Discussion:
Why is breaking the 6-prime better?
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c***@gmail.com
2020-06-20 18:00:10 UTC
Permalink
I'll admit I'm not very skilled, but I am trying to understand the game and ultimately improve. In the position below why is breaking the six point prime with 8/2* better than running with 20/15 10/9 thus maintaining the prime?

Only edge I can see is hitting offers 9% more gammon chances with 1.9% less game winning chances. Your comments are appreciated.

XGID=b-aBBBBBB-A-----bbccBb----:1:-1:1:51:0:0:0:0:10

X:Michael O:eXtremeGammon
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O O O | | O X O | +---+
| O O O | | O X O | | 2 |
| O | | O | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | O | |
| | | |
| X X | | X X X X |
| X X X | | X X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 116 O: 154 X-O: 0-0
Cube: 2, O own cube
X to play 51

1. XG Roller++ 8/2* eq:+1.173
Player: 82.43% (G:57.64% B:3.49%)
Opponent: 17.57% (G:2.38% B:0.14%)

2. XG Roller++ 10/9 7/2* eq:+1.140 (-0.033)
Player: 81.38% (G:57.10% B:3.44%)
Opponent: 18.62% (G:2.59% B:0.15%)

3. XG Roller++ 20/15 10/9 eq:+1.129 (-0.044)
Player: 84.31% (G:48.67% B:2.82%)
Opponent: 15.69% (G:1.58% B:0.12%)

4. XG Roller++ 7/6 7/2* eq:+1.127 (-0.046)
Player: 80.72% (G:57.36% B:3.51%)
Opponent: 19.28% (G:2.66% B:0.14%)

5. XG Roller++ 7/2* 2/1 eq:+1.107 (-0.066)
Player: 80.75% (G:56.14% B:2.91%)
Opponent: 19.25% (G:2.92% B:0.16%)


eXtreme Gammon Version: 2.10
b***@gmail.com
2020-06-21 00:52:41 UTC
Permalink
Post by c***@gmail.com
I'll admit I'm not very skilled, but I am trying to understand the game and ultimately improve. In the position below why is breaking the six point prime with 8/2* better than running with 20/15 10/9 thus maintaining the prime?
Only edge I can see is hitting offers 9% more gammon chances with 1.9% less game winning chances. Your comments are appreciated.
XGID=b-aBBBBBB-A-----bbccBb----:1:-1:1:51:0:0:0:0:10
X:Michael O:eXtremeGammon
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O O O | | O X O | +---+
| O O O | | O X O | | 2 |
| O | | O | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | O | |
| | | |
| X X | | X X X X |
| X X X | | X X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 116 O: 154 X-O: 0-0
Cube: 2, O own cube
X to play 51
1. XG Roller++ 8/2* eq:+1.173
Player: 82.43% (G:57.64% B:3.49%)
Opponent: 17.57% (G:2.38% B:0.14%)
2. XG Roller++ 10/9 7/2* eq:+1.140 (-0.033)
Player: 81.38% (G:57.10% B:3.44%)
Opponent: 18.62% (G:2.59% B:0.15%)
3. XG Roller++ 20/15 10/9 eq:+1.129 (-0.044)
Player: 84.31% (G:48.67% B:2.82%)
Opponent: 15.69% (G:1.58% B:0.12%)
4. XG Roller++ 7/6 7/2* eq:+1.127 (-0.046)
Player: 80.72% (G:57.36% B:3.51%)
Opponent: 19.28% (G:2.66% B:0.14%)
5. XG Roller++ 7/2* 2/1 eq:+1.107 (-0.066)
Player: 80.75% (G:56.14% B:2.91%)
Opponent: 19.25% (G:2.92% B:0.16%)
eXtreme Gammon Version: 2.10
Basically you don't want him to anchor and as you said, hitting/keeping him from anchoring earns you quite a few more gammons at little risk. The thing is, the opponent's offensive position isn't as formidable as you may think. Even if you are hit back you simply enter immediately and either continue the blitz or remake the 6 prime. No harm no foul to try for the closeout.

