From the chouette

Post by Tim Chow
The position below arose in a chouette I was in. The team was X and
there was a lively discussion about wins versus gammons, which I will
tell you more about later, when I post the rollout.
XGID=--A-CbD-E---b-----bcbbb-B-:1:1:1:51:0:0:3:0:10
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 | | O O O O X |
| O | | O O O O X |
| | | O |
| | | |
| | | |
| |BAR| |
| X | | |
| X | | X |
| X | | X X | +---+
| O X | | X O X | | 2 |
| O X | | X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 126 O: 122 X-O: 0-0
Cube: 2, X own cube
X to play 51

Losing the acepoint anchor can be eliminated.
I think the question is whether to make a
three and a half-point board with the two point blot,
anticipating a board strengthening or whether to
safety the two point blot to make it harder for O
to break O's 5 point.
I see the candidates as being 8/2 and 8/3 4/3.

8/3 4/3 seems a more natural play -- O is hardly dying
to break the 5 point anyway so I'll play that.

It might seem anti-QF but note Tim's intro. His (implicit)
promise is that he has something interesting to say about the
wins-versus-gammons tradeoff.
This intro seems to make a pedestrian play more likely because
even with a routine play, there's nothing to preclude such a
fascinating discussion. Tim might say "Although 8/3 4/3 is correct,
it is an interesting fact that 24/23 6/1 wins more gammons."

In other words, Tim's intro means that the standard argument for
innovative plays that: "The checker play must be interesting or Tim
wouldn't have a fascinating comment to make." no longer holds.

Only 50% confidence this time.

Paul

Peter

2020-07-11 10:47:12 UTC

Me too or mee to.

Post by Paul Epstein
It might seem anti-QF but note Tim's intro. His (implicit)
promise is that he has something interesting to say about the
wins-versus-gammons tradeoff.
This intro seems to make a pedestrian play more likely because
even with a routine play, there's nothing to preclude such a
fascinating discussion. Tim might say "Although 8/3 4/3 is correct,
it is an interesting fact that 24/23 6/1 wins more gammons."
In other words, Tim's intro means that the standard argument for
innovative plays that: "The checker play must be interesting or Tim
wouldn't have a fascinating comment to make." no longer holds.
Only 50% confidence this time.
Paul

Paul Epstein

2020-07-11 14:01:37 UTC

Post by Peter

Me too or mee to.

Is "Mitu" an option or is that pronounced differently?

Paul

Peter

2020-07-11 14:13:10 UTC

Post by Peter

Me too or mee to.

Is "Mitu" an option or is that pronounced differently?

The bird?

Post by Paul Epstein
Paul

Paul Epstein

2020-07-17 08:16:28 UTC

Losing the acepoint anchor can be eliminated.
I think the question is whether to make a
three and a half-point board with the two point blot,
anticipating a board strengthening or whether to
safety the two point blot to make it harder for O
to break O's 5 point.
I see the candidates as being 8/2 and 8/3 4/3.
8/3 4/3 seems a more natural play -- O is hardly dying
to break the 5 point anyway so I'll play that.
It might seem anti-QF but note Tim's intro. His (implicit)
promise is that he has something interesting to say about the
wins-versus-gammons tradeoff.
This intro seems to make a pedestrian play more likely because
even with a routine play, there's nothing to preclude such a
fascinating discussion. Tim might say "Although 8/3 4/3 is correct,
it is an interesting fact that 24/23 6/1 wins more gammons."
In other words, Tim's intro means that the standard argument for
innovative plays that: "The checker play must be interesting or Tim
wouldn't have a fascinating comment to make." no longer holds.
Only 50% confidence this time.
Paul

Didn't I call it exactly right?
What a victory!
Although the boring play was correct, it wasn't anti-QF
because the point of the posting was all about the subsequent discussion.

Kudos to me!

Paul

Michael

2020-07-11 11:45:38 UTC

I belong to the group that vored for the tradeoff.
24/23 8/3

b***@gmail.com

2020-07-14 05:42:21 UTC

An obvious play and an obvious exception.

