Can you play "slow"?
Darse Billings
>I have had a longstanding argument with one of my backgammon opponents
>about whether or not you can play "slowly". I feel that the answer is
>yes and is tied to crossovers. In a game where you are trying to save a
>gammon you try to maximize crossovers. Therefore, it seems logical to
>me that in a game where you are trying to preserve your timing that you
>could minimize crossovers and attempt to play slow. My opponents
>argument centers on the fact that pips are pips. Any comments?
In terms of backgammon probabilities, it is wrong to say "pips are pips".
It would be true if our move was simply based on the sum of the two
dice, but because we use each die independently, things are not so
simple. The fact that rolling 61 is not the same as rolling 43 has
many implications toward correct backgammon strategy.
There are many different situations that demonstrate this fact, some of
which are familiar, some more subtle. Some common examples are found in
bear off situations. For instance, having two men on the 2 point is much
worse than having one on the 1 and one on the 3, yet both positions have
two men and four pips remaining.
x
position: . x . x . x
chance of getting both men off: 26/36 34/36
Here is a more subtle example. Suppose you are in a no-contact race,
with two men left in the outfield on the 7 and 13 points, and you have
to play a 1. In the diagram, you just played 18-13, and have a 1 left.
24 23 22 21 20 19 18 17 16 15 14 13
+------------------------------------------+
| O O O O O O | | O X |
| O O O O O O | | O |
| | | O |
| | | |
| | | |
| |BAR| |v X to play 1
| | | |
| | | |
| X | | |
| X X X X X X | | |
| X X X X X X | | X |
+------------------------------------------+
1 2 3 4 5 6 7 8 9 10 11 12
BAR: O-0 X-0 OFF: O-0 X-0 Cube: 1 scottsalisbury rolled 1 5.
Moving either man gives us a crossover, but the correct move is 7-6,
moving the man on 7 into the home table. If "pips are pips" were true, it
wouldn't matter which man we move. Here the goal is to get the last two
men home, and our move maximizes the probability of having both men home
next roll, by effectively increasing the flexibility of the outfield men.
With 7-6, any combined seven or more accomplishes the goal, which is not
true had we chosen 13-12. In the latter case, a 43, 52, 53 or 54 will
force us to leave one man in the outfield and move one man further into
the inner board, instead of having both men home, which will result in the
probable loss of half a roll.
In race situations (including saving gammons), it is usually correct to
move a man to the 6 point in preference to any other use of the roll.
This should be fairly obvious, but I have seen several errors of this
type in games and books, including the holy Magriel.
Maximizing crossovers usually has the effect of using sixes more
efficiently, and more generally of using a wider range of rolls
effectively. But in certain positions, maximizing crossovers is not
the appropriate goal.
Suppose you have one man behind a 5-prime, outfield men on the 13 and
12 points, and all other considerations are race oriented. Since any 6
will be used to jump over the prime (a much higher priority), it is
correct to use a 1 to move 12-11, rather than the crossover 13-12,
because we gain the most overall flexibility by having an efficient use
for *fives*. Maximizing crossovers is really just a short-cut
generalization, but it does lead us to the best position most of the time.
Now in situations where timing is important, it may be necessary to
slow down as much as possible. You are right in thinking that the same
considerations arise (in reverse), but minimizing crossovers may not be
the best way to achieve the true goal in the position.
If you are trying to preserve your strong home board (say you have a
point behind a prime and are hoping to hit), it is often correct to
simply minimize crossovers (but the intended use of sixes may alter
this). If you are behind a prime where your sixes are also blocked, it
may be more important to move all your other men home quickly, so that
sixes cannot be used at all (the ultimate in favourable inefficiency).
In a prime vs prime contest, however, things are often rather complicated.
The correct move may depend on a number of factors, including position of
the prime and the number of trapped men, so I would hesitate to suggest
any general guidelines. Perhaps if you gave some specific examples, a
stronger player than myself could comment on the proper way to proceed.
Cheers, - Darse.
--
char*p="char*p=%c%s%c;main(){printf(p,34,p,34);}";main(){printf(p,34,p,34);}
Erik Gravgaard
: I have had a longstanding argument with one of my backgammon opponents
: yes and is tied to crossovers. In a game where you are trying to save a
: gammon you try to maximize crossovers. Therefore, it seems logical to
: me that in a game where you are trying to preserve your timing that you
: could minimize crossovers and attempt to play slow. My opponents
: argument centers on the fact that pips are pips. Any comments?
Pips are pips, but you do have techniques to slow down your speed.