I would suggest you playing this out v. XG as many times as you like until you're comfortable knowing that hitting is the correct play. Ctrl + C to copy the position, ctrl + P to paste it into XG. From there Setup >> Play from Position. Play out the hitting roll. It will go quickly as you don't need to play out the entire game to understand what is happening in the near future.

Stick
Tim Chow
2020-06-21 03:08:20 UTC
Permalink
Post by c***@gmail.com
Only edge I can see is hitting offers 9% more gammon chances with 1.9% less
game winning chances. Your comments are appreciated.
I would add that, although it's not the case here, sometimes breaking the
prime to attack not only wins more gammons, but wins more games. It depends
on how strong the opponent's offensive position is. In such positions, I
think it's good to ask, "What am I afraid of?" Getting hit is certainly
one thing you might be afraid of, but letting your opponent anchor and play
a holding game is also something you should be at least somewhat afraid of.

Here's a variant of your position where your opponent's position is weaker,
and the computer hits even at double match point, when gammons don't matter.

XGID=b-aBBBBBB-A------bccBb-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 X O O |
| O O | | O X O O |
| O | | O |
| | | |
| | | |
| |BAR| |
| | O | |
| | O | |
| | | |
| X X | | X X X X |
| X X X | | X X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 116 O: 140 X-O: 0-0/1
Cube: 1
X to play 51

1. Rollout¹ 8/2* eq:+0.806
Player: 90.30% (G:61.14% B:5.48%)
Opponent: 9.70% (G:1.10% B:0.10%)
Confidence: ±0.004 (+0.802..+0.810) - [100.0%]

2. Rollout¹ 20/15 10/9 eq:+0.789 (-0.017)
Player: 89.46% (G:51.19% B:6.27%)
Opponent: 10.54% (G:0.69% B:0.07%)
Confidence: ±0.005 (+0.785..+0.794) - [0.0%]

3. Rollout¹ 20/14 eq:+0.785 (-0.021)
Player: 89.27% (G:50.35% B:6.24%)
Opponent: 10.73% (G:0.62% B:0.04%)
Confidence: ±0.004 (+0.781..+0.790) - [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
Paul Epstein
2020-06-21 09:48:10 UTC
Permalink
Post by Tim Chow
I would add that, although it's not the case here, sometimes breaking the
prime to attack not only wins more gammons, but wins more games. It depends
on how strong the opponent's offensive position is.
I think the fact that breaking the prime wins more games is something I would have expected.
There is significant crunching danger without 20/15.
I would probably have (wrongly) played 20/15 OTB in the OP's position..
It's a great counter-example to Stick's DMP rule since 20/15 can fairly
be said to be clear at DMP since the crunching danger is really palpable.

Paul
Tim Chow
2020-06-21 14:12:37 UTC
Permalink
Post by Paul Epstein
I think the fact that breaking the prime wins more games is something
I would have expected.
There is significant crunching danger without 20/15.
I would probably have (wrongly) played 20/15 OTB in the OP's position..
It's a great counter-example to Stick's DMP rule since 20/15 can fairly
be said to be clear at DMP since the crunching danger is really palpable.
I don't quite follow what you're saying here. In the first sentence, did
you mean to say that you would have expected that *leaping* the prime wins
more games?

Your first sentence as written says that you would have expected 8/2* to
win more games. And surely it's pretty clear that 8/2* wins more gammons.
What then would have motivated you to have played 20/15?

And by the way, there are no counter-examples to Stick's DMP rule. If you
think you've found one then it means you don't understand the rule properly,
or you're nit-picking at an amazingly good rule that many of the world's
top players love.

---
Tim Chow
Paul Epstein
2020-06-21 14:58:21 UTC
Permalink
Post by Tim Chow
Post by Paul Epstein
I think the fact that breaking the prime wins more games is something
I would have expected.
There is significant crunching danger without 20/15.
I would probably have (wrongly) played 20/15 OTB in the OP's position..
It's a great counter-example to Stick's DMP rule since 20/15 can fairly
be said to be clear at DMP since the crunching danger is really palpable.
I don't quite follow what you're saying here. In the first sentence, did
you mean to say that you would have expected that *leaping* the prime wins
more games?
Your first sentence as written says that you would have expected 8/2* to
win more games. And surely it's pretty clear that 8/2* wins more gammons.
What then would have motivated you to have played 20/15?
And by the way, there are no counter-examples to Stick's DMP rule. If you
think you've found one then it means you don't understand the rule properly,
or you're nit-picking at an amazingly good rule that many of the world's
top players love.
I did make a mistake (I know that's hard to believe but I did) and I think
you made an accurate guess about what the mistake was.
Please substitute "leaping" for "breaking". I'm not surprised that leaping
the prime wins more games and I would have (wrongly) leapt the prime OTB.

