The tricky 3away 4away double

[William C. Bitting]

wcb vs abc: score: 4-3 match: 7 X on roll double?
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O X O | | O X |
| O O | | O X |
| O | | O X |
| | | |64
| O 4 | | X O |
| O X X | | X O |
| O X X | | O X X X O |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

What are the double take points here? Looks like
the my double point is only 40% in a last
roll situation, but at this match score things
get complicated this early. By my calculation
the trailer needs 35% to take, but only 30%
to recube. Contemplating the cube going from
1 straignt to 4, then it looks like my double
point is 61%.

Therefore, is my double window really 61% to 70%?

I'd also rate my gammon chances from here as
excellent - whatever that may mean. How does one
figure this in the picture?

It looked like an easy double / drop position
to me. I don't take doubles like this, but I've
learned that strong players often find takes
which don't tempt me. Any thoughts? Yep, I got
took on this one. ::))

Thanks, wcb on FIBS

[Kit Woolsey]

William C. Bitting (wbit...@crl.com) wrote:
: wcb vs abc: score: 4-3 match: 7 X on roll double?

: +24-23-22-21-20-19-+---+18-17-16-15-14-13-+
: | O X O | | O X |
: | O O | | O X |
: | O | | O X |
: | | | |64
: | O 4 | | X O |
: | O X X | | X O |
: | O X X | | O X X X O |
: +-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

: What are the double take points here? Looks like
: the my double point is only 40% in a last
: roll situation, but at this match score things
: get complicated this early. By my calculation
: the trailer needs 35% to take, but only 30%
: to recube. Contemplating the cube going from
: 1 straignt to 4, then it looks like my double
: point is 61%.

: Therefore, is my double window really 61% to 70%?

This kind of thinking can lead to very confusing conclusions. The
calculations which give the trailer a "35% takepoint" assume that the
trailer will NEVER redouble. That is obviously way off -- with the
leader's take point on the redouble being 40% the trailer will redouble
as soon as he reaches about an even game.

To see how important taking the recube into consideration is, let's
suppose that the trailer's strategy is to redouble immediately. In this
case, his take point would obviously be 32% (his equity behind 4 away, 2
away), since he would be playing for the match. This is much lower than
the 35% assuming the trailer never redoubles.

However, the trailer can obviously do better than automatically
redoubling, which indicates that the true take point is considerably less
than 32%. How much less? That is not clear. Here is the approach which
I use to get a reasonable answer:

First, let's assume that the trailer will be redoubling very aggressively
-- so aggressively, in fact, that he will never lose his market (this is
pretty close to reality). Thus, any time the trailer wins the game, he
will win 4 points and the match. It also means that the trailer will lose
4 points some of the time, either because he gets gammoned or because he
redoubles and then loses. For this position, I estimate that the trailer
will lose 4 points just under half of the time that he loses the game
(admittedly, this is just a guess, but even if I am wrong by a bit it
won't affect the results too much).

If the trailer loses 2 points he is behind 1 away, 4 away, with 17%
equity. If he loses 4 points, he has 0% equity. Thus, if he loses the
game, by my above assumption his average equity will be about 9%. If he
wins the game he will win the match, by my assumption of his never
risking losing his market.

Thus, we have the following results:

Pass: 32%
Take and win: 100%
Take and lose: 9%

So the trailer gains 68% if he takes and is right, and loses 23% if he
takes and loses. This is just about 3 to 1 odds, so by my assumptions
the trailer has a take if he can win the game about 25 or 26% of the
time. Gammons have already been figured in -- we are just looking at win
percentages.

What O's actual win percentage in the position is I leave to everybody's
judgment. However, this approach does give a realistic way of taking the
recube leverage into account. Without doing so, it is easy to come to
some ridiculous conclusions.

Incidentally, I was wcb's opponent when this positions came up, and I did
choose to accept the double.

Kit

[Chuck Bower]

In article <5f0gor$r...@crl11.crl.com>,

William C. Bitting <wbit...@crl.com> wrote:
>wcb vs abc: score: 4-3 match: 7 X on roll double?
> +24-23-22-21-20-19-+---+18-17-16-15-14-13-+
> | O X O | | O X |
> | O O | | O X |
> | O | | O X |
> | | | |64
> | O 4 | | X O |
> | O X X | | X O |
> | O X X | | O X X X O |
> +-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
>
>What are the double take points here? Looks like
>the my double point is only 40% in a last
>roll situation, but at this match score things
>get complicated this early. By my calculation
>the trailer needs 35% to take, but only 30%
>to recube. Contemplating the cube going from
>1 straignt to 4, then it looks like my double
>point is 61%.
>
>Therefore, is my double window really 61% to 70%?
>

>I'd also rate my gammon chances from here as
>excellent - whatever that may mean. How does one
>figure this in the picture?
>
>It looked like an easy double / drop position
>to me. I don't take doubles like this, but I've
>learned that strong players often find takes
>which don't tempt me. Any thoughts? Yep, I got
>took on this one. ::))
>
>Thanks, wcb on FIBS

Good question. I realize Kit has already answered. Here is
another way to go about this (and one I actually use over the table).
My method takes the gammons into account right from the start. Bob
Koca has a technique which works out to the same answer as mine
(so therefore mathematically identical) but he starts with the gammonless
window and THEN folds in the gammons. Anyway here is MY method.