Normally you would try to find ways to kill certain high numbers (6'es &
5'es normally). This way your average roll in terms of pips moved goes
down considerably.
--
Erik Gravgaard (erikg) --------------------------
Pres. of the Danish Backgammon Life is a series of up
Federation and down equity decisions
er...@inet.uni-c.dk - Paul Magriel
--------------------------
Kit Woolsey
: I have had a longstanding argument with one of my backgammon opponents
: about whether or not you can play "slowly". I feel that the answer is
: yes and is tied to crossovers. In a game where you are trying to save a
: gammon you try to maximize crossovers. Therefore, it seems logical to
: me that in a game where you are trying to preserve your timing that you
: could minimize crossovers and attempt to play slow. My opponents
: argument centers on the fact that pips are pips. Any comments?
Of course you can play "slowly" the way you describe. For example, let's
suppose you are playing a typical bar point holding game -- you have two
men on your opponents bar point, and everybody else on your side of the
board, while he has his midpoint and maybe his eight point. You are
hoping to be able to outwait him so he has to leave the first shot. If
you bring all your outfield checkers into your inner board then if you
throw a six you will be the one who is forced to run with one checker and
leave the shot. However if you leave a checker or two in the outfield
(which is what you would call minimizing crossovers), then you will be
able to hold the fort. This is called saving sixes.
Of course, things aren't always that simple. For example, suppose your
opponent has two men on your ace point and you have a full prime in front
of him and want to hold that prime as long as possible. Now your best
strategy is to bring all your men in as quickly as possible, preferable
putting a spare or two on the bar point to handle fives. This way you
make it so you don't have to play sixes, and your prime lasts longer.
This is called killing sixes.
The bottom line is that you do have some control of the timing of your
position in spite of the fickle dice. However the desired strategy
depends on the type of problem -- it isn't just a question of minimizing
or maximizing crossovers.
Kit
Scott Salisbury
paul.j...@jhuapl.edu
> In race situations (including saving gammons), it is usually correct to
> move a man to the 6 point in preference to any other use of the roll.
> This should be fairly obvious, but I have seen several errors of this
> type in games and books, including the holy Magriel.
>
I've often wondered about this. In a race when bringing several men into your
inner board, it seems to me that moving to the six point is preferrable. But I
have had people tell me that a "good" distribution of the men is somtimes more
important to improve efficiency and avoid wasting rolls when you
eventually start bearing off. So my question is: In a race, should I just try
and get all my men home as fast as possible and then worry about distribution,
even if I end up stacking the 5 and 6 points, or should distribution be a
consideration as I'm bringing them in?
pj
Kit Woolsey
: In article <3d9t43$b...@scapa.cs.ualberta.ca>, <da...@cs.ualberta.ca> writes:
: > In race situations (including saving gammons), it is usually correct to
: > move a man to the 6 point in preference to any other use of the roll.
: > This should be fairly obvious, but I have seen several errors of this
: > type in games and books, including the holy Magriel.
: >
: I've often wondered about this. In a race when bringing several men into your
: inner board, it seems to me that moving to the six point is preferable. But I
: have had people tell me that a "good" distribution of the men is sometimes more
: important to improve efficiency and avoid wasting rolls when you
: eventually start bearing off. So my question is: In a race, should I just try
: and get all my men home as fast as possible and then worry about distribution,
: even if I end up stacking the 5 and 6 points, or should distribution be a
: consideration as I'm bringing them in?
Good question. The answer lies in looking ahead to see what we are
trying to avoid happening in the later stages of the bearoff.
What we are trying to avoid is wasting pips. By this, I mean not being
able to play the full pips on the dice. If you roll a five and can only
use it to take a checker off the three point, you have wasted two pips.
To see how this costs, suppose in the ending you have two checkers on the
ace point, one on the two point, and one on the three point, and roll
6-4. You can only take two of the checkers off, wasting several pips.
If you could have organized things earlier so that in this position you
had one checker on the four point and one on the three point (same pip
count, but more men off), then you could have taken both men off and won
the game. Thus, wasted pips translates into more rolls to bear off.
How do we avoid wasted pips? It should be obvious that wasted pips come
from having a bunch of men on the ace and two points, since we are forced
to use larger numbers to take these checkers off. So our goal in the
bearoff is to take as many men off as we can, avoiding dumping checkers
on the low points.
How do these checkers get onto the low points? This often happens when
we have gaps in our board. For example, suppose we have six checkers on
the six point and nobody on the five point when we start bearing off.