Paul

Tim Chow
2020-06-21 14:23:05 UTC
Permalink
For good measure, here's a variant that illustrates the tipping point
in the other direction, where getting hit is worse for X than in the
original position.

XGID=b-aBBBBBB-A------bccbBb---:1:-1:1:51:0:0:0:0:10

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-+
| O O | | O O X O | +---+
| O O | | O O X O | | 2 |
| O | | O | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | O | |
| | | |
| X X | | X X X X |
| X X X | | X X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 118 O: 144 X-O: 0-0
Cube: 2, O own cube
X to play 51

1. Rollout¹ 21/16 10/9 eq:+1.147
Player: 87.39% (G:44.05% B:2.25%)
Opponent: 12.61% (G:1.33% B:0.09%)
Confidence: ±0.006 (+1.141..+1.153) - [60.0%]

2. Rollout¹ 8/2* eq:+1.146 (-0.001)
Player: 83.53% (G:54.24% B:2.87%)
Opponent: 16.47% (G:2.80% B:0.14%)
Confidence: ±0.007 (+1.138..+1.153) - [37.6%]

3. Rollout¹ 21/15 eq:+1.140 (-0.007)
Player: 87.21% (G:44.15% B:2.23%)
Opponent: 12.79% (G:1.54% B:0.12%)
Confidence: ±0.006 (+1.134..+1.147) - [2.4%]

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

---
Tim Chow
Paul Epstein
2020-06-21 07:04:24 UTC
Permalink
Post by c***@gmail.com
I'll admit I'm not very skilled, but I am trying to understand the game and ultimately improve. In the position below why is breaking the six point prime with 8/2* better than running with 20/15 10/9 thus maintaining the prime?
Only edge I can see is hitting offers 9% more gammon chances with 1.9% less game winning chances. Your comments are appreciated.
Your question can be broken down into two parts:
How is the play consistent with the results in terms of the favourable
gammons won/ single games won/ gammons lost/ single games lost breakdown?

Once we accept the above breakdown, why is the play good?

The first question has been handled by others but not the second question.
If we lose a single game instead of winning it, then our score moves from
+2 to -2 (a penalty of 4). If we get a gammon instead of a single game,
our score moves from +2 to +4 (a gain of 2).
Your 1.9% and 9% stats are accurate (which is great).
Applying the penalty and gain above, we get a penalty of 1.9% * 4
and a gain of 9% * 2.
Since the gain is larger than the penalty, the play is stronger than
the play it's being compared with.

This leads to a third question but it's a question for me.
Why is the above analysis provided rather than just assuming that the
OP knows how to perform these kind of single win/ gammon tradeoffs?

The reason is that the "Only edge I can see" phrase indicates that
you might not understand this point since this "only" edge is the
entire justification for the play.

For example, the main criterion of the goodness of a restaurant is
probably the food quality. So a person wouldn't normally say
"The only thing I like about the restaurant is that the food's great."

Paul
c***@gmail.com
2020-06-21 14:14:20 UTC
Permalink
Post by Paul Epstein
This leads to a third question but it's a question for me.
Why is the above analysis provided rather than just assuming that the
OP knows how to perform these kind of single win/ gammon tradeoffs?
The reason is that the "Only edge I can see" phrase indicates that
you might not understand this point since this "only" edge is the
entire justification for the play.
Paul
Excellent point Paul, thank you. I needed to apply my EV (expected value) analysis from poker to reach your mathematical conclusion. Now I can transfer a poker tool to my BG game.

Appreciate the thoughtful comments from everyone.
Michael
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