splitting when opp. has a free drop available
Chuck Bower
Thanks to all those who responded to my request for a
reference to Hal's compilation of opening rolls and results
from his matches. (Dec. 1990 Chicago Point.) That worked
so well I thought I'd try another!
As I've mentioned previously, I'm working on an article about
opening rolls, replies, and cube decisions in post Crawford
matches. I am looking for a reference to the following (if
it exists):
When the trailer in a post Crawford match is at even-away
(that is, needs exactly 2, 4, 6,... points to win the match)
opens with 21, 41, or 51, playing 6/5 is CLEARLY INFERIOR to
playing 24/23 with the 1. The reason: the only way this
game will continue is if this fresh blot (on trailer's 5-pt)
is hit! You get all the downside for the split play and
none of the upside. If, on the other hand, trailer splits
24/23, then bad rolls by leader will still result in the
him/her exercising the free drop, BUT in most of the games
in which leader takes, trailers equity will be better than
in games that started with the slot (and were subsequently
continued).
I will hopefully explain this better in the article! The reason
I ask for a reference is that I'd like to give proper credit
(in print) to the person who first wrote up the above.
Chuck
bo...@bigbang.astro.indiana.edu
c_ray on FIBS
Mark Damish
Chuck Bower (bo...@bigbang.astro.indiana.edu) wrote:
[...]
:
: When the trailer in a post Crawford match is at even-away
: (that is, needs exactly 2, 4, 6,... points to win the match)
: opens with 21, 41, or 51, playing 6/5 is CLEARLY INFERIOR to
: playing 24/23 with the 1. The reason: the only way this
: game will continue is if this fresh blot (on trailer's 5-pt)
: is hit! You get all the downside for the split play and
: Chuck
: bo...@bigbang.astro.indiana.edu
: c_ray on FIBS
If you've accidently/intentionally slotted at even-away post crawford,
and your blot is not hit, wouldn't the correct cube action be a
non-double, continuing to play (for the gammon), and doubling when
you became an underdog?
--
...Mark Damish mda...@bbn.com
Unknown
On Mon, 19 Jan 1998 15:12:47 GMT, mda...@bbn.com (Mark Damish) wrote:
>
>If you've accidently/intentionally slotted at even-away post crawford,
>and your blot is not hit, wouldn't the correct cube action be a
>non-double, continuing to play (for the gammon), and doubling when
>you became an underdog?
Anytime you win the opening roll, and he doesn't equalize; in other
words, whenever he is going to pass anyway, you might as well play on.
When you come to a place where your game could go downhill on many of
your rolls (though still ahead as it stands) now you can double and
let him guess whether to take.
Another stunt: when he has a must-take (against 3 away) play on till
the game is almost gammonish enough to tempt him to pass. The right
arithmetic is, that he should take unless he figures to get gammoned
more times than he wins the game. But that can be hard to figure.
So, again, let him guess. Anytime you do that, the man can go wrong.
deekay
Gary Wong
mda...@bbn.com (Mark Damish) writes:
> Chuck Bower (bo...@bigbang.astro.indiana.edu) wrote:
> : When the trailer in a post Crawford match is at even-away
> : (that is, needs exactly 2, 4, 6,... points to win the match)
> : opens with 21, 41, or 51, playing 6/5 is CLEARLY INFERIOR to
> : playing 24/23 with the 1. The reason: the only way this
> : game will continue is if this fresh blot (on trailer's 5-pt)
>
> and your blot is not hit, wouldn't the correct cube action be a
> non-double, continuing to play (for the gammon), and doubling when
> you became an underdog?
I don't think this can be right. Let's suppose you've just slotted your 5
point; the leader has missed; and you play on without doubling. The chequer
play will go something like this: having missed your slot, she'll split and
aim for an advanced anchor which is very valuable to her at this match
score. On the other hand, winning a single game is very bad for you since
it brings you to double match point (which you could get to simply by
doubling). Therefore you'll be trying very hard for the gammon -- to the
point of holding a prime and aiming to be hit to try for another chequer
back, and risky plays like that. As a stab in the dark let's say the game
proceeds something like this: you have a significant advantage in that your
5 point will probably be made, but the leader will be avoiding gammonish games
so gammons will still be relatively unlikely --
You win a gammon: 10%
You win single: 44%
Leader wins single: 44%
Leader wins gammon: 2%
Of the 44% of the games you win, let's say that in somewhat less than half of
them you will have been an underdog at some point (wave hands and mention
"Bayes theorem" here -- I'm willing to go into details if anybody disagrees
but I doubt it's important) and managed to get a cube accepted. So a complete
breakdown is:
event probability match equity total
You win a gammon: 10% 100% 10%
You win (cube at 2): 20% 100% 20%
You win (cube at 1): 24% 50% 12%
You lose: 46% 0% 0%
---
42%
which is less than the 50% match equity you could claim simply by doubling.
