cube decision
Wayne King
13 18 19 24
+-----------------------------------------+ X
| . X . . . O | | X X X X X . |
| X O | | X X X X |
| | | X X X |
| | | | ---
| | | | | 1 |
| |BAR| | ---
| | | |
| | | |
| | | O |
| | | O O O O O |
| X . . . . O | | O O O O O O |
+-----------------------------------------+ O
12 7 6 1
Pipcounts: O = 86, X = 86
Match Score O-3 away
X-4 away
O on roll. Cube action?
The following position came up in my 2nd round match of Snoopy's
tournament. As O this position puzzles me. O has many market losers which
would seem to point to doubling, yet X has a very efficient re-double if
O misses. I would appreciate any thoughts as to (1) what is the correct
cube action and (2) how one in general would take into account an opponents
re-double when deciding whether or not to double.
Thanks in advance.
Wayne King (wking on FIBS)
Kit Woolsey
: 13 18 19 24
: Thanks in advance.
Very interesting problem. I could write a book about match cube
decisions like this (come to think of it, I *have* written such a book).
The score 3 away, 4 away is perhaps the trickiest match score of all.
The first step toward attacking any decision on whether or not to double
should always be to put yourself in the other guy's shoes and ask if he
should take. Sometimes this solves the problem quickly. If the answer
is no, or maybe not, then the double is automatic. If he has a monster
take then probably you shouldn't be doubling unless the position is
super-volatile (which admittedly this one is). In this sort of position
if your opponent has a Big take you probably should not be doubling if
you are ahead in the match, since he has more cube leverage. However if
you are behind in the match then you should be inclined to double if
there is a sufficient chance you will lose your market. However if his
take is fairly close, then it is usually correct to double even if you
are ahead in the match.
Now, to the actual position. In order to avoid overly complex math, I'm
going to make some rough assumptions -- the way I would do at the table.
The idea is to make these assumptions about equally favorable for both
players, so you can get a good approximation of the equity in the
position. Let's suppose that if O hits the shot he always wins a single
game (he might not, but that may be compensated for by a possible
gammon). If O misses the shot X does have huge cube leverage, since O's
take point is 40%. Let's assume that X will redouble, O will take, and
that X will win 60% of the time. O has 16 hitting numbers out of 36.
Therefore: 4/9 of the time O will be ahead 1 away, 4 away, for 83%
equity. 5/9 of the time they will play for the match, with O's equity
40%. Averaging these out, O's equity is about 64%. Since if X passed
O's equity at 4 away, 2 away is 68%, it looks like X has a fairly close
decision, so it might be right for O to double since a lot rides on the
next roll.
Let's see if this turns out to be correct. Suppose O doesn't double. If
he hits by our assumptions he will win and be ahead 2 away, 4 away for
68% equity -- this happens 4/9 of the time. If he misses X won't be
flinging the cube over automatically, so let's just assume that X will
win a 1-game 60% of the time and O will win a 1-game 40% of the time.
Since O is missing 5/9 of the time, he will win 2/5 of these, so he will
win 2/3 of the time for 68% equity and lose 1/3 of the time for 50%
equity. This averages to 62% equity. Since we already estimated O's
equity in the match at 64% if he doubles, it looks like it is correct to
double.
I make no claims that this is the correct answer. I made several rough
and questionable assumptions, and if you change some of them it might
well change the final result. Also I give no guarantees that my
arithmetic is correct. However, this is the approach one should take at
the table.
Kit
Robert Koca
Wayne King (wk...@ritz.mordor.com) wrote:
: 13 18 19 24
: +-----------------------------------------+ X
: | . X . . . O | | X X X X X . |
: | X O | | X X X X |
: | | | X X X |
: | | | | ---
: | | | | | 1 |
: | |BAR| | ---
: | | | |
: | | | |
: | | | O |
: | | | O O O O O |
: | X . . . . O | | O O O O O O |
: +-----------------------------------------+ O
: 12 7 6 1
: Pipcounts: O = 86, X = 86
: Match Score O-3 away
: X-4 away
As part of his analysis kitwoolsey wrote:
>Therefore: 4/9 of the time O will be ahead 1 away, 4 away, for 83%
>equity. 5/9 of the time they will play for the match, with O's equity
>40%. Averaging these out, O's equity is about 64%.
should be 59%.
and wrote:
"If O misses the shot X does have huge cube leverage, since O's
take point is 40%. Let's assume that X will redouble, O will take, and
that X will win 60% of the time."
and in next paragraph, "Suppose O doesn't double. ... If he misses X won't be
flinging the cube over automatically, so let's just assume that X will
win a 1-game 60% of the time and O will win a 1-game 40% of the time."