Stick

Tim Chow

2020-07-16 03:30:59 UTC

XGID=--A-CbD-E---b-----bcbbb-B-:1:1:1:51:0:0:3:0:10

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 | | O O O O X |
| O | | O O O O X |
| | | O |
| | | |
| | | |
| |BAR| |
| X | | |
| X | | X |
| X | | X X | +---+
| O X | | X O X | | 2 |
| O X | | X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 126 O: 122 X-O: 0-0
Cube: 2, X own cube
X to play 51

OTB, I suggested that we play 8/3 4/3. Someone else on the team suggested
24/23 8/3 instead. We both agreed that 24/23 8/3 would lose more gammons.
I said that it wasn't even clear to me that 24/23 8/3 would win more often,
but my teammate was convinced that 24/23 8/3 would win more often. The
captain listened to all the debate with interest, and finally decided to
play 24/23 8/3.

Question: Did the captain follow Stick's rule? He had never heard of Stick,
let alone Stick's DMP rule, but if he had, he might have thought that he
was following it. He evidently felt that the DMP play was clear. (And as
it turns out, the computer agrees.) He couldn't assess the win/gammon
tradeoff, so he applied the principle: When the DMP play is clear, make it.

But 24/23 8/3 isn't the bot play, so it follows that the captain *did not*
follow Stick's DMP rule, since Stick's DMP rule is infallible. As Stick
points out, this position falls into the category of obvious exceptions.
Shame on us for failing to follow Stick's DMP rule.

1. Rollout¹ 8/3 4/3 eq:-0.933
Player: 10.11% (G:0.83% B:0.02%)
Opponent: 89.89% (G:17.08% B:0.57%)
Confidence: ±0.002 (-0.935..-0.930) - [100.0%]

2. Rollout¹ 8/3 2/1 eq:-0.942 (-0.009)
Player: 9.40% (G:0.69% B:0.02%)
Opponent: 90.60% (G:16.21% B:0.61%)
Confidence: ±0.002 (-0.944..-0.940) - [0.0%]

3. Rollout¹ 6/1 2/1 eq:-0.944 (-0.011)
Player: 9.56% (G:0.65% B:0.01%)
Opponent: 90.44% (G:16.62% B:0.59%)
Confidence: ±0.002 (-0.946..-0.942) - [0.0%]

4. Rollout¹ 8/2 eq:-0.946 (-0.014)
Player: 9.43% (G:0.60% B:0.01%)
Opponent: 90.57% (G:16.62% B:0.53%)
Confidence: ±0.002 (-0.949..-0.944) - [0.0%]

5. Rollout¹ 6/1 4/3 eq:-0.951 (-0.018)
Player: 9.27% (G:0.73% B:0.02%)
Opponent: 90.73% (G:16.80% B:0.66%)
Confidence: ±0.002 (-0.953..-0.949) - [0.0%]

6. Rollout¹ 8/7 8/3 eq:-0.985 (-0.053)
Player: 9.63% (G:0.84% B:0.03%)
Opponent: 90.37% (G:20.95% B:1.15%)
Confidence: ±0.002 (-0.988..-0.983) - [0.0%]

7. Rollout¹ 8/7 6/1 eq:-1.006 (-0.074)
Player: 9.09% (G:0.74% B:0.02%)
Opponent: 90.91% (G:21.45% B:1.19%)
Confidence: ±0.002 (-1.009..-1.004) - [0.0%]

8. Rollout¹ 24/23 8/3 eq:-1.061 (-0.128)
Player: 14.80% (G:2.92% B:0.13%)
Opponent: 85.20% (G:41.67% B:2.34%)
Confidence: ±0.003 (-1.064..-1.058) - [0.0%]

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

---
DMP
---

XGID=--A-CbD-E---b-----bcbbb-B-:0:0:1:51:0:0:0:1:10

X:Player 1 O:Player 2
Score is X:0 O:0 1 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O | | O O O O X |
| O | | O O O O X |
| | | O |
| | | |
| | | |
| |BAR| |
| X | | |
| X | | X |
| X | | X X |
| O X | | X O X |
| O X | | X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 126 O: 122 X-O: 0-0/1
Cube: 1
X to play 51

