On 1/16/2024 3:00 PM, [email protected] wrote:

BTW, XG's estimate that we lose with the safe play
0.02% seems like a massive overestimate to me.

Yes, I agree. I just did a 1 million game rollout and X won every
game. An interesting feature of the rollout is that X won a backgammon
22 times! Of course there's no guarantee that XG is playing correctly
but I think this makes sense. If O rolls 21 then 8/6 7/6 should yield
the best chances of running off the gammon, and that should offset the
slight increase in the risk of losing a backgammon.

As for your original position, these decisions can be tough to figure
out OTB, but if your chances of winning a gammon are over 70% (and
getting hit seriously damages your winning chances) then you should
probably play safe. You can estimate your gammon winning chances by
using standard racing formulas. Running off the gammon is not exactly
the same as winning a normal race, but it's close enough for the
formulas to be useful.

---
Tim Chow

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On 1/18/2024 3:36 PM, Stick Rice wrote:

There is zero chance of the opponent losing a backgammon after we make the safe play in the original position. Even after an immediate roll of [21] and we play both to the six point the opponent is on roll with a 3 roll position. No matter what we

roll over the course of two rolls [21 followed by 21 for eg] we get off the backgammon. Even 3 ply knows this.

It took me a while, but I finally figured out what XG was doing.
As you suggested, we start by giving the opponent a roll of 21,
which is played 8/6 7/6. That gives us the following position
(discussion continues below diagram).


XGID=-CDCb------------bagc-----:1:-1:-1:12:0:0:3:0:10

Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+12-11-10--9--8--7-------6--5--4--3--2--1-+
| O O | | O O | +---+
| O | | O O | | 2 |
| | | O O | +---+
| | | O |
| | | 7 |
| |BAR| |
| | | |
| | | X |
| | | X X X |
| | | O X X X |
| | | O X X X |
+13-14-15-16-17-18------19-20-21-22-23-24-+
Pip count X: 20 O: 122 X-O: 0-0
Cube: 2, O own cube
O to play 12

1. 4-ply 8/6 7/6 eq:-1.839
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:83.91% B:0.01%)

2. 4-ply 21/20 8/6 eq:-1.862 (-0.023)
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:86.19% B:0.01%)

3. 4-ply 21/20 21/19 eq:-1.883 (-0.044)
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:88.27% B:0.00%)

eXtreme Gammon Version: 2.19.211.pre-release


Now suppose X rolls something like 65, taking two checkers off, and
then O rolls 21 again. Evidently, 21/20 and 8/6 and 21/18 have exactly
the same equity, but for whatever reason, XG chooses 21/20 8/6, which
loses some backgammons but gives it better chances of getting off the
gammon.


XGID=-CDAb------------a-ic-----:1:-1:-1:21:0:0:3:0:10

Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+12-11-10--9--8--7-------6--5--4--3--2--1-+
| O | | O O | +---+
| | | O O | | 2 |
| | | O O | +---+
| | | O |
| | | 9 |
| |BAR| |
| | | |
| | | X |
| | | X X |
| | | O X X |
| | | O X X X |
+13-14-15-16-17-18------19-20-21-22-23-24-+
Pip count X: 14 O: 119 X-O: 0-0
Cube: 2, O own cube
O to play 21

1. 4-ply 21/20 8/6 eq:-1.929
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:92.36% B:0.57%)

2. 4-ply 21/18 eq:-1.929
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:92.95% B:0.00%)

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 1/19/2024 8:19 AM, I wrote:

Now suppose X rolls something like 65, taking two checkers off, and
then O rolls 21 again. Evidently, 21/20 and 8/6 and 21/18 have exactly
the same equity

Correction: 21/20 8/6 is apparently slightly better.

XGID=-CDAb------------a-ic-----:1:-1:-1:21:0:0:3:0:10

Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+12-11-10--9--8--7-------6--5--4--3--2--1-+
| O | | O O | +---+
| | | O O | | 2 |
| | | O O | +---+
| | | O |
| | | 9 |
| |BAR| |
| | | |
| | | X |
| | | X X |
| | | O X X |
| | | O X X X |
+13-14-15-16-17-18------19-20-21-22-23-24-+
Pip count X: 14 O: 119 X-O: 0-0
Cube: 2, O own cube
O to play 21

1. Rollout¹ 21/20 8/6 eq:-1.9246
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:91.89% B:0.57%)
Confidence: ±0.0001 (-1.9247..-1.9244) - [100.0%]

2. Rollout¹ 21/18 eq:-1.9252 (-0.0007)
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:92.52% B:0.00%)
Confidence: ±0.0001 (-1.9253..-1.9251) - [0.0%]

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller++
Search interval: Gigantic

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 1/20/2024 5:32 AM, [email protected] wrote:

Besides making an error in your previous post, your logic (as well as Stick's) is hard to follow.
You say that "evidently ... and ... have exactly the same equity." However, such an assertion can't
possibly be "evident" unless we can show that all future sequences (of any possible ply) lead to
the same outcome. It's not like you attempted to show this and made an error in your demonstration:
you didn't attempt to show it.

I attempted to "show" it by quoting the bot as an oracle, but
of course the problem was that I wasn't looking at enough decimal
places.

---
Tim Chow

--- SoupGate-Win32 v1.05
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