The problem for you is the "You win (cube at 1)" row. Unfortunately this is
a very common event; you're struggling for a gammon and your opponent is
struggling to win, and a lot of the time you'll just meet in the middle,
playing the game out to completiong having been too good to double the
entire way through. You have very little to win in this situation (it only
brings you to double match point, which you could already get to with the
cube) but you're risking losing the entire match if your opponent gets lucky
and takes the game away from you. Risking a lot to win a little is not worth
it; you're better off claiming with the cube and playing at DMP.
Cheers,
Gary (GaryW on FIBS).
--
Gary Wong, Computer Science Department, University of Auckland, New Zealand
ga...@cs.auckland.ac.nz http://www.cs.auckland.ac.nz/~gary/
Unknown
On 20 Jan 1998 12:29:42 +1300, Gary Wong <ga...@cs.auckland.ac.nz>
wrote:
Definitely there is a lot more to it than my previous post implied.
Among other things, you don't want to let it get to the point where
YOU are the guy making the guess. One thing is certain. If you start
with a big advantage (3-1, maybe 4-2) you might want to play on if his
response is really weak (5-1 or 5-2 or 4-1 or 2-1, or a running
number) thinking that you may really blast him, and in no case will
you be worse than even after the next exchange.
What you don't want is to become the underdog, which will put you at
something less than the 50% you could have had by cashing.
(As a practical matter, I would (try to) cash as soon as he has a
forward anchor.)
Here is a benchmark:
3-1 6-3 (running)
(plays on, hoping to blitz)
6-4 (24/18,13/9) 6-3 (running)
Any other roll from him, even 6-2 or 5-3 hitting your blot, leaves you
at least an even game, according to JF7. 6-3 is his best, and leaves
you at 48.8%.
Is it worth looking for the blitz, risking this one unfortunate result
(you miss, he anchors)? Darned if I know.
Interesting puzzle.
deekay
Mark Damish
Gary Wong (ga...@cs.auckland.ac.nz) wrote:
:
: I don't think this can be right. Let's suppose you've just slotted your 5
: Gary (GaryW on FIBS).
[...]
I guess I didn't explain my (partial) logic behind the non-double,
and the followup. I'll use -2-1 for the examples.
For the double play:
If I make the double play, he will drop, after rolling weakly.
After, which
rolls am I a favorite/dog/underdog? Does your opponent know? With one-sided
gammons, and a gammon price of 1 on a 1-cube, very few non-hitting
moves. Are you a favorite against your opponent in a 1-ptr? Does he
overplay/underplay the not getting gammoned aspect? How well can you/your
opponent evaluate an early/middle game position, when gammons
don't count? All things to consider.
Typical Result: I have a 50% chance to win the match on the next turn
(new game) after the double play.
For the non double play:
If I am a favorite to win the game, then ALL of the gammons, however
few there seem to be, are free... ...For this roll. That is, if I am
a favorite, and a favorite to remain the favorite, it doesn't cost
anything to roll, but I lose equity by starting the new game at 50%.
The next roll, this has to be evaluated again. I'm not playing on
not matter what. As Kit says, "Every roll is a new cube decision".
The real danger, is that you become a big underdog in one roll.
Perhaps when there are enough combinations for this to happen,
outweighing your (now not so free) gammons, it would be the time
to double. In the mean time, you have had x free rolls to win
a gammon, and the match. Another thing worth considering, if
you continue rolling/evaluating, Whose mistakes are costlier?
Which side is it easier to evaluate the correct cube action from?
If your opponents mistakes (Taking a drop, dropping a take) are
costlier, you have gained at this score. If his side is harder
to evaluate than yours, than you gain by having easier decisions
to make.
Typical Result: I win many more games than I lose, either because
I double after the 1st move, and my opponent drops,
or because he is overly gammon concience. The
gammons that I get, are virtually free, offset by
the cost of a big negative swing in one turn, but
I feel that it is profitable, to play, and examine
the position every turn. If this logic holds up,
than, I will win more than 50% of the matches
by not doubling on my first turn after the opening
turn with a slot.
It is easy that I have missed an important point, and could be incorrect.
This presentation is pretty vague, and without a proof, the logic
'seems' correct.
The next question in line then becomes: Could it possibly be profitable
to slot with an opening 21, at -2-1 post crawford, to gain extra gammons
if the above logic is correct?
...Mark
--
...Mark Damish mda...@bbn.com
Kit Woolsey
Mark Damish (mda...@bbn.com) wrote:
<snip>
: If I am a favorite to win the game, then ALL of the gammons, however
: few there seem to be, are free... ...For this roll. That is, if I am
: a favorite, and a favorite to remain the favorite, it doesn't cost
: anything to roll, but I lose equity by starting the new game at 50%.
This is not true. Just being a favorite to remain the favorite does not
give you an automatic free shot for the next roll. The reason is that
when things go badly on the next exchange you have cost yourself
considerable equity (you have to play the game as an underdog when you
could have been playing the next game at even money), while if things go
well on the next exchange you haven't gained all that much since most of
the time you won't get the gammon (either because you just don't get it
or because you are forced to cash sometime in the future). Thus, the
cost of a few bad sequences may be greater than the gain from many good
sequences.
