doubles, redoubles, re-redoubles, etc.

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Stuart Cracraft

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Apr 16, 1995, 3:00:00 AM4/16/95
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Hi -- one of the things that bugs me about computer backgammon
programs I've played is that doubling can go on forever until
the cube is inflated far beyond reasonable proportions.

A couple of questions on this:

- what are the rules in a real game on number of doubles?

- what does Jellyfish do?

- are there any limits to the number of doubles in Jellyfish
or the basic backgammon rules?

--Stuart

Michael J Zehr

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Apr 16, 1995, 3:00:00 AM4/16/95
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The game rules do not limit how high the cube can get. Thus it's
properly realistic that a computer program will turn the cube to a high
number.

In practice the cube doesn't get that high all that often. 32 and
64-cubes are games to talk about later, and remember. (Gather round
grandkids, let me tell you about the time I won a 64-bagger while box in
Harvard Square against 4 opponents....)

Most of the time when I've seen a computer turn the cube too high it's
because it's missed some basic feature of the position like timing. The
human and computer keep doubling and the computer usually gets wiped
out. This is unlikely to happen with Jellyfish, or at least if it
thinks it's a double, you can be reasonably certain it is probably
favored to win. *grin*

You don't see the cube do this in human games for a variety of reasons.
One is that if you double someone and they beaver, and next turn they
double you, you're going to reconsider whether you've properly evaluated
the positions.

Another reason is the non-linear valuing of money. A player will tend
to be more conservative with both doubles and takes when the cube gets
high. Mathematically you should treat the cube exactly the same way,
but in practice we tend to value a second $1000 (for example) as more
costly to lose than the first $1000. There are lots of perfectly good
reasons why people do this and why computers don't.

-michael j zehr

PS. Consider:

1 1
^
0 1 0 0 1 | recube?

Equity is exactly 0, so if you want to maximize variance, it's a double
(and beaver... and an aardvark... etc.) But if you want to minimize
variance, you settle the game for $0.

David Montgomery

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Apr 16, 1995, 3:00:00 AM4/16/95
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In article <3ms1a7$1...@senator-bedfellow.MIT.EDU> ta...@ATHENA.MIT.EDU (Michael J Zehr) writes:
>Most of the time when I've seen a computer turn the cube too high it's
>because it's missed some basic feature of the position like timing. The
>human and computer keep doubling and the computer usually gets wiped
>out. This is unlikely to happen with Jellyfish, or at least if it
>thinks it's a double, you can be reasonably certain it is probably
>favored to win. *grin*
>

Ed O'Laughlin told me that KG had gotten the cube up to 512
vs Jellyfish in a position in which KG had a single checker of
Jellyfish's trapped behind a full prime (with Jellyfish having no
checkers off). KG had walked the prime *backwards* out into the
outfield far enough that Jellyfish thought it was the favorite, even
though it was primed.

David Montgomery
monty on FIBS


Christopher Yep

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Apr 17, 1995, 3:00:00 AM4/17/95
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In article <3ms1a7$1...@senator-bedfellow.MIT.EDU>,

Michael J Zehr <ta...@ATHENA.MIT.EDU> wrote:

>PS. Consider:
>
>1 1
> ^
>0 1 0 0 1 | recube?
>
>Equity is exactly 0, so if you want to maximize variance, it's a double
>(and beaver... and an aardvark... etc.) But if you want to minimize
>variance, you settle the game for $0.

Just a slight correction,
Lower player is a 19/36 favorite, so his equity is > 0.
(No beaver, etc. and settlement > 0)

This leaves open questions which I have wondered about for awhile:
Are there any backgammon positions (other than the initial position,
before either player has rolled) where:

1. The equity is 0? [money play]
2. The player on roll has a 50% chance to win the game? [1 pt. match (no cube)]


Chris

Kit Woolsey

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Apr 17, 1995, 3:00:00 AM4/17/95
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Christopher Yep (chri...@soda.CSUA.Berkeley.EDU) wrote:

: This leaves open questions which I have wondered about for awhile:

: Are there any backgammon positions (other than the initial position,
: before either player has rolled) where:

: 1. The equity is 0? [money play]
: 2. The player on roll has a 50% chance to win the game? [1 pt. match (no cube)]


1) I know of a couple. One which is very easy to see is as follows:

X has one checker on 9 point, O has one checker on 6 point, X owns cube,
X is on roll. X wins outright on 12 of his rolls. Since all of his
rolls get him to at least the 6 point (where he has a claim or break-even
on O's decision whether or not to take a redouble), in essence X wins 1/4
of the 24 rolls he fails to get off immediately (since O gets off on 3/4
of his rolls), which comes to the desired 18 out of 36.

Another example which is more complex but my trusty computer says is so is:

X has two checkers on 4 point and one checker on 6 point, O has three (or
four) checkers on ace point, X owns cube, and X is on roll. Check it out
if you want to spend some pencil and paper time.

An example of a contact position might be as follows:

X has a closed board -- his other three checkers are two on O's 3 point
and one on O's 7 point. O's position: 3 on 1 point, 3 on 2 point, 4 on 4
point, 4 on 5 point, 1 on 12 point. X is on roll, cube is in center
(money game, Jacoby rule in use). Note that X has exactly 18 hitting
numbers, and if he misses O certainly has a claim with the cube. If we
assume that after hitting X's gammon chances are less than half his losing
chances (which seems like a proper assumption to me) then it is not
correct for X to double now. Therefore X wins when he hits, loses when he
misses, for equity of 0.

2) With no cube in play, I don't know any zero equity positions. If there
were one in a race I'm sure our regurgitating computer programs would
have spit it out by now and I would have heard of it. I guess in theory
there could be one in a contact position, but that would be awfully hard
to prove -- keep in mind that "gin" positions just aren't 100% gin.

Kit

Robert Macmillan

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Apr 18, 1995, 3:00:00 AM4/18/95
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> From: mo...@cs.umd.edu (David Montgomery)

>
> Ed O'Laughlin told me that KG had gotten the cube up to 512
> vs Jellyfish in a position in which KG had a single checker of
> Jellyfish's trapped behind a full prime (with Jellyfish having no
> checkers off). KG had walked the prime *backwards* out into the
> outfield far enough that Jellyfish thought it was the favorite, even
> though it was primed.

Have you considered the possibility that Jellyfish calculated that there
was a significant chance of it breaking through the prime while it was
being walked back in, and then winning?

I'm not saying it had, mind!

Robert

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