4a 3a cube action

Walt

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May 9, 2012, 6:41:27 PM5/9/12

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XGID=--AABC-------------d----a-:1:1:1:00:1:2:0:5:10

X:You O:O
Score is X:1 O:2 5 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O |
| | | O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X | +---+
| | | X X | | 2 |
| | | X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 28 O: 25 X-O: 1-2/5
Cube: 2, X own cube
X on roll, cube action

//Walt

badgolferman

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May 9, 2012, 7:01:25 PM5/9/12

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Double/Take

Bradley K. Sherman

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May 9, 2012, 7:21:09 PM5/9/12

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Walt <walt_...@yahoo.com> wrote:
>Score is X:1 O:2 5 pt.(s) match.
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | | | O O |
> | | | O |
> | | | O |
> | | | O |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | X | +---+
> | | | X X | | 2 |
> | | | X X X X | +---+
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
>Pip count X: 28 O: 25 X-O: 1-2/5
>Cube: 2, X own cube
>X on roll, cube action

Double.

--bks

Paul

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May 10, 2012, 3:45:56 AM5/10/12

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I agree with Stick's incredibly helpful response to a previous problem
in this same area of backgammon --

"There are many key elements one needs to grasp here in order to
understand the position.

1) The according to score take point.
2) A solid understanding of some workable racing formula. For this
position at a glance I would prefer epc.
3) How to apply that racing formula to get a win % instead of just a
proper money cube action.

I think an understanding of all of the above will make your decision
clear. If you can't do any of those points that's a problem area and
you should address it. "

But the problem itself, Paul. Why don't you answer that if it's so
straightforward?
Tell me your cube action.

My answer is that I don't have a clue -- Trice's Backgammon Boot Camp
is the best reference on this type of problem that I know.

Paul Epstein

Tim Chow

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May 10, 2012, 8:43:15 PM5/10/12

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This sort of decision depends to some extent on who your opponent is,
but let's first try to figure out what the bot would do. O needs 40%
winning chances to take. X will often bear off in four rolls, because
he has seven checkers and can afford one miss. However, missing twice
isn't too unlikely here, and low doublets don't save X a roll. This
is somewhere between a four-roll and a five-roll position for X; I'd
guess an EPC of around 33 or 34.

What about O? O's raw pip count is lower than X's, but her
distribution is very awkward. She'll likely miss once or even twice
on her first roll. Another miss after that is pretty likely. I'd
estimate that she'll have three misses on average, and sometimes four
misses. That means she'll be off in four rolls on average, and
sometimes five rolls. Doublets often don't save O a roll. So O's EPC
is again somewhere between a four-roll and a five-roll position, but I
think closer to four rolls than to five rolls, so an EPC of 31 or 32
is my guess.

This would be ND/T for money, but since O's take point is so high, we
have to think again. The most likely ways for O to win are: (1) X
takes five rolls and O gets off in four rolls, and (2) X takes four
rolls and O gets off in three rolls. Neither option by itself would
be enough for O to take, I think, but together (plus some other
variations) I'd guess they add up to more than 40%. Not sure though.
So against the bot, I'd redouble.

Against a human opponent, it would depend on various factors. If I
thought my opponent was pretty good at assessing this kind of cube
action for money but didn't understand the score, then I'd probably
hold the cube, figuring I'd still get a take next turn even if I
technically lost my market. Also, if my opponent didn't understand
the score then I'd figure my chances would be better than 60% when
leading 2a3a, and I wouldn't want to risk the entire match on the luck
of the next few dice rolls.

---
Tim Chow

Stick

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May 11, 2012, 2:57:08 AM5/11/12

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You underestimate both players' epcs. X is easy to figure out as it
still falls under the umbrella of a 'nice' position. It's true that
nice positions with 7 or 8 checkers typically waste closer to 6.5 pips
than 7 but that is compensated here by the fact that we waste on sixes
and it isn't truly the nicest of positions. I would estimate the
wastage at 7.5 giving X an epc of 35.5.