1. Rollout¹ 24/23 8/3 eq:-0.740
Player: 13.02% (G:2.50% B:0.14%)
Opponent: 86.98% (G:30.34% B:2.21%)
Confidence: ±0.003 (-0.743..-0.736) - [100.0%]

2. Rollout¹ 24/23 6/1 eq:-0.751 (-0.011)
Player: 12.46% (G:2.10% B:0.03%)
Opponent: 87.54% (G:31.61% B:2.29%)
Confidence: ±0.003 (-0.754..-0.748) - [0.0%]

3. Rollout¹ 8/3 4/3 eq:-0.792 (-0.052)
Player: 10.40% (G:1.44% B:0.03%)
Opponent: 89.60% (G:20.10% B:1.61%)
Confidence: ±0.003 (-0.795..-0.789) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2

---
Tim Chow

b***@gmail.com

2020-07-16 06:52:21 UTC

Post by Tim Chow
XGID=--A-CbD-E---b-----bcbbb-B-:1:1:1:51:0:0:3:0:10
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 | | O O O O X |
| O | | O O O O X |
| | | O |
| | | |
| | | |
| |BAR| |
| X | | |
| X | | X |
| X | | X X | +---+
| O X | | X O X | | 2 |
| O X | | X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 126 O: 122 X-O: 0-0
Cube: 2, X own cube
X to play 51
OTB, I suggested that we play 8/3 4/3. Someone else on the team suggested
24/23 8/3 instead. We both agreed that 24/23 8/3 would lose more gammons.
I said that it wasn't even clear to me that 24/23 8/3 would win more often,
but my teammate was convinced that 24/23 8/3 would win more often. The
captain listened to all the debate with interest, and finally decided to
play 24/23 8/3.
Question: Did the captain follow Stick's rule? He had never heard of Stick,
let alone Stick's DMP rule, but if he had, he might have thought that he
was following it. He evidently felt that the DMP play was clear. (And as
it turns out, the computer agrees.) He couldn't assess the win/gammon
tradeoff, so he applied the principle: When the DMP play is clear, make it.
But 24/23 8/3 isn't the bot play, so it follows that the captain *did not*
follow Stick's DMP rule, since Stick's DMP rule is infallible. As Stick
points out, this position falls into the category of obvious exceptions.
Shame on us for failing to follow Stick's DMP rule.
1. Rollout¹ 8/3 4/3 eq:-0.933
Player: 10.11% (G:0.83% B:0.02%)
Opponent: 89.89% (G:17.08% B:0.57%)
Confidence: ±0.002 (-0.935..-0.930) - [100.0%]
2. Rollout¹ 8/3 2/1 eq:-0.942 (-0.009)
Player: 9.40% (G:0.69% B:0.02%)
Opponent: 90.60% (G:16.21% B:0.61%)
Confidence: ±0.002 (-0.944..-0.940) - [0.0%]
3. Rollout¹ 6/1 2/1 eq:-0.944 (-0.011)
Player: 9.56% (G:0.65% B:0.01%)
Opponent: 90.44% (G:16.62% B:0.59%)
Confidence: ±0.002 (-0.946..-0.942) - [0.0%]
4. Rollout¹ 8/2 eq:-0.946 (-0.014)
Player: 9.43% (G:0.60% B:0.01%)
Opponent: 90.57% (G:16.62% B:0.53%)
Confidence: ±0.002 (-0.949..-0.944) - [0.0%]
5. Rollout¹ 6/1 4/3 eq:-0.951 (-0.018)
Player: 9.27% (G:0.73% B:0.02%)
Opponent: 90.73% (G:16.80% B:0.66%)
Confidence: ±0.002 (-0.953..-0.949) - [0.0%]
6. Rollout¹ 8/7 8/3 eq:-0.985 (-0.053)
Player: 9.63% (G:0.84% B:0.03%)
Opponent: 90.37% (G:20.95% B:1.15%)
Confidence: ±0.002 (-0.988..-0.983) - [0.0%]
7. Rollout¹ 8/7 6/1 eq:-1.006 (-0.074)
Player: 9.09% (G:0.74% B:0.02%)
Opponent: 90.91% (G:21.45% B:1.19%)
Confidence: ±0.002 (-1.009..-1.004) - [0.0%]
8. Rollout¹ 24/23 8/3 eq:-1.061 (-0.128)
Player: 14.80% (G:2.92% B:0.13%)
Opponent: 85.20% (G:41.67% B:2.34%)
Confidence: ±0.003 (-1.064..-1.058) - [0.0%]
¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.19.207.pre-release
---
DMP
---
XGID=--A-CbD-E---b-----bcbbb-B-:0:0:1:51:0:0:0:1:10
X:Player 1 O:Player 2
Score is X:0 O:0 1 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O | | O O O O X |
| O | | O O O O X |
| | | O |
| | | |
| | | |
| |BAR| |
| X | | |
| X | | X |
| X | | X X |
| O X | | X O X |
| O X | | X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 126 O: 122 X-O: 0-0/1
Cube: 1
X to play 51
1. Rollout¹ 24/23 8/3 eq:-0.740
Player: 13.02% (G:2.50% B:0.14%)
Opponent: 86.98% (G:30.34% B:2.21%)
Confidence: ±0.003 (-0.743..-0.736) - [100.0%]
2. Rollout¹ 24/23 6/1 eq:-0.751 (-0.011)
Player: 12.46% (G:2.10% B:0.03%)
Opponent: 87.54% (G:31.61% B:2.29%)
Confidence: ±0.003 (-0.754..-0.748) - [0.0%]
3. Rollout¹ 8/3 4/3 eq:-0.792 (-0.052)
Player: 10.40% (G:1.44% B:0.03%)
Opponent: 89.60% (G:20.10% B:1.61%)
Confidence: ±0.003 (-0.795..-0.789) - [0.0%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2
---
Tim Chow

