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# What is the doubling window at 4 away 2 away?

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### Hugh McNeil

Feb 22, 2003, 8:59:05 AM2/22/03
to

"Jørgen Lyng"

. First I computed the doubling window
> at 2 away 4 away and got this:
>
> Doubling window 78 - 83 %
> opponents take point 17 %
>
> When I try to do the same for 4 away 2 away it all goes wrong.
>
> I got a doubling window that said 22 - 25 % which naturally is wrong.
>
> When I look in Snowie 4 it says that both players have a take point
> around 18 % at that score, is that right? I would guess that the
> player with 2 away would have a higher take point?
>

18 % is about right. You have to adjust the leader's take point to account
for gammons. For a real eye opener, look at snowie's take point for 2-Away,
5-Away.

17.5/ (50 - 40) + 17.5 = 17.5/ 27.5 ~= 64% required to double... when there
aren't any gammons involved.

Feb 22, 2003, 2:31:20 PM2/22/03
to

"Jørgen Lyng" <nos...@zpost4660.dk> wrote in message
news:rdoe5v0kbna8pq2hn...@4ax.com...
> Hi there
>
> I am trying to compute the doubling window for different scores with
> Kit Woolseys match equity table. First I computed the doubling window

> at 2 away 4 away and got this:
>
> Doubling window 78 - 83 %
> opponents take point 17 %
>
> When I try to do the same for 4 away 2 away it all goes wrong.
>
> I got a doubling window that said 22 - 25 % which naturally is wrong.
>
> When I look in Snowie 4 it says that both players have a take point
> around 18 % at that score, is that right? I would guess that the
> player with 2 away would have a higher take point?
>
> Anyway I would like to know what the doubling window is at 4 away 2
> away, and it would be a big help if someone could include the
> calculations.
>
> Greetings
> Jorgen Lyng
> Spamfilter: Drop z
> --
> With Kind Regards
> Jorgen Lyng
> Denmark

A similar question was asked a while ago on this newsgroup, so since I have
done the calculations, I can send you an Excel spreadsheet with the results
(as I did for several people). As I can't see your workings, I assume you
are trying to calculate 'dead-cube' figures (i.e. assuming that the 'taking'
player will never ReDouble for the rest of the game. Also, in the
risk/reward equations, you need to include a factor representing the gammon
rate to be used. (it is normal to assume equal gammon rates for both
players). 'Racing' takepoints (gammon rate of 0%) will produce very
different Doubling Points from, say, a gammon rate of 20%. I can send you
the risk/reward equations if you need them to check against. And don't
forget to include any automatic ReDoubles if the score warrants it (i.e at
2-away, 4-away , the doubled opponent will have an automatic ReDouble).
Snowie gives a range of doubling points and takepoints according to how much
ReDouble leverage is assumed, so you need to be careful in how you interpret
the theory panel to avoid working on the wrong scenario.

Feb 22, 2003, 3:04:39 PM2/22/03
to
For a given match score, Snowie will allow you to alter the gammon rates for
both players to produce a particular game scenario, but Snowie's match
equity table uses a different standard gammon rate from Kit's (I believe
Snowie uses 26%, Kit 21%, but I'll stand corrected), which Snowie assumes
will be the case for subsequent games in the match, and that will give
different results from 'Kit-derived' ones.

Once you have done the calculations, take them purely as an intellectual
exercise, because in reality, 1) gammon rates in real games are rarely
equal, throwing the computed figures off; and 2) the taking player will, in
many cases, have some ReDouble leverage (vig.), which throws the figures off
yet again. Nevertheless, it is well worth doing, to give you a better
understanding of a complex subject.

news:b38j22\$1us\$1...@news7.svr.pol.co.uk...

### Hugh McNeil

Feb 22, 2003, 5:18:03 PM2/22/03
to
> Here is my problem
>
> 2. Black is behind 1 - 3 to 5 = 4 away 2 away
>
> White drops 2 away 3 away 60 %
>
> White takes and wins 100 %
>
> White takes and loses 2 away 2 away 50 %
>
> Gain = 100 - 60 % = 40 %, risk = 60 - 50 % = 10 %

I think gain should be 100 - 50 = 50%.

> White's takepoint = 10/40 = 25%

Then this becomes 20 %.

Snowie's 18 % comes from somewhat different match score winning percentages.

>
> No double Black wins 3 away 2 away 40%
>
> Double Black wins 2 away 2 away 50 %

>
> No double Black loses 4 away 1 away 17 %

Reasonable (if looking at Kit's match score table).

>
> Double Black loses 0 %
>
> Dobling window right side = 100% - 25% = 75 %

I don't know where these numbers suddenly appeared from...

>
> Dobling window left side : (17 x 100) / 17 + 60 = around 22 %

This seems right...

>
> Real bad, where did I go wrong?

