The two legal 33s differ in equity by about one trillionth.
But (particularly if you're having trouble sleeping), why not try
to use your combinatorial logic to figure out which is correct?
I guessed wrong, by the way.
I suppose zero is close to a trillionth so the two equities could
be the same.
But they aren't -- your opinion really does matter.
Paul
XGID=-ECE--A-----------A-aaa---:1:1:1:33:6:8:3:0:10
X:Daniel O:eXtremeGammon
Score is X:6 O:8. Unlimited Game, Jacoby Beaver +13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O O O |
| | | |
| | | |
| | | |
| | | |
| |BAR| |
| | | X X |
| | | X X |
| | | X X X | +---+
| | | X X X | | 2 |
| | | X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 50 O: 12 X-O: 6-8
Cube: 2, X own cube
X to play 33
I think your proof is correct. Below is a rollout with XG's
strongest settings, with variance reduction *turned off* and with
36^4 = 1679616 trials. The results are as expected.
XGID=-ECE--A-----------A-aaa---:1:1:1:33:0:0:3:0:10
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-+
| X | | O O O |
| | | |
| | | |
| | | |
| | | |
| |BAR| |
| | | X X |
| | | X X |
| | | X X X | +---+
| | | X X X | | 2 |
| | | X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 50 O: 12 X-O: 0-0
Cube: 2, X own cube
X to play 33
1. Rollout¹ 18/9 6/3 eq:-1.1209
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:12.09% B:0.00%)
Confidence: ±0.0003 (-1.1212..-1.1206) - [53.4%]
2. Rollout¹ 18/6 eq:-1.1209
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:12.09% B:0.00%)
Confidence: ±0.0003 (-1.1212..-1.1206) - [46.6%]
¹ 1679616 Games rolled.
Dice Seed: 271828
Moves and cube decisions: XG Roller++
Search interval: Gigantic
eXtreme Gammon Version: 2.19.207.pre-release
Interestingly, though, if we turn *on* variance reduction
and repeat the rollout, then XG is very confident that 18/9
6/3 is slightly better. (It actually reaches 100% confidence
very early on in the rollout and never wavers.) So this is
some kind of bug in XG. In my version of XG, I can examine
just how many times X loses a gammon. After 18/9 6/3, it
loses a gammon 203015 times, and after 18/6, it loses a gammon
203045 times. So it doesn't seem to be a bug in the way it
performs the rollout trials, but a bug in the way it does the
variance reduction, or calculates the numbers that it chooses
to display.
XGID=-ECE--A-----------A-aaa---:1:1:1:33:0:0:3:0:10
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-+
| X | | O O O |
| | | |
| | | |
| | | |
| | | |
| |BAR| |
| | | X X |
| | | X X |
| | | X X X | +---+
| | | X X X | | 2 |
| | | X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 50 O: 12 X-O: 0-0
Cube: 2, X own cube
X to play 33
1. Rollout¹ 18/9 6/3 eq:-1.1209
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:12.09% B:0.00%)
Confidence: ±0.0000 (-1.1209..-1.1209) - [100.0%]
2. Rollout¹ 18/6 eq:-1.1211 (-0.0002)
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:12.11% B:0.00%)
Confidence: ±0.0000 (-1.1211..-1.1211) - [0.0%]
¹ 1679616 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller++
Search interval: Gigantic
So why does XG give us this 11.4% nonsense??
I wasn't using > 4 ply reasoning above so why couldn't XG do what I did?
On 12/5/2021 6:44 AM, peps...@gmail.com wrote:
So why does XG give us this 11.4% nonsense??I don't know exactly, but I discovered something interesting.
I wasn't using > 4 ply reasoning above so why couldn't XG do what I did?
Look what happens if I force XG to perform a 1-ply analysis
of O's decision after each of X's possible plays. For some
reason, after 18/6, if O rolls 31, then all of O's choices are
evaluated equally as 1.000. When this happens, it seems to me
that XG has a chance of misplaying the roll.
This may also partly explain the variance reduction thing, since
I believe that luck is calculated using 1-ply analysis.