Let's look at your slotting example. You roll 2-1 and play 13/11, 6/5,
and let us say he rolls 5-2 and plays 13/8, 13/11. No question that you
are the clear favorite now, and no question that most of the time you
will be the favorite after the next exchange. However in the bad
variations (you don't cover and he hits, or you cover and he rolls 6-6
for example), you are now a clear underdog and, instead of playing from
even money you are playing at a disadvantage.
Do the gains when things go ok (i.e. you cover and he doesn't roll a
crusher) -- that is, your gammon possibilities, compensate for the bad
scenarios. I don't have any proof, but my guess is that they do not.
What about stronger starts, such as 3-1 for you, 6-2 for him. The jury
is still out, buy I believe it is theoretically correct to play on for
the gammon on a start such as this.
Kit
Chuck Bower
In article <34c48f2e....@news.salzburg.co.at>, Donald Kahn <> wrote:
(Concerning trailer NOT doubling at first opportunity at any post Crawford
score,)
(snip)
>Definitely there is a lot more to it than my previous post implied.
>Among other things, you don't want to let it get to the point where
>YOU are the guy making the guess.
(snip)
YES! A good point which is almost never made in these debates
(as, for example, when to double at the -2,-2 score).
It is fun to discuss the rare, special, esoteric situations on the
newsgroup. But in REAL play, often the "correct" technical decision
should take a back seat to the practical ones.
If it is technically a mistake not to double at first opportunity
post-Crawford, it can't be wrong by much. I'd guess a small fraction
of a a percent in match equity units. But, if you wait and then make
a mistake, it could be quite significant. Maybe you'll even forget
that you hadn't doubled! Don't be too skeptical; this happened a
couple years ago in the finals at Istanbul, with a HUGE amount of
money up for grabs (in the tens of thousands of $ if memory serves me).
There are a lot of demands on a player's concentration during a
match (and especially near the end of a match). Turning the cube
immediately frees your mind to concern itself with things which can't
be so easily solved, like how to best move the checkers.
I can't argue against a player who chooses to go for a swindle
by holding off cubing. If you are CLEARLY the stronger player (and
thus suspect that your opp might get confused) and are sharp enough
to keep track of the cube position and still make your best plays,
etc. then it's probably worth some equity. But if you ever screw
up, it might take a lot of tricks to make up for the one big error.
Chuck
bo...@bigbang.astro.indiana
c_ray on FIBS
Gary Wong
mda...@bbn.com (Mark Damish) writes:
> Gary Wong (ga...@cs.auckland.ac.nz) wrote:
> :
> : I don't think this can be right. Let's suppose you've just slotted your 5
> : Gary (GaryW on FIBS).
> [...]
>
> I guess I didn't explain my (partial) logic behind the non-double,
> and the followup. I'll use -2-1 for the examples.
> If I am a favorite to win the game, then ALL of the gammons, however
> few there seem to be, are free... ...For this roll. That is, if I am
> a favorite, and a favorite to remain the favorite, it doesn't cost
> anything to roll, but I lose equity by starting the new game at 50%.
> not matter what. As Kit says, "Every roll is a new cube decision".
> The real danger, is that you become a big underdog in one roll.
Ah, now I think about it harder after reading your second post I'm more
convinced. You are right that you have effectively a "free roll" until
you become the underdog (almost like losing your market in reverse); I
believe I was wrong after all to enumerate the probabilities the way I
did in my previous article because they are not independent. I think
you're quite right, sorry for missing the point the first time around.
> Perhaps when there are enough combinations for this to happen,
> outweighing your (now not so free) gammons, it would be the time
> to double.
Hmmm. After you double, your match equity can never be greater than 50%
(since your opponent can bring you to 50% simply by dropping). Your opponent
will take if and only if her winning chances are at least 50% -- neither
gammons nor volatility affect her decision.
I don't think volatility should affect your decision, either. I suspect
that unlike normal money play, it is a correct double if and only if it is
a correct take -- ie. there is no "window" where it is a double/drop. You
lose your `market' the instant you get it (which is back to front from the
normal sense -- you want to double when _behind_ rather than ahead), so
there's no need to double early because the position is volatile. This
means the "danger" of becoming a big underdog in one roll doesn't matter --
your equity before you roll is simply an average of all the possible
equities after you roll, which means you either have so many potential
disaster rolls that you are _already_ an underdog (ie. correct double/take);
or there are sufficiently many good rolls for you that overall you remain
the favourite (ie. no double/drop, and continue to hope for the gammon).
In practice I doubt it really matters. Once you get a few rolls away from
the opening, chances are one of several things will have happened: your
opponent becomes a clear favourite (double/take); you become a clear
favourite (play on for gammon); or you reach a position where the advantage
is not clear cut, which I believe must be a double by Woolsey's Rule which
still applies.
> The next question in line then becomes: Could it possibly be profitable
> to slot with an opening 21, at -2-1 post crawford, to gain extra gammons
> if the above logic is correct?
Ummm... intuitively I still believe it isn't, but you've shaken what I used
to think was right so I'm not sure any more :-) Perhaps it is, I'd have to
think some more. And if you're right not to force your opponent to exercise
their free drop, the Holland rule becomes pretty pointless too.
Cheers,
Gary (GaryW on FIBS).