Feb 22, 2003, 8:42:36 PM2/22/03
to

"Jørgen Lyng" <nos...@zpost4660.dk> wrote in message
news:24pf5vc8mmj7o8kqc...@4ax.com...
>
>
> I have my calculations here:
>
> 1. Black is ahead 3 - 1 to 5 = 2 away 4 away
>
> White drops 1 away 4 away 17 %
>
> White takes and wins 2 away 2 away 50%
>
> White takes and loses 0%
>
>
> No double Black wins 1 away 4 away 83%
>
> Double Black wins 100 %
>
> No double Black loses 2 away 3 away 60 %
>
> Double Black loses 2 away 2 away 50 %
>
> Whites takepoint is 17 %
>
> Dobling window right side = 100% - 17% = 83 %
>
> Dobling window left side : (60 x 100) / 60 + 17 = around 78 %
>
> Blacks doubling window is 78 - 83 %
> White's takepoint = 17 %
>
> I guess that this is correct?

So far so good. Black's Doubling Point (left-hand side of window) = 60/77 =
77.92%

> Here is my problem
>
> 2. Black is behind 1 - 3 to 5 = 4 away 2 away
>
> White drops 2 away 3 away 60 %
>
> White takes and wins 100 %
>
> White takes and loses 2 away 2 away 50 %
>
> Gain = 100 - 60 % = 40 %, risk = 60 - 50 % = 10 %
>

> White's takepoint = 10/40 = 25%
>

> No double Black wins 3 away 2 away 40%
>
> Double Black wins 2 away 2 away 50 %
>
> No double Black loses 4 away 1 away 17 %
>

> Double Black loses 0 %
>
> Dobling window right side = 100% - 25% = 75 %
>

> Dobling window left side : (17 x 100) / 17 + 60 = around 22 %
>

> Real bad, where did I go wrong?

Ok, here's where you erred. The definitions of Risk and Gain you used in
this calculation are wrong. The Gain is the match equity from Winning
having doubled, minus the match equity from Winning, having NOT doubled. So

Gain = MatchEquity(DoubleTake,WIN) - MatchEquity(NoDouble,WIN)

= 50% - 40% = 10%

Similarly,

Risk = MatchEquity(NoDouble,LOSE) - MatchEquity(DoubleTake,LOSE)

= 17% - 0% = 17%

Using the risk versus gain equation p = Risk / (Risk + Gain),

p = 17 / ( 17 + 10) = 63% approx.

This is the bottom of the doubling window for gammon rate = 0%. However, in
practice, the trailer (doubler) will normally have quite a few gammons still
when he hits 63% , so this will enable him to double earlier than 63%. It
depends on the exact gammon rate you use, but the window opens at or near
the 50% mark while there is still a reasonable amount of contact, which is
why you see good players doubling early with only the slightest advantage at
this score. Even just the chance of hitting an indirect shot in the opening
can be enough.

### Hugh McNeil

Feb 23, 2003, 11:34:48 AM2/23/03
to
You are going wrong in forgetting that the trailer will automatically
redouble after being cubed. So the risk is 60% - 0 = 60

gain is 100-83 = 17

Therefore 60/ 60 + 17 = 60/77

"Jørgen Lyng" <nos...@zpost4660.dk> wrote in message

news:0nfh5v8afdbv03lq0...@4ax.com...

> Adam Stocks wrote:
>
> >Ok, here's where you erred. The definitions of Risk and Gain you used in
> >this calculation are wrong. The Gain is the match equity from Winning
> >having doubled, minus the match equity from Winning, having NOT doubled.
So
> >
> >Gain = MatchEquity(DoubleTake,WIN) - MatchEquity(NoDouble,WIN)
> >
> >= 50% - 40% = 10%
> >
> >
> >Similarly,
> >
> >Risk = MatchEquity(NoDouble,LOSE) - MatchEquity(DoubleTake,LOSE)
> >
> >= 17% - 0% = 17%
>

> I had hoped I could use your explanation to calculate the doubling
> window in any case, but if I try to use it at 2 away 4 away it fails.
>
> 2 away 4 away
>
> Gain = 100% - 83% = 17%
>
> Risk = 60% - 50% = 10%

>
> p = Risk / (Risk + Gain),
>

> p = 10 / ( 10 + 17) = 37% approx.
>
> I know it should be about 78%
>
> What is wrong?

### Alef

Feb 23, 2003, 1:04:08 PM2/23/03
to
Of the different ways I've worked to improve my backgammon I've found
studying match equity tables to be the least rewarding. The vast majority of
cube decisions occur when estimating accurate equity is not that realistic.

It is satisfying to be able to work out specific drop points, but in terms
of actually improving my play over the board I gain far more from reading
books and gammonline. Really *understanding* a position is often not that
mathematical. For me the more practical strategists focus on how to think
about positions (Magriel, Woolsey's "New Ideas") rather than how to
specifically calculate (Kleinman, Lamford's "Improve").