For O it is fair to say between a four roll and a five roll if you
haven't toyed with epc positions enough to have a point of reference.
I would not expect it to be towards the lower end and would settle on
the exact middle myself, 32.5. This still keeps it as a gigantic ND
for money.

Stick

Walt

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May 16, 2012, 11:54:50 AM5/16/12

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On 5/9/2012 6:41 PM, Walt wrote

X is behind in the pipcount and behind in all the adjusted pipcounts I
know how to compute, so it would seem to be no double.

The key to understanding why this is a cube is that the cube is dead
after it's turned to 4, so all X needs is a slight advantage to cube.
Generally, if you're on roll and down by 4 pips in the race it's 50-50.
Here X is down by three, and since he has more occupied points the epc
deficit is only about 1. That makes X the clear favorite to win, so
ship it.

At 0-0 to 5, recubing would be a massive blunder.

XGID=--AABC-------------d----a-:1:1:1:00:1:2:0:5:10

X:Player 1 O:Player 2

Score is X:1 O:2 5 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O |
| | | O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X | +---+
| | | X X | | 2 |
| | | X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 28 O: 25 X-O: 1-2/5
Cube: 2, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble
Player Winning Chances: 55.79% (G:0.00% B:0.00%)
Opponent Winning Chances: 44.21% (G:0.00% B:0.00%)
Redouble/Take
Player Winning Chances: 55.78% (G:0.00% B:0.00%)
Opponent Winning Chances: 44.22% (G:0.00% B:0.00%)

Cubeless Equities: No Double=+0.116, Double=+0.799

Cubeful Equities:
No redouble: +0.567 (-0.232)
Redouble/Take: +0.799
Redouble/Pass: +1.000 (+0.201)

Best Cube action: Redouble / Take

Rollout:
1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ą 0.001 (+0.565..+0.568)
Confidence Double: ą 0.000 (+0.799..+0.799)

Double Decision confidence: 100.0%
Take Decision confidence: 100.0%

Duration: 3.5 seconds

eXtreme Gammon Version: 2.03, MET: Kazaross XG2

//Walt

Paul

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May 16, 2012, 4:05:28 PM5/16/12

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On May 11, 1:43 am, Tim Chow <tchow12...@yahoo.com> wrote:
> On May 9, 6:41 pm, Walt <walt_ask...@yahoo.com> wrote:
>
>
>
>
>
> > XGID=--AABC-------------d----a-:1:1:1:00:1:2:0:5:10
>
> > X:You O:O
> > Score is X:1 O:2 5 pt.(s) match.
> > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > | | | O O |
> > | | | O |
> > | | | O |
> > | | | O |
> > | | | |
> > | |BAR| |
> > | | | |
> > | | | |
> > | | | X | +---+
> > | | | X X | | 2 |
> > | | | X X X X | +---+
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 28 O: 25 X-O: 1-2/5
> > Cube: 2, X own cube
> > X on roll, cube action
>
> This sort of decision depends to some extent on who your opponent is,

> ...

No, it doesn't! Holding loses a massive 0.232 equity. You would need
an exceptionally weak opponent to justify a play throwing that much
equity away.

Paul

Tim Chow

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May 18, 2012, 8:25:11 PM5/18/12

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On May 16, 4:05 pm, Paul <pepste...@gmail.com> wrote:
> > This sort of decision depends to some extent on who your opponent is,
> > ...
>
> No, it doesn't! Holding loses a massive 0.232 equity. You would need
> an exceptionally weak opponent to justify a play throwing that much
> equity away.

This depends on what you mean by an "exceptionally weak opponent."

The bot rollout is predicated on the assumption that if you lead 2a3a,
then your MWC is 60%, and if you trail 4a Crawford, then your MWC is
18%.

I haven't actually tried swapping in a different match equity table,
but I think that if your MWC at 2a3a were, say, 67% and your MWC at 4a
Crawford were, say, 25%, then holding the cube would be correct.
Would your opponent have to be "exceptionally weak" for these
percentages to apply? Maybe; it depends on your definition.

Now you could counter that against someone who is that weak, you
should still double because your opponent might drop. But I don't
think that many players, even weak ones, would drop this cube.

---
Tim Chow