Is it not an obvious exception? This is like Gilderoy Lockhart obvious. I didn't spend but maybe two seconds on this problem.

Stick

Paul Epstein

2020-07-17 08:13:54 UTC

But isn't Stick's rule meant for very strong players?
I know that "very strong" is a loose term.
But the fact that your captain had never heard of Stick means
that he doesn't follow contemporary backgammon practice and never
takes an interest in major tournaments and doesn't look at backgammon websites etc.
"Obvious" in this context doesn't mean "obvious" to everyone, no
matter how weak.

Paul

Tim Chow

2020-07-18 02:17:17 UTC

Post by Paul Epstein
But isn't Stick's rule meant for very strong players?

Yes. That's why it's infallible. To a sufficiently strong player,
all decisions are obvious. Any apparent counterexample to
Stick's rule is just an obvious exception, and Stick's rule itself
says that it applies only in positions that are not obvious exceptions.

Note that in this case, my teammate understood at least one
aspect of the position better than I did. Namely, he saw that
24/23 was the DMP play. So he was at least strong enough
to get that far.

---
Tim Chow

b***@gmail.com

2020-07-18 03:33:29 UTC

Post by Paul Epstein
But isn't Stick's rule meant for very strong players?

Yes. That's why it's infallible. To a sufficiently strong player,
all decisions are obvious. Any apparent counterexample to
Stick's rule is just an obvious exception, and Stick's rule itself
says that it applies only in positions that are not obvious exceptions.
Note that in this case, my teammate understood at least one
aspect of the position better than I did. Namely, he saw that
24/23 was the DMP play. So he was at least strong enough
to get that far.
---
Tim Chow

So...not going to answer if this is an obvious exception?

Stick

Paul Epstein

2020-07-18 09:21:32 UTC

Post by Paul Epstein
But isn't Stick's rule meant for very strong players?

Yes. That's why it's infallible. To a sufficiently strong player,
all decisions are obvious. Any apparent counterexample to
Stick's rule is just an obvious exception, and Stick's rule itself
says that it applies only in positions that are not obvious exceptions.
Note that in this case, my teammate understood at least one
aspect of the position better than I did. Namely, he saw that
24/23 was the DMP play. So he was at least strong enough
to get that far.
---
Tim Chow

So...not going to answer if this is an obvious exception?

