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### Anthony Patz

May 11, 1997, 3:00:00 AM5/11/97
to

There has been a lot of discussion on the need to double before you
'lose your market'. Is this an irrevocable occurance?

Suppose you're playing along, and suddenly, oops- you either weren't
concentrating or didn't know better - and there goes your market...So
now you're stuck with playing on for gammon.

Is there any practical justification for playing one of your following
rolls less than optimally, so as to get back into the doubling window?

### Kevin Cline

May 12, 1997, 3:00:00 AM5/12/97
to

a...@aztec.co.za (Anthony Patz) wrote:

>There has been a lot of discussion on the need to double before you
>'lose your market'. Is this an irrevocable occurance?
>
>Suppose you're playing along, and suddenly, oops- you either weren't
>concentrating or didn't know better - and there goes your market...So
>now you're stuck with playing on for gammon.

Losing your market simply means that your opponent will no longer take the
double. You can still gain equity by doubling. For example, suppose you are
in a two roll bearoff situation with winning probability of 65% (equity
0.40). You should double, and your opponent should take. But you make a
mistake and roll instead. Now you are in a one-roll situation with
probability of winning 93%. You should still double, but your opponent will
now drop.

>Is there any practical justification for playing one of your following
>rolls less than optimally, so as to get back into the doubling window?

No, unless you are playing with a drunk for money.

### Anthony Patz

May 12, 1997, 3:00:00 AM5/12/97
to

clines@delete_this.airmail.net (Kevin Cline) wrote:

{snipped} - and there goes your market...So

>>now you're stuck with playing on for gammon.

>Losing your market simply means that your opponent will no longer take the
>double. You can still gain equity by doubling. For example, suppose you are
>in a two roll bearoff situation with winning probability of 65% (equity
>0.40). You should double, and your opponent should take. But you make a
>mistake and roll instead. Now you are in a one-roll situation with
>probability of winning 93%. You should still double, but your opponent will
>now drop.

>>Is there any practical justification for playing one of your following
>>rolls less than optimally, so as to get back into the doubling window?

>No, unless you are playing with a drunk for money.

I unneccsarily complicated the example by refferring to playing on for
gammon (I had a particular situation in mind). I agree one can
increase equity by casing, but sometimes by a lot less than having a
double accepted. In theory, if the take point is not too far below, it
pays to 'go back' and pick up the extra eqity. I was just wondering if
it was practical at all.

Suppose your opponents take point is 22% and you're at 80%. By cashing
you gain 0.2 points. If you were back at 75% you could double for an
expected 1.5 points and gain 0.7 points instead.

### Morten Daugbjerg Hansen

May 12, 1997, 3:00:00 AM5/12/97
to

In <5l6orn\$1ls\$1...@proxy01.iafrica.com> a...@aztec.co.za (Anthony Patz) writes:

>>>Is there any practical justification for playing one of your following
>>>rolls less than optimally, so as to get back into the doubling window?

>Suppose your opponents take point is 22% and you're at 80%. By cashing

>you gain 0.2 points. If you were back at 75% you could double for an
>expected 1.5 points and gain 0.7 points instead.

Seems there is a few misunderstandings regarding equity.

If you have 80%, it also means that your opponent have 20%....

The difference is 60%, giving an equity of 0.60. doubling out earns therefore
0.40 equity.

It earns you 20%, but also takes away the 20% loss, therefore 'counting twice'

If you have 75%, your equity is 0.50
If you double, and opponent accept, youre right you will win 1.5 point, but
again your opponent will win 0.5 point, giving you a total equity of ONE point.
excactly the same as doubling out in the first example....

Thus you wouldnt have earned by playing down to 75 %.

There's an even easier and more logic way to realize these things:

When you double your opponent, he can either drop and lose one point, or
IF HE THINK HE WILL LOSE LESS THAN ONE POINT IN AVERAGE he will take....