For years I put off learning match equity because it's intimidating. Now
that I've done work on using them I've just not found them so worthwhile.
Maybe they'll become more valuable when I'm ready to play in the Monte Carlo

-Alef

Feb 23, 2003, 2:07:53 PM2/23/03
to

"Alef" <alefro...@nospamthankyou.mac.com> wrote in message
news:BA7EBD73.2095%alefro...@nospamthankyou.mac.com...

You are not alone Alef - which is why I included a caveat along those lines
in my earlier post in this thread. During my early experience of matchplay
bg, (as an Intermediate strength player), I stumbled across match equity
tables on some bg website of other, and thought, "I must learn this stuff
parrot fashion, otherwise I will lose most of my matches". I hurredly
scribbled down Woolsey's MET for all lengths up to 9-away,9-away, and took
it with me to my first live tournament. By the time I arrived at my bed &
breakfast, I was too tired to memorise it, and went to sleep. The next day,
without the 'required knowledge', I won the Consolation. I quickly came to
the conclusion that in fact, it was better to concentrate my efforts on
improving my positional judgement and other aspects of my game, since, as
you say, the reality didn't often bear close relation to the theory, and if
it did, it was, at the time, too difficult to be of much practical
over-the-board use. Coincidentally, the previous day before this thread's
original question was asked, a player on GamesGrid asked exactly the same
question (about the DP at 2-away,4-away). After the figures were quoted, I
said that it was all very well knowing the doubling window percentages, but
backgammon is more of an art than a science, and you need artistry/skill to
know when you hit the windows.

Of course, later, it is much easier to cope with the extra information load
caused by METs and the like , because you get to a stage where the
fundamental stuff is second nature anyway (the concepts behind the MET
figures ARE fundamental to matchplay, but the exact percentages are NOT).
It is perfectly possible to become a good bg player with minimal studying of
MET entries, simply by experience, and players can study the detail in METs
as and when they feel ready for it.

That's one of the beauties of the game - it has many levels on which it can
be played/studied, according to the individual player.

### Gregg Cattanach

Feb 24, 2003, 5:42:33 AM2/24/03
to
news:b3b61s\$5kd\$1...@newsg2.svr.pol.co.uk...

>
> You are not alone Alef - which is why I included a caveat along those
lines
> in my earlier post in this thread. During my early experience of
matchplay
> bg, (as an Intermediate strength player), I stumbled across match equity
> tables on some bg website of other, and thought, "I must learn this stuff
> parrot fashion, otherwise I will lose most of my matches". I hurredly
> scribbled down Woolsey's MET for all lengths up to 9-away,9-away, and took
> it with me to my first live tournament.

One great tool I found to help come up with the numbers on the MET
(Woolsey's) is the 'Turner Formula'. This makes it unnecessary to memorize
all those numbers, and this simple algebraic formula gets you to the right
number on Woolsey's table within 1 percentage point for all scores up to
11-away, 11-away.

First, you must memorize the Crawford score numbers, so just memorize this
series: 30, 25, 17, 15, 10, 9, 6, 5, 3, 3. These are the trailer's equity
at 2-away, 3-away, 4-away, etc. Crawford.

Turner Formula:
((24 / T + 3) * D) + 50 where:
T is the number of points the trailer has to go
D is the difference between the two scores.

This is quite easily done in your head, especially because 24 divides evenly
with so many numbers. If T is 5, then I just round (24 / T) to 5, if T is 7
I round (24 / T) to 3-1/2 and it T is 9 I use (24 / T) as 2-2/3. After
completing the formula there are 5 'perverse' scores that need adjustment
at 2-away 5-away, 2-away 6-away, 2-away 7-away, 2-away 8-away, 2-away
11-away. For 2-away 11-away subtract 3 points. For the other 4 add 2
points to each, (or to be most precise actually at 3 points for 6-away and
7-away). Your final result for any score up to 11-away 11-away is always
+-1 of the Woolsey number and 80% of the time exact.

For those that use 'Neil's Numbers' which is also an excellent system,
you'll see that the (24 / T + 3) part is exactly Neil's number.

This much math can be done in your head, and figuring out a take point is
often quite important in lots of match situations. In my experience,
figuring the take point comes up 10 times more often than figuring the
minimum doubling point. The reason is when I'm doubling, it is usually true
that I want to be near my opponent's take point. So I'm either figuring my
take point (if being doubled) or my opponent's take point (if I'm doubling.)

Take point: (PS - TL) \ (TW - TL)
PS=ME if passed
TL=ME if take and lose
TW=ME if take and win

This is still the risk / (risk + gain) formula: Risk = (PS - TL) Gain =
(TW-PS) but the - PS and + PS elements in the denominator cancel out.

Hope this helps.

Gregg C.