No, it isn't an obvious exception because it's not obvious to me and
I'm stronger than most players who enter backgammon events.

Paul

b***@gmail.com

2020-07-18 12:54:55 UTC

Post by Paul Epstein
But isn't Stick's rule meant for very strong players?

Yes. That's why it's infallible. To a sufficiently strong player,
all decisions are obvious. Any apparent counterexample to
Stick's rule is just an obvious exception, and Stick's rule itself
says that it applies only in positions that are not obvious exceptions.
Note that in this case, my teammate understood at least one
aspect of the position better than I did. Namely, he saw that
24/23 was the DMP play. So he was at least strong enough
to get that far.
---
Tim Chow

So...not going to answer if this is an obvious exception?

No, it isn't an obvious exception because it's not obvious to me and
I'm stronger than most players who enter backgammon events.
Paul

What's your average PR? Maybe I'll survey this week and report back.

Stick

Paul Epstein

2020-07-18 15:19:43 UTC

Post by Paul Epstein
But isn't Stick's rule meant for very strong players?

Yes. That's why it's infallible. To a sufficiently strong player,
all decisions are obvious. Any apparent counterexample to
Stick's rule is just an obvious exception, and Stick's rule itself
says that it applies only in positions that are not obvious exceptions.
Note that in this case, my teammate understood at least one
aspect of the position better than I did. Namely, he saw that
24/23 was the DMP play. So he was at least strong enough
to get that far.
---
Tim Chow

So...not going to answer if this is an obvious exception?

No, it isn't an obvious exception because it's not obvious to me and
I'm stronger than most players who enter backgammon events.
Paul

What's your average PR? Maybe I'll survey this week and report back.

I don't keep careful records but I'll estimate myself at 6.0

Paul

Tim Chow

2020-07-19 15:29:19 UTC

Post by b***@gmail.com
What's your average PR? Maybe I'll survey this week and report back.

Here's how I recommend conducting the survey.

1. Ask the player what they would play. If they say 24/23 then stop, and
count that as a vote for 24/23.

2. If they don't split, then ask them, "What's the DMP play?" See if you
can get them to switch to 24/23 for money. If so, stop, and count that
as a vote for 24/23.

3. If they still won't split, ask them how sure they are. If they express
some uncertainty, record that as "an exception, but not obvious."

4. If they're confident about not splitting for money, but aren't sure that
24/23 is the DMP play, record that as yet another case.

5. The remaining people are sure that 24/23 is the DMP play and are sure
that it's not the money play. These are the "obvious exception" people.

---
Tim Chow

Tim Chow

2020-07-19 01:23:31 UTC

Post by b***@gmail.com
So...not going to answer if this is an obvious exception?

What do you mean? I already said it was. Twice.

---
Tim Chow

Paul Epstein

2020-07-18 08:51:51 UTC

Post by Paul Epstein
But isn't Stick's rule meant for very strong players?

Yes. That's why it's infallible. To a sufficiently strong player,
all decisions are obvious. Any apparent counterexample to
Stick's rule is just an obvious exception, and Stick's rule itself
says that it applies only in positions that are not obvious exceptions.
Note that in this case, my teammate understood at least one
aspect of the position better than I did. Namely, he saw that
24/23 was the DMP play. So he was at least strong enough
to get that far.

But did he know that 24/23 was the DMP play? Or is it that he guessed it
and that his guess was right? This is where people underestimate the degree
of luck in backgammon. People talk about "luck" in the sense of how the rolls
impact your equity. However, since most non-forced plays involve choosing between
<= 3 reasonable alternatives, another extremely important source of luck is
whether you make the right play by chance. That's why PR performances fluctuate
so much. [Of course, here, your team was unlucky in this sense but my point is
that (unless he really was 100% sure about his DMP comment), he would have been
lucky at DMP].
I don't think I would have played 24/23 at DMP. I think the question of when
and how break-acepoint decisions depend on match score would make an
excellent article. Has this topic been covered before?