In your case , youre asking whether you can get more than one point by playing
accept the cube if he loses LESS than one point on average.

Therefore i will give Kevin rigth :

>clines@delete_this.airmail.net (Kevin Cline) wrote:

>>No, unless you are playing with a drunk for money.

YUP, because you might worsen your position from 95% to maybe 82%, and get a drunk
to accept a wrong cube, however it is very risky because you might get below 75%
and have made an even bigger mistake yourself, so this approach isnt recommendable
unless you think you play extremely well, and your opponent is extremely drunk,
and in this case it is probably better to cash and get on with a new game
and offer your opponent another drink :-)

Hope this makes some sense to you...

Morten Daugbjerg -- md on FIBS

### Chuck Bower

May 12, 1997, 3:00:00 AM5/12/97
to

In article <5l6orn\$1ls\$1...@proxy01.iafrica.com>,

(snip)

>
>I unneccsarily complicated the example by refferring to playing on for
>gammon (I had a particular situation in mind). I agree one can
>increase equity by casing, but sometimes by a lot less than having a
>double accepted. In theory, if the take point is not too far below, it
>pays to 'go back' and pick up the extra eqity. I was just wondering if
>it was practical at all.
>

>Suppose your opponents take point is 22% and you're at 80%. By cashing
>you gain 0.2 points. If you were back at 75% you could double for an
>expected 1.5 points and gain 0.7 points instead.

Hold it a second. You have miscalculated the equity in this
example. You forgot to subtract your 25% losses:

E = 2*( 0.75 - 0.25 ) = 1.0

If you cash (at 80%) then you get the same 1.0.

As far as you original question (paraphrased) "...is it ever
correct to make a worse percentage play in order to go from a cash
back into the doubling window--so that your opponent will have a
take...?" I think the answer is NO (assuming both sides play
optimally). With a cash, you get the value of the cube. For your
opponent to properly accept, s/he must have more equity by taking
than by dropping. Since "dropping" gives you the value of the cube,
"taking" must mean that you get less than the value of the cube in
the long run.

One last thing to keep in mind (if you're not confused enough
already by what I've said...) There is an initialism often used in
the literature--CPW which stands for "cubeless probability of winning".
This is what most rollouts report. That is the value of the game
IF THE CUBE IS BANNED FROM USE. In simple races, for example, you
can usually take with less than 25% CPW because the cube allows you
to turn some potential losses into wins.

The 25% rule is a good learning tool for Backgammon 101, but
the real picture is more complicated.

Chuck
bo...@bigbang.astro.indiana.edu
c_ray on FIBS

### Michael J Zehr

May 13, 1997, 3:00:00 AM5/13/97
to

In article <5l4ja5\$j8a\$1...@proxy01.iafrica.com> a...@aztec.co.za writes:
>There has been a lot of discussion on the need to double before you
>'lose your market'. Is this an irrevocable occurance?
>
>Suppose you're playing along, and suddenly, oops- you either weren't
>concentrating or didn't know better - and there goes your market...So

>now you're stuck with playing on for gammon.
>
>Is there any practical justification for playing one of your following
>rolls less than optimally, so as to get back into the doubling window?
>

Well... the answer is probably no, although it depends on whether you're
assuming your opponent is perfect or not.

To see this, look at it from an equity viewpoint: (This is written
assuming money play. The same thing applies more or less with match
play, the example is much harder to explain because gammons count, etc.)

You're cruising along with a cubeless of equity of about .5-.55, which
You forget to double, and now your equity with the cube in the center
doesn't know to drop, spin the cube, and your game is now worth more
than 1.00.)

First of all, it might not be correct to play for a gammon. If the
correct cube action is double/drop, your equity after rolling (but before
the dice stop spinning, in otherwords the average of your equity of all
rolls if you choose not to double) might be < 1.00. Suppose one of
these sequences happens, and your opponent gets a decent roll, and it's
now a correct double/take. If it's double/take, your equity after
doubling is < 1.00. Is there any reason to prefer this over the 1.00
you'd get by cubing immediately?