Before beginning, I point out that the game winning chances and
gammon fractions I'm working with are CUBELESS. That is, I'm trying
to surmise the values that JF level-6 cubeless rollouts would come
up with, for example. The drop/take and double/no double points are
thus quoted for cubeless results. This all works out in the end, as
I hope you will see.

1) I first estimate X's (cubeless) gammon win fraction. That is, I
ask myself what percentage of X's wins (assuming cubeless play) will
be gammons. JF level-6 rollouts indicate that from the starting
position (standard setup for a BG game), 27% of all games will end
in gammon (or backgammon). (NOTE: I ignore BG's in my method.)
Now, is X more likely, less likely, or about typical to win a gammon?
O's four checkers back look good for gammon chances, but the anchor
helps fend off some. Still, overall, I'd say "MORE likely" by a bit,
so let's choose a gammon win fraction for X of 33%. Why 33%? Well,
for one thing, it's a "round number" (1/3). But if you ask "why not
50%", I point out that 50% is the gammon fraction for a typical blitz,
and the anchor makes O much more secure than that. So I "guess" 33%.

2) I now need to know O's cubeless gammon win fraction. With only
one checker back, that should make gammons less likely. X is on roll
with several blots, and should probably play agressively (and hit)
so this loose play combined with the fact that he/she has no anchor leads
me to believe that gammon losses for X are still in the picture. So
overall I'd say a little less than the normal 27%. How about 25%
(= 1/4, another round number).

3) Now we calculate O's drop point ASSUMING THE CUBE WILL NEVER BE
USED BY X. Here you need to know match equities. I have a formula
which does a decent job of reproducing the Woolsey-Heinrich Table.
There are other formulas, or you can just memorize the table. Anyway,
here is how I procede:

If O passes, then s/he will be behind -4,-2 (read "4-away, 2-away)
which is 32%. Taking and winning (without gammons) will lead to -2,-3
or 60%. Taking and losing is either -4,-1 and 17% (if no gammon) or
0% if gammoned. In step 1) above we got 1/3 gammons, so 1/3 between
17% and 0% is about 12%. Thus taking and losing gives O 12% match
winning chances. Thus O RISKS 32 - 12 = 20 to gain 60 - 32 = 28. This
corresponds to needing to win 20 / (20 + 28) = 5/12 = 42%.

4) Next step is to fold in the cube. Assume that O will have a perfectly
efficient cube. This occurs by redoubling at EXACTLY X's drop/take point.
And where is that? If X drops, s/he will be 40% in the match. Take is
for the match, so X's drop take point is 40%, which is 60% as seen from
O's viewpoint. Multiply the above 42% (d/t if no cube) by 60% giving
25%, which is O's d/t point with a PERFECTLY EFFICIENT CUBE. Now the
true d/t is somewhere between these two extremes (25% and 42%). Based
on some work by Rick Janowski, I use 70% efficiency, which means 70% of
the way down from 42 to 25. That's about 30%.

4.5) Now stop and go back to the position. Does it look like O can
win 30%? Heck if I know. Well, maybe I do. Think of money play.
Does O have a money take here? X has a lot of work to "gin" this
game. Make the 20-point (and the bar-point would be nice). Get
that checker around from the 5 point. Clean up those blots. Then
win a "3-point game". Looks like a fairly easy money take. Given
"typical" gammon fractions, money take points are in the high 20's
(remember, we mean high 20's CUBELESS), so O is probably better than
30% (cubless) ==> take.

5) Time to calculate the "last roll doubling point". Compare the
difference in match scores between doubling and not doubling. If
X doesn't double, then s/he will be either -2,-4 (no gammon) or
-1,-4 (gammon). Go 1/3 (remember where this came from) between
68% and 83%, or 73%. With a double, you go 1/3 of the way between
-1,-4 (83%) and 100% or 88%. So double GAINS 15% (88 - 73). That's
the upside. Not doubling and losing leaves X 25% (remember that
gammon fraction from step 2) of the way from -3,-3 (50%) and
-3,-2 (40%) or about 48%. Doubling and losing leaves X 25% of
the way between -3,-2 (40%) and 0%, or 30%. The downside (risk from
doubling) is thus 18% (48 - 18). So the double risks 18 to gain 15.
Then the doubling window opens (at the "last roll doubling point")
at 18/ (15 + 18) = 18/33 = 54%.

5.5) Does it look like X can win more than 54% (cubeless). I think
so. Thus X should CONSIDER doubling.

6) Finally look for market losers. From Robertie's "Advanced BG",
give X a good roll (but not "best") and O a bad roll (but not worst).
Will O still have a take (be better than 30%) next time X gets a
chance to cube? A good roll for X is something that points on the bar
point (around 15/36 rolls); say 61. A bad roll for O is entering
but not hitting back and not making a new point; say 43.
This results in something like:

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O X O | | O O X |

| O O | | O X |
| O | | O |
| | | |
| | | |

| | | |64
| | | |
| | | |
| O X | | |
| O X | | |
| O X X | | X X O |
| O X X | | X X X X O |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

Can O now win 30% or more cubeless? It looks close. Also X's
gammon chances have probably gone up a bit, which means that O's
d/t point has also gone up a bit (above 30%). My guess is that
this is now a pass. That means that X probably should have
doubled in the original position, but it's pretty close. Here
knowing your opponent might help "break the tie".

In conclusion, it looks like your decision to double was
reasonable. Your opponent's take was also wise. Don't feel too bad.
The rolls didn't cooperate. You can't help that, unless you're one
of those hackers who has figured out how to manipulate FIBS dice.

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