XGID=-aa-BBCaC---cB---bbcbB-A--:0:0:1:55:0:0:0:0:10
X:Player 1 O:Player 2

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X X |
| X O O | | O O X |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| O X | | X |
| O X | | X X X |
| O X O | | X X X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 151 O: 162 X-O: 0-0
Cube: 1
X to play 55
--
BD

On 12/9/2022 4:26 AM, BlueDice wrote:
> XGID=-aa-BBCaC---cB---bbcbB-A--:0:0:1:55:0:0:0:0:10
> X:Player 1 O:Player 2
>
> Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X O O | | O O X X |
> | X O O | | O O X |
> | | | O |
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | O X | | X |
> | O X | | X X X |
> | O X O | | X X X O O |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 151 O: 162 X-O: 0-0
> Cube: 1
> X to play 55

Tough one. The first play I'd consider is 21/11(2). The main
disadvantage is that this play abandons X's straggler. What else
is there? We could hit with 6/1*, after which it seems we should
play 8/3(2) with the next two 5's, and then some other 5. This
play is great when it works, but is pretty bad if O hits back,
and even if O doesn't hit back right away, X still has to
extricate his back checkers.

Other plays include 13/3(2), which I don't like because it
disconnects X's position and doesn't do anything to get the back
checkers going, and 21/16(2) 13/8(2), which tries not to abandon
the back checker but doesn't look better than 21/11(2). Or we
could hit 6/1* and not make the 3pt; e.g. 21/15(2) 13/8 6/1*.
This could be correct but it still look to me that if we hit
then we should make the 3pt.

Not sure at all but OTB, I'd probably go with my first instinct
of 21/11(2).

---
Tim Chow

On Friday, December 9, 2022 at 2:08:02 PM UTC, Tim Chow wrote:
> On 12/9/2022 4:26 AM, BlueDice wrote:
> > XGID=-aa-BBCaC---cB---bbcbB-A--:0:0:1:55:0:0:0:0:10
> > X:Player 1 O:Player 2
> >
> > Score is X:0 O:0. Unlimited Game
> > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > | X O O | | O O X X |
> > | X O O | | O O X |
> > | | | O |
> > | | | |
> > | | | |
> > | |BAR| |
> > | | | |
> > | | | |
> > | O X | | X |
> > | O X | | X X X |
> > | O X O | | X X X O O |
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 151 O: 162 X-O: 0-0
> > Cube: 1
> > X to play 55
> Tough one. The first play I'd consider is 21/11(2). The main
> disadvantage is that this play abandons X's straggler. What else
> is there? We could hit with 6/1*, after which it seems we should
> play 8/3(2) with the next two 5's, and then some other 5. This
> play is great when it works, but is pretty bad if O hits back,
> and even if O doesn't hit back right away, X still has to
> extricate his back checkers.
>
> Other plays include 13/3(2), which I don't like because it
> disconnects X's position and doesn't do anything to get the back
> checkers going, and 21/16(2) 13/8(2), which tries not to abandon
> the back checker but doesn't look better than 21/11(2). Or we
> could hit 6/1* and not make the 3pt; e.g. 21/15(2) 13/8 6/1*.
> This could be correct but it still look to me that if we hit
> then we should make the 3pt.
>
> Not sure at all but OTB, I'd probably go with my first instinct
> of 21/11(2).
>
> ---
> Tim Chow

Anything other than (A) 21/16(2) 8/3(2) is a blunder
I looked at the equity swing after opp's reply rolls.
Comparing (A) with (B) 21/11(2) below.
Equities for non-doublets count twice.

The top 3 rolls that favour (A):
42; Swing = 1.432
54; Swing = 0.962
43; Swing = 0.962

The top 3 rolls that favour (B):
66; Swing = 0.694
61; Swing = 0.592
11; Swing = 0.300

1. XG Roller++ 21/16(2) 8/3(2) eq:+0.447
Player: 56.88% (G:26.63% B:1.31%)
Opponent: 43.12% (G:10.97% B:0.52%)

2. XG Roller++ 21/16(2) 13/8(2) eq:+0.331 (-0.115)
Player: 56.47% (G:18.89% B:0.65%)
Opponent: 43.53% (G:8.90% B:0.33%)

3. XG Roller++ 21/11(2) eq:+0.289 (-0.157)
Player: 55.18% (G:18.64% B:0.69%)
Opponent: 44.82% (G:9.12% B:0.35%)

4. XG Roller++ 21/16 8/3(2) 6/1* eq:+0.254 (-0.192)
Player: 51.93% (G:28.27% B:1.50%)
Opponent: 48.07% (G:14.93% B:1.07%)

5. XG Roller++ 13/3(2) eq:+0.165 (-0.282)
Player: 49.85% (G:23.18% B:0.82%)
Opponent: 50.15% (G:10.20% B:0.36%)
--
BD

On 12/10/2022 1:32 PM, BlueDice wrote:
> Anything other than (A) 21/16(2) 8/3(2) is a blunder

Fantastic problem!!

What I find hard to see is that O's hitting aces are
apparently not such terrible news for X, compared to
how O's aces play after 21/11(2). (That O's sixes are
duplicated to hit and anchor is easier to see.)

---
Tim Chow

On Sunday, December 11, 2022 at 2:07:28 PM UTC, Tim Chow wrote:
> On 12/10/2022 1:32 PM, BlueDice wrote:
> > Anything other than (A) 21/16(2) 8/3(2) is a blunder
> Fantastic problem!!
>
> What I find hard to see is that O's hitting aces are
> apparently not such terrible news for X, compared to
> how O's aces play after 21/11(2). (That O's sixes are
> duplicated to hit and anchor is easier to see.)
>
> ---
> Tim Chow

> What I find hard to see is that O's hitting aces..

21, 41 and 51 would have been anchor making rolls after 21/11(2)
giving O a small equity gain on these rolls compared to hitting after 21/16(2) 8/3(2).
O gains much more after 31, 11 & 61 but even these 3 added together do not compensate
for the swing on 42 between the above plays.
--
BD