In theory, no. In practice, the matter might be different.

What you need to weigh is the chance for your opponent to make a
mistake. What you're risking is the sum of the chance that your
opponent incorrectly takes now, plus the amount you might risk if you
have to give over a cube that is a correct take *for*that*opponent*,
and end up in a position with an equity < 1.00. What you stand to gain
is the chance that you'll end up with a position in which your opponent
will incorrectly take later. Seems to me you're not getting very good
odds on the deal. If your opponent is that likely to make a mistake,
you might as well try the "hesitation double": "hmm... well... umm...
all right... I guess it's a double" and turn the cube. :-)

With match play involved, the gammons are activated, and this gets a lot
harder to explain why it would be wrong. But keep in mind that it still
might be a position in which it is a double/drop, but your match equity
gain after an average roll is still less than the match equity gain from
cashing. Of course, once it becomes correct to play on for a gammon,
then that's the right thing to do, but again, why would you ever want to
intentionally worsen your position until it's a correct take?

Hope this helps,
Michael Zehr

### Michael J Zehr

May 19, 1997, 3:00:00 AM5/19/97
to

In article <5l6orn\$1ls\$1...@proxy01.iafrica.com> a...@aztec.co.za writes:
>I unneccsarily complicated the example by refferring to playing on for
>gammon (I had a particular situation in mind). I agree one can
>increase equity by casing, but sometimes by a lot less than having a
>double accepted. In theory, if the take point is not too far below, it
>pays to 'go back' and pick up the extra eqity. I was just wondering if
>it was practical at all.
>
>Suppose your opponents take point is 22% and you're at 80%. By cashing
>you gain 0.2 points. If you were back at 75% you could double for an
>expected 1.5 points and gain 0.7 points instead.

In a *money* game, until you turn the cube, your maximum equity against
a perfect opponent is 1.0, regardless of how much of that comes from
doubling. Whether your expected equity with no cube is .6 or .9, a
double/drop gives you +1.0. A double and *correct* take gives you an
equity < 1.0. So if your cubeless equity is .6, you could gain .4 by a
double/drop, or you could make a poor play, drop your cubeless equity
to, say, .5, then double, and gain .45 equity to be at .95. Sure, you
"picked up" an extra .05 from your double, but you basically lost .1

The key to remember is that if it is a correct take for your opponent,
your equity is less than if it's a correct drop for your opponent.

Let's extend this concept further -- suppose you're holding the cube, so
it might actually be correct to play on for a gammon. If so, your
equity from playing on *must* be greater than or equal to 1.0 times the
cube value. So if you try to get to a position in which it is a correct
take for your opponent, you must reduce your equity to below 1.0 times
the cube value. Since this represents a net loss, the equity you gave
up to reach that position must be more than the extra equity you
'gained' at the moment of turning the cube. (This might be where some
of the confusion somes from. You don't really gain that equity by
it's just a matter of whether you're going to make the optimal play to
get that equity or not.)

There are also positions in which it's correct to cash, i.e. you don't
have enough gammon threat to have an equity greater than 1.0 times the
cube value.

But of course, we don't always play against perfect opponents. (I
mentioned this in my earlier posting on this topic... in fact, much of
this is a rehash, but the fact that the question was raised again makes
me wonder if my article made it everywhere.)

Suppose you have the choice between two positions:

A. Cubeless equity .6, equity for double/take 1.1, chance your opponent
will incorrectly take = 10%.

B. Cubeless equity .7, equity for double/take 1.3, chance your opponent
will incorrectly take = 0%.

Obviously your equity against that opponent is higher for 1.1. So you
might have a position in which the correct move against that opponent
when you hold the cube is different than the correct move against that
opponent when you don't hold the cube, and might even be different than
the correct move against a different opponent.

But without knowing *exactly* how your opponent will make mistakes, we