm doing badly enough if I miss to make it a hold.
> I believe this reasoning is sound.
> > I thought this might be the case and that's why my double was by no
> > means confident. The mystery (to me) is that the equity figures
> > don't make sense. If there's not much to double about, why does D/T
> > still give me 0.437??
> Redoubling as a backgamer is a little different from your typical
> redoubling decision. After a bad exchange, you typically have higher
> chances of getting gammoned than in a "typical" advantageous position.
>
> More generally, rules of thumb about the relationship between the
> equity and the cube action don't always hold for backgame positions.
> Dirk Schiemann discusses this point briefly in his book "Theory of
> Backgammon," though I think he only explicitly considers cube actions
> in which the backgamee is on roll, rather than post-hit backgamer
> cube actions.

I think my 3s aren't quite as good as they seem. I actually rolled a 33 after doubling
(which is not one of the better 3s admittedly) and XG thought that increased my
equity by 0.276 judging it to be below the joker threshold. When I'm stuck so far back,
XG might have time for the ace and six. 3's are market losers, yes but not by so much
that I need to double now.
Thanks for your thoughts on this.

Paul