--------------
After 18/9 6/3
--------------
XGID=-ECF-----A----------aaa---:1:1:-1:13:0:0:3:0:10
X:Player 1 O:Player 2
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 |
| | | |
| | | |
| | | |
| | | |
| |BAR| |
| | | 6 X |
| | | X X |
| | | X X X | +---+
| | | X X X | | 2 |
| X | | X X X | +---+
+13-14-15-16-17-18------19-20-21-22-23-24-+
Pip count X: 38 O: 12 X-O: 0-0
Cube: 2, X own cube
O to play 13
1. 1-ply 4/Off eq:+1.030
Player: 100.00% (G:2.99% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
2. 1-ply 5/4 3/Off eq:+1.014 (-0.016)
Player: 100.00% (G:1.43% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
3. 1-ply 5/2 3/2 eq:+1.014 (-0.016)
Player: 100.00% (G:1.38% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
4. 1-ply 4/1 3/2 eq:+1.009 (-0.021)
Player: 100.00% (G:0.92% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
5. 1-ply 5/2 4/3 eq:+1.009 (-0.021)
Player: 100.00% (G:0.91% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
6. 1-ply 5/1 eq:+1.009 (-0.021)
Player: 100.00% (G:0.89% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
----------
After 18/6
----------
XGID=-ECE--B-------------aaa---:1:1:-1:13:0:0:3:0:10
X:Player 1 O:Player 2
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 |
| | | |
| | | |
| | | |
| | | |
| |BAR| |
| | | X X |
| | | X X |
| | | X X X | +---+
| | | X X X X | | 2 |
| | | X X X X | +---+
+13-14-15-16-17-18------19-20-21-22-23-24-+
Pip count X: 38 O: 12 X-O: 0-0
Cube: 2, X own cube
O to play 13
1. 1-ply 4/Off eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
2. 1-ply 5/4 3/Off eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
3. 1-ply 5/2 3/2 eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
4. 1-ply 5/2 4/3 eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
5. 1-ply 5/1 eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
6. 1-ply 4/1 3/2 eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
eXtreme Gammon Version: 2.19.207.pre-release
Yes, I think that resolves it.
After 18/6, XG sometimes misplays (or intends to misplay) 31.
This results in XG underestimating its gammons after 18/6 and therefore wrongly preferring 18/6.
Surprising (to me) to see such a basic bug in a program that strong.
On 12/5/2021 8:50 AM, peps...@gmail.com wrote:
Yes, I think that resolves it.
After 18/6, XG sometimes misplays (or intends to misplay) 31.
This results in XG underestimating its gammons after 18/6 and therefore wrongly preferring 18/6.
Surprising (to me) to see such a basic bug in a program that strong.I'm no longer certain that it's a "bug." If it's just a matter of
the neural net misevaluating a position, I don't consider that a bug,
even if it looks to a human like a "simple" position.
On the other hand, with variance reduction, what you're supposed to
do is add a random variable whose expected value is zero. Ensuring
that the expected value is zero doesn't require perfect evaluations
of positions. But somehow it seems that whatever XG is adding does
not converge to zero in the limit of more and more trials. Maybe I
am underestimating the difficulties in ensuring that the expected
value is literally zero, but this part looks like a bug to me.
---
Tim Chow
On Sunday, December 5, 2021 at 9:44:43 PM UTC-5, Tim Chow wrote:if that wasn't clear.
On 12/5/2021 8:50 AM, peps...@gmail.com wrote:
Yes, I think that resolves it.
After 18/6, XG sometimes misplays (or intends to misplay) 31.
This results in XG underestimating its gammons after 18/6 and therefore wrongly preferring 18/6.
Surprising (to me) to see such a basic bug in a program that strong.I'm no longer certain that it's a "bug." If it's just a matter of
the neural net misevaluating a position, I don't consider that a bug,
even if it looks to a human like a "simple" position.
On the other hand, with variance reduction, what you're supposed to
do is add a random variable whose expected value is zero. Ensuring
that the expected value is zero doesn't require perfect evaluations
of positions. But somehow it seems that whatever XG is adding does
not converge to zero in the limit of more and more trials. Maybe I
am underestimating the difficulties in ensuring that the expected
value is literally zero, but this part looks like a bug to me.
---I only skimmed the thread so if what I'm saying is wrong ignore it, but XG with variance reduction turned on gets the right answer too? Felt to me like it was suggested that was an issue, it's not. Paul originally posted a 4 ply analysis, not rollout,
Tim Chow
StickYes, I would kind of expect a 4 ply analysis to give the right answers, particularly since I didn't find it hard to solve the problem by hand.
On 12/6/2021 1:43 PM, J R wrote:
I only skimmed the thread so if what I'm saying is wrong ignore it,
but XG with variance reduction turned on gets the right answer too?