Paul

Tim Chow

2020-07-19 01:25:08 UTC

Post by Paul Epstein
But did he know that 24/23 was the DMP play?

I don't know what you mean by "know." We have no rigorous mathematical
proof that 24/23 is an equilibrium play at DMP.

---
Tim Chow

Paul Epstein

2020-07-19 08:25:49 UTC

Post by Paul Epstein
But did he know that 24/23 was the DMP play?

I don't know what you mean by "know." We have no rigorous mathematical
proof that 24/23 is an equilibrium play at DMP.

One common pattern (the most common in fact) is that, when a non-obvious
decision needs to be made, a person regularly makes backgammon statements
which are sometimes right and sometimes wrong. These may be of the form:
"X is the best play" or "X would be the best play at DMP".

Sometimes these statements are shown to be right (assuming the bot knows
the truth) and sometimes wrong.

Unless the opinion-giver has a very high accuracy record, it makes no sense
to say that the speaker "knew" the play whenever bot-vindicated. Lucky
guessing also often enters the picture.

I wasn't making the tedious point that if you're less than 99.99% sure about
something, you don't know it. I was saying that "knowing" something requires
more than "thinking something which is later shown to be correct."

Paul

Paul Epstein

2020-07-19 08:33:43 UTC

Post by Paul Epstein
But did he know that 24/23 was the DMP play?

I don't know what you mean by "know." We have no rigorous mathematical
proof that 24/23 is an equilibrium play at DMP.

One common pattern (the most common in fact) is that, when a non-obvious
decision needs to be made, a person regularly makes backgammon statements
"X is the best play" or "X would be the best play at DMP".
Sometimes these statements are shown to be right (assuming the bot knows
the truth) and sometimes wrong.
Unless the opinion-giver has a very high accuracy record, it makes no sense
to say that the speaker "knew" the play whenever bot-vindicated. Lucky
guessing also often enters the picture.
I wasn't making the tedious point that if you're less than 99.99% sure about
something, you don't know it. I was saying that "knowing" something requires
more than "thinking something which is later shown to be correct."
Paul

There's a philosophical conundrum that illustrates the point:
Mary looks at the fuel gauge which indicates that her car has a full tank
of petrol. However, she doesn't realise that her fuel gauge is completely
broken and always indicates a full tank.
Her fuel tank is actually full.

Did Mary know that her tank was full?

Paul

Tim Chow

2020-07-19 15:22:57 UTC

Post by Paul Epstein
Unless the opinion-giver has a very high accuracy record, it makes no sense
to say that the speaker "knew" the play whenever bot-vindicated. Lucky
guessing also often enters the picture.

With this definition, there are almost zero decisions where I know the
right play. The exceptions are the small number of positions where I've
previously looked at a bot verdict and memorized it.

---
Tim Chow

Paul Epstein

2020-07-19 18:26:02 UTC

With this definition, there are almost zero decisions where I know the
right play. The exceptions are the small number of positions where I've
previously looked at a bot verdict and memorized it.

Suppose that you are confident enough about a play that you'd be happy
to take a prop where you win 1 unit if your play is bot-vindicated and
lose 10 units otherwise. And suppose that play is correct. I would
say that you "knew" the right play.
What I'm saying corresponds to something like 95% certainty. From an
expected-value viewpoint, 95% certain means willing to risk 19 units to
gain one but most people would require more than 95% certainty to do this.

Paul

Tim Chow

2020-07-19 18:34:37 UTC

Post by Paul Epstein
Suppose that you are confident enough about a play that you'd be happy
to take a prop where you win 1 unit if your play is bot-vindicated and
lose 10 units otherwise. And suppose that play is correct. I would
say that you "knew" the right play.

Come on. This is flimsier than a Gettier counterexample. All I need to
"know" something here is to love taking risky bets and be lucky. No
intellectual capacity whatsoever is required for this kind of "knowledge."

---
Tim Chow

Paul Epstein

2020-07-19 20:16:48 UTC

So how do you define "knowing the right play"?
I tried to investigate this by encouraging people to give confidence
scores to accompany their quiz answers.

One person adopted the idea -- me.