Every time we roll a five we are forced to take a checker to the ace
point, and as we have seen this will lead to later wastage. This is the
reason that it is important to bear in smoothly, making sure there are
some checkers on the five and four points, so that if we roll fives and
fours in the bearoff when we still have men on the six point we are not
forced to bear them in deep. Magriel suggests the following exercise:
Set up the board with one player having all his checkers on the 6 point,
while the other player has three checkers on each of the 4, 5, 6, 7, and
8 points. As you can see, the pip count is even. Now roll out the
position giving both players the same dice rolls and playing
simultaneously. It will usually be a tie, but you will see that if
anybody wins it is usually the player with the better distribution.
The concept of putting a lot of checkers on the five and four points
shouldn't be carried too far, since there is another way to waste pips in
the bearoff. Suppose you have five men on the five point and two men on
the six point. If you then roll more than two sixes before rolling a lot
of fives, the next six will have to be played by taking a checker off the
five point, wasting a pip. Thus having a lot of men on the six point is
good; but you still want to have decent distribution.
The ideal structure you should be aiming for when bringing the checkers
in is sort of a triangle -- more on the six point, then the five point,
etc. If you look at the position: 5 on the 6, 4 on the 5, 3 on the 4, 2
on the 3, and 1 on the two this is about what you should be aiming for.
Of course taking checkers off is important also, which is why it is good
to bring them in. Old saying: You have to bring them in before you can
take them off.
The bottom line is that both bringing the checkers in and good
distribution are important, and you should strive for a good balance. Of
course the best racing strategy is simply to roll large doubles -- if you
do that successfully it won't matter much how you bear in your checkers.
Kit
Darse Billings
I should qualify my above statement to ensure clarity. When you are
bearing in to your home board in a race position, you usually want to
have a fairly even distribution of men over your 6, 5, and 4 points,
rather than one large stack on the 6 point. Kit's reply explains most
of the reasons behind this, and I highly recommend trying the exercise
(from Magriel's book) that he gave.
The example I discussed was a position where the inner board already had
a perfect distribution (two men on each point), so filling gaps in the
home board was not a factor. Given this, you almost always want to move
a man to the 6 point rather than some other move in the outfield.
Moving a man in leaves you with one less man in the outfield, which, in
general, increases the flexibility in how future rolls are used.
This is completely analogous to the bearing off phase, where it is
almost always correct to take a man off the board if possible, rather
than making some other move which improves distribution. Think of it as
bearing men off of the outfield. Good distribution helps you to avoid
wasting pips and not miss a bear-off, so deliberately not bearing off
when you can is usually illogical.
M. Livenspargar
<clip>
> This is completely analogous to the bearing off phase, where it is
> almost always correct to take a man off the board if possible, rather
> than making some other move which improves distribution. Think of it as
> bearing men off of the outfield. Good distribution helps you to avoid
> wasting pips and not miss a bear-off, so deliberately not bearing off
> when you can is usually illogical.
Speaking of which, when IS it a good idea to move a man rather than bear
one off in a race situation? I seem to recall seeing an example once upon
a time, but can't recall the situation. Will some kind soul post such a
position and give the rational?
Walter Trice
is, 3 on the ace-point, 1 each on the 2 and 4, and 5 on the 3. With a 2 to
play, 4/2 rather than 2/0 is the play that minimizes mean rolls to bear off.
The rationale is that you are more likely to miss twice after bearing off
than to miss once after the smoothing play. The swing rolls are numbers
like 4-3 where you lose the opportunity to fill the gap with another 2.
I wrote a computer program to list these positions and plays several years
ago, and both Bill Robertie (Advanced Backgammon Vol.2) and Danny Kleinman
(But Only the Hogs Win Backgammons) have used the list to write about plays
of this type.
There are only about 300 positions where these plays come up out of 54,263
possible home board configurations. They have little practical significance
because they are so rare and so little equity is lost when you miss one. Also
it is extremely difficult to figure out over the board whether such a play is
right. E. g., given that 4/2 is the right 2 in 315100, you might think it
would also be the right 2 in 414100, but in that case you should take the
checker off. Naturally the right play will also depend on the opponent's
position -- when winning it's more often right to smooth, and when losing it's
more often right to rip 'em off.
-- Walter Trice
Walter Trice
for 15 checkers in the home board has 3 on the 4, 5 on the 5, and 7 on the
6. This wastes 7.07 pips, on average, in the bearoff. Kit's 5 on the 6, 4
on the 5, etc. wastes 7.35 pips. If possible you would rather not start with
men on the 3 and 2. The concept is that with a supply of checkers on the 4,
5, and 6 you always have constructive ways to play your 3s, 2s, and 1s by
moving them to lower points (if you can't actually use them to bear off a
man.)
Walt