Liveliness of the cube
Vobis Customer
Dear all,
I have a question concerning the liveliness of the cube. In a money game, assuming a
dead cube the takepoint is 25%; assuming a completely alive cube the takepoint becomes
20%. Common wisdom says that the real takepoint is something like 21.5% (corresponds to
an equity of -0.57). This would mean that one considers the cube to be alive to 70%. How
can we compute mathematically this number?
Also, in some scores for example 3-away 4-away the live takepoint is 19% but the dead
takepoint is around 34%, what is considered to be the real takepoint? Instinctively, I
would guess that the recube of the trailer is more alive than usual due to the very high
takepoint of 40% of the redouble. Again, I would be very interested in how one could
compute this number.
Thanks in advance,
Jacques (ORSA on fibs)
Kit Woolsey
Vobis Customer (torr...@omedia.ch) wrote:
: Dear all,
: I have a question concerning the liveliness of the cube. In a money game, assuming a
: dead cube the takepoint is 25%; assuming a completely alive cube the takepoint becomes
: 20%. Common wisdom says that the real takepoint is something like 21.5% (corresponds to
: an equity of -0.57). This would mean that one considers the cube to be alive to 70%. How
: can we compute mathematically this number?
No, we can't. It depends on the type of positions. Two examples:
a) A long race. Here the trailer is likely to have a reasonably
efficient recube if things go his way, so the cube is relatively alive.
b) A holding game -- way behind in the race (so must hit a shot), but the
trailer having a perfect prime which he will be able to maintain for
several rolls. In this case, if the trailer does hit his shot he will
suddenly become a huge favorite and lose his market by a mile. Thus, the
cube is relatively dead.
The above are examples of positions where gammons are impossible or very
unlikely. If gammons are in the air, things get more complex still. For
example, consider a blitz position. Assuming the trailer has a close
pass/take decision, this means that his win percentage is way above 25%
(to compensate for the many gammons he loses). Thus, he will be able to
get in even more recubes than normal. Also, this type of position tends
to lead to very efficient recubes when the game turns around, since
usually the trailer makes his improvements slowly. Therefore, the cube
is even more alive than normal.
The 21.5% figure is the generally agreed figure for the "average"
position. However, the actual number definitely depends on the position
in question.
: Also, in some scores for example 3-away 4-away the live takepoint is 19% but the dead
: takepoint is around 34%, what is considered to be the real takepoint? Instinctively, I
: would guess that the recube of the trailer is more alive than usual due to the very high
: takepoint of 40% of the redouble. Again, I would be very interested in how one could
: compute this number.
Yes, the cube is more alive than usual due to the takepoint of the
redouble. And, once again, for the reasons above, there is no way to
compute this number.
Kit
Chuck Bower
In article <334674...@omedia.ch>,
Vobis Customer <torr...@omedia.ch> wrote:
>I have a question concerning the liveliness of the cube. In a money game,
>assuming a dead cube the takepoint is 25%; assuming a completely alive cube
>the takepoint becomes 20%. Common wisdom says that the real takepoint is
>something like 21.5% (corresponds to an equity of -0.57). This would mean
>that one considers the cube to be alive to 70%.
Is this a typo? I don't follow. CRB
>How can we compute
>mathematically this number? Also, in some scores for example 3-away 4-away
>the live takepoint is 19% but the dead takepoint is around 34%, what is
>considered to be the real takepoint? Instinctively, I would guess that the
>recube of the trailer is more alive than usual due to the very high
>takepoint of 40% of the redouble. Again, I would be very interested in how
>one could compute this number.
This is a good question. Kit has answered it, but more can be
said. And who better to answer it than (long-winded) me?! How
about a "parable" to illustrate (not to be confused with parabola,
hyperbola, or hyperbole, although this last might also apply):
Suppose you are in a city, and you find out that at 6:00 PM at the
corner of 80th St. and Central Ave., a rich (BG playing) person is
going to be handing out money. It's now 5:45, and your standing
at 50th and Central. You don't have a car, this city has no taxis.
Lucky for you there is a bus line going along Central in the right
direction. There's good news and bad news--the bus is an "Express".
That usually means "fast" so you can get there on time, but it also
means it doesn't stop at every corner, and this one stops at 75th
street, but then not until 85th St.
More good news! you realize that if you get off at 75th St,
you can run and still make it by 6:00. More bad news: between
75th and 80th on central is a BAD NEIGHBORHOOD. You might
make it safely, but you might get mugged and lose the money you
already have in your pocket!
More good news! Between 80th and 85th is a GOOD NEIGHBORHOOD.
More bad news: if you don't get off until 85th St. you'll be ten
minutes late, and some of the money will already be handed out.
(But there will still be some money available.)
So you have a dilemma--do you get off at 75th Street and take
the chance you'll get mugged, the reward being you make it in
time for the philanthropy. Or do you get off at 85th, knowing
your subsequent run will be safe, but showing up late and losing
some of the money you would have made by arriving on time?
What you REALLY want is a local bus! These stop at every
street and even though they are slower getting to the far end
(100th Street) you could get to where you want to go (80th Street)
on time. Unfortunately, there is no local bus running.
Backgammon theorists (Keeler, Spencer, Zadeh, and Kobliska)
back in the 70's came up with a "continuous" model for backgammon
which works like a "local" bus. They developed an algorithm
for determining optimal drop/take points for gammonless games.
You just wait until your winning chances are 80% and double. Your
opponent can either drop or take; it doesn't matter. Your equity
is the same in either case. Unfortunately, REAL backgammon is a
"discontinuous" game. It's like the "Express" bus. You can double
"early", your opponent takes, and you may get mugged or you may make
it unscathed for the payout. You can double "late" when your
opponent must drop, but now your payout isn't as much. (The latter
is known as "losing your market".) BG players have a dilemma, too!
Building off of the above four pioneers (and possibly others)
Rick Janowski developed a modified continuous model for money play
WITH GAMMONS, BACKGAMMONS, BEAVERS, and JACOBY RULE. "Modified"
means he took into account that the cube is seldom used with
perfect efficiency ("perfect efficiency" occurs when you get lucky
and the bus stops at 80th St. because of a flat tire)! Taking it
from there, I have since applied these methods and those of Woolsey
("How to Play Tournament BG") to develop a modified continuous model
for tournament matches.
If you have access to past r.g.bg posts (for example, through
DejaNews on the WWW) you can look up many posts I've made where I
apply this model to REAL LIVE BG positions. You can also look up
references for the other works mentioned above. BUT REMEMBER WHAT
KIT SAID! My methods are only approximate. Some positions
will work quite well; others (like his holding game with LARGE
race deficit) not so well. The modified continuous model is better
than the plain continuous model, but it does not have the true
DIScontinuities of REAL backgammon. Still, I believe it's a fur piece
better than guessing. (Maybe that's just because I'm a bad guesser...)
Chuck
bo...@bigbang.astro.indiana.edu
c_ray on FIBS
Robert-Jan Veldhuizen
On 08-apr-97 00:11:30, Chuck Bower wrote:
[amusing parable featuring buses, streets and mugs snipped]
Thanks for this great story, hehe !
I just missed one thing though: what to do if the bus never gets further than
50th street because it turns around and drives you to 0th street instead ?
Use the halving cube ? When ?
--
Zorba/Robert-Jan