Felt to me like it was suggested that was an issue, it's not. Paul
originally posted a 4 ply analysis, not rollout, if that wasn't clear.
I did a rollout with over 1.6 million trials, moves and cube decisions
XGR++, Gigantic move filter, variance reduction turned on. The result incorrectly suggested that 18/9 6/3 is better than 18/6, when the truth
is they're equal.
I only skimmed the thread so if what I'm saying is wrong ignore it, but XG with variance reduction turned on gets the right answer too? Felt to me like it was suggested that was an issue, it's not. Paul originally posted a 4 ply analysis, not rollout,if that wasn't clear.
On 12/5/2021 8:50 AM, peps...@gmail.com wrote:
Surprising (to me) to see such a basic bug in a
program that strong.
I'm no longer certain that it's a "bug." If it's just a
matter of the neural net misevaluating a position,
Can I translate the above two paragraphs as:
On 12/10/2021 1:48 AM, MK wrote:
Can I translate the above two paragraphs as:Yes, it's a free country.
On Saturday, December 11, 2021 at 1:56:05 AM UTC, Tim Chow wrote:
On 12/10/2021 1:48 AM, MK wrote:
Can I translate the above two paragraphs as:Yes, it's a free country.
What country do you assign this forum to?
On 12/10/2021 1:48 AM, MK wrote:
Can I translate the above two paragraphs as:
Yes, it's a free country.
The relevant country for assessing MK's right to
translate is MK's country of residence, which he
has said is the United States.
On Saturday, December 11, 2021 at 1:56:05 AM UTC, Tim Chow wrote:
Yes, it's a free country.
What country do you assign this forum to?
On December 10, 2021 at 6:56:05 PM UTC-7, Tim Chow wrote:
On 12/10/2021 1:48 AM, MK wrote:
Can I translate the above two paragraphs as:
Yes, it's a free country.
You can't go more than a few days without feeling
the urge to be a jackass jerk, can you
On December 11, 2021 at 7:24:48 AM UTC-7, Tim Chow wrote:
The relevant country for assessing MK's right to
translate is MK's country of residence, which he
has said is the United States.
People, please just ignore this senseless jackass...
1. 4-ply 18/6 eq:-1.114
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:11.40% B:0.00%)
2. 4-ply 18/9 6/3 eq:-1.121 (-0.007)
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:12.10% B:0.00%)
But what is wrong with my proof that the choices are equivalent?
Since our opponent is guaranteed to bear off in four rolls, we are simply trying
to max our probability of saving the gammon.
If our opponent takes exactly two rolls to bear off then 18/6 loses a gammon to 54,
and 18/9 6/3 loses a gammon to 21.
If the opponent takes more than two rolls to bear off, both plays save the gammon.
So what am I missing??
What makes this particularly puzzling is that it's hard to see how a miscounting could
drop as little equity as 0.7%. If the plays were between 2% to 5% apart, I'd be less puzzled.
On 5-12-2021 0:17, peps...@gmail.com wrote:
1. 4-ply 18/6 eq:-1.114
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:11.40% B:0.00%)
2. 4-ply 18/9 6/3 eq:-1.121 (-0.007)
Player: 0.00% (G:0.00% B:0.00%)
Opponent: 100.00% (G:12.10% B:0.00%)
I can't test it right now, but the "weird stuff" might have to do with
play #1 using values from the bear-off database and play #2 using the
neural net (at first).
----------
After 18/6
----------
XGID=-ECE--B-------------aaa---:1:1:-1:13:0:0:3:0:10
X:Player 1 O:Player 2
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 |
| | | |
| | | |
| | | |
| | | |
| |BAR| |
| | | X X |
| | | X X |
| | | X X X | +---+
| | | X X X X | | 2 |
| | | X X X X | +---+
+13-14-15-16-17-18------19-20-21-22-23-24-+
Pip count X: 38 O: 12 X-O: 0-0
Cube: 2, X own cube
O to play 13
1. 1-ply 4/Off eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
2. 1-ply 5/4 3/Off eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
3. 1-ply 5/2 3/2 eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
4. 1-ply 5/2 4/3 eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
5. 1-ply 5/1 eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
6. 1-ply 4/1 3/2 eq:+1.000
Player: 100.00% (G:0.00% B:0.00%)
Opponent: 0.00% (G:0.00% B:0.00%)
eXtreme Gammon Version: 2.19.207.pre-release
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