Paul

Tim Chow

2020-07-21 02:15:55 UTC

Post by Paul Epstein
So how do you define "knowing the right play"?

I don't know. You were the one who introduced the term into this discussion,
not I. I don't think it has a clear meaning.

---
Tim Chow

Paul Epstein

2020-07-21 10:09:13 UTC

Post by Paul Epstein
So how do you define "knowing the right play"?

I don't know. You were the one who introduced the term into this discussion,
not I. I don't think it has a clear meaning.
---
Tim Chow

You strongly implied that your captain deserves commendation for
recognising the correct DMP play.

However, if someone made a correct guess in a coin toss, I doubt that you
would think this reflected good understanding, or anything deserving praise.

What is your criterion for judging whether a backgammon recommendation is
lucky or whether it derives from knowledge?

Paul

Peter

2020-07-21 11:00:34 UTC

Post by Paul Epstein
So how do you define "knowing the right play"?

I don't know. You were the one who introduced the term into this discussion,
not I. I don't think it has a clear meaning.
---
Tim Chow

You strongly implied that your captain deserves commendation for
recognising the correct DMP play.
However, if someone made a correct guess in a coin toss, I doubt that you
would think this reflected good understanding, or anything deserving praise.
What is your criterion for judging whether a backgammon recommendation is
lucky or whether it derives from knowledge?

I'd toss a coin.

Tim Chow

2020-07-21 16:30:01 UTC

Post by Paul Epstein
You strongly implied that your captain deserves commendation for
recognising the correct DMP play.
However, if someone made a correct guess in a coin toss, I doubt that you
would think this reflected good understanding, or anything deserving praise.
What is your criterion for judging whether a backgammon recommendation is
lucky or whether it derives from knowledge?

If I implied commendation, that was a miscommunication on my part.

My point is that for a "rule" or heuristic to be of practical value (rather
than merely be infallible, as Stick's rule is), it has to be usable OTB by
players who aren't already infallible.

Assume toward a contradiction that Stick's DMP rule is supposed to be of
practical value to fallible players. Then presumably the recommended procedure
goes something like this. First, try to figure out what the DMP play is, and
assess whether the DMP play is "clear." Then assess whether the position is
of a type where the money play is "obviously" not the DMP play. If the win
and gammon tradeoff is still unclear to you, and the DMP play is clear, then
just make the DMP play.

This procedure could break down for various reasons. First, you could
misjudge the DMP play, or misjudge how clear it is. Second, you might not
recognize the position as an "obvious" exception. Third, the position might
have a non-obvious win/gammon tradeoff that works out against the DMP play.

I number these "first," "second," and "third" because that's the logical
order. If you can't identify the DMP play, then the rest of the procedure
doesn't make much sense (or at least you can't expect it to produce any kind
of reliable conclusion). So that's the first step.

Returning to the example at hand, my point was that the captain got as far
as assessing 24/23 to be the clear DMP play. I didn't even get that far.
I don't think it matters whether the captain "knows" whether 24/23 is the
DMP play or gets "lucky." The point is that if one is trying to figure out
where things broke down, then for the captain, it *wasn't* at step 1. No
amount of further DMP training for the captain would help the captain at
step 1, because the outcome would be the same (namely, 24/23). On the other
hand, one could reasonably point out that the reason the heuristic broke
down for me was that my understanding of DMP is lacking.

I haven't arrived at a contradiction yet, but the remainder of the proof is
left as an exercise for the reader.

---
Tim Chow

Paul Epstein

2020-07-18 09:03:41 UTC

From your discussion, I think the OTB analysis and discussion was excellent.
However, it's a difficult game so good analysis, discussion, and thought
doesn't guarantee a non-blunder, let alone correct play.
As I've said, my version of the DMP rule is "When deciding on a checkerplay
decision, try to determine the DMP play and give some weight to it."
This is valuable advice, and I don't think the advice is "too obvious to
be worth stating". (Not that anyone said it was).

It's a good thing that your team followed my version of the DMP rule, because
it leads to stronger play in general even though it led your captain astray
in this particular case.

Paul

Michael

2020-07-16 18:54:16 UTC