Surely if X wins 60% of the time in the first case (after doubling)
X will win significantly more than that in the second case (with
cube access). As a rough measure of this importance consider a pure
race in which pipcount is tied 80-80 (this position may very well become close
to this). In a money game, equity to player on roll without cube access is
.02 if cube is neutral then equity is +.25. I would think that if X wins 60% cubeless after a miss by O, a good approximation to equity with neutral cube
is that X wins 70% single game and loses 30% single game. This changes result by
about 1% (5/9*10%) of time, X goes to 50% instead of 68%
My conclusion is that not a double. 59% < 61%
,Robert Koca
bobk on FIBS
ko...@orie.cornell.edu
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Please, don't throw knives.
Frank Bommarito
Kit Woolsey <kwoo...@netcom.com> wrote:
>Wayne King (wk...@ritz.mordor.com) wrote:
>
>: 13 18 19 24
>: +-----------------------------------------+ X
>: | . X . . . O | | X X X X X . |
>: | X O | | X X X X |
>: | | | X X X |
>: | | | | ---
>: | | | | | 1 |
>: | |BAR| | ---
>: | | | |
>: | | | |
>: | | | O |
>: | | | O O O O O |
>: | X . . . . O | | O O O O O O |
>: +-----------------------------------------+ O
>: 12 7 6 1
>
>: Pipcounts: O = 86, X = 86
>
>: Match Score O-3 away
>: X-4 away
>
>: O on roll. Cube action?
>
skills come completely from playing. It is by experience that I make
double and drop decisions.
I have seen this position all two many times. If I am X, I am hoping for
a double ( I am behind in the match and would love an opportunity to win
quickly ). I am not worried about a gammon - I just have too few men left
out of home for that. If O misses, I am sure to double back and feel that
I have a great chance for victory. If O hits, I am 4away 1 away - indeed
a tough position to be in.
I would take the following approach in this situtation -
1. Do I feel that my opponent is a better player?
If yes, I double as O and take as X. (Try to end the match against a
better player as appeal)
2. Do I feel that I am better than my opponent?
If Yes, I dont double as O - Dont want to give my opponent any lucky
chances - I can outskill them to the end. ( No sense in betting the farm
on a hunch when you own a horse ) (This is essentially how Las Vegas lives)
3. Am I about even with my opponent?
A. Has he been getting lucky when he needs it?
if yes - see number 2
if no - see number 1
Math blesses only a small few - way to few to cover those who play BG.
So, feel monitors the rest. This I believe is the reason why a computer
will never be the "best" player in the world.
Every expert who has commented on the newsgroup ( I think all ) has noted
exceptions to the math choices provided.
When the math show 64 to 61 % - or 59 to 61 % - this is too much for the
humans (most of us) to figure out - Thats why feel is so important.
Tom Johnson has software that I am considering purchasing. It would be
interesting to see how this software evaulates the above position.
I hope this is not to much rambling on - sorry if it is.
Frank Bommarito (champion)
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Usenet rec.games.backgammon gateway
Approach like that is not gonna take u in the right direction.
Sorry, it might be rude, but I just couldn't help it
Igor
Kit Woolsey
: Wayne King (wk...@ritz.mordor.com) wrote:
: : 13 18 19 24
: : +-----------------------------------------+ X
: : | . X . . . O | | X X X X X . |
: : | X O | | X X X X |
: : | | | X X X |
: : | | | | ---
: : | | | | | 1 |
: : | |BAR| | ---
: : | | | |
: : | | | |
: : | | | O |
: : | | | O O O O O |
: : | X . . . . O | | O O O O O O |
: : +-----------------------------------------+ O
: : 12 7 6 1
: : Pipcounts: O = 86, X = 86
: : Match Score O-3 away
: : X-4 away
: As part of his analysis kitwoolsey wrote:
: >Therefore: 4/9 of the time O will be ahead 1 away, 4 away, for 83%
: >equity. 5/9 of the time they will play for the match, with O's equity
: >40%. Averaging these out, O's equity is about 64%.
: should be 59%.
Of course Bob is correct here. I mentally did my 4/9 backwards. Note my
disclaimer about my math!
: and wrote:
: "If O misses the shot X does have huge cube leverage, since O's
: take point is 40%. Let's assume that X will redouble, O will take, and
: that X will win 60% of the time."
: and in next paragraph, "Suppose O doesn't double. ... If he misses X won't be
: flinging the cube over automatically, so let's just assume that X will
: win a 1-game 60% of the time and O will win a 1-game 40% of the time."
: Surely if X wins 60% of the time in the first case (after doubling)
: X will win significantly more than that in the second case (with
: cube access). As a rough measure of this importance consider a pure
: race in which pipcount is tied 80-80 (this position may very well become close
: to this). In a money game, equity to player on roll without cube access is
: .02 if cube is neutral then equity is +.25. I would think that if X wins 60% cubeless after a miss by O, a good approximation to equity with neutral cube
: is that X wins 70% single game and loses 30% single game. This changes result by
: about 1% (5/9*10%) of time, X goes to 50% instead of 68%
Not taking the cube access into account was one of the rough
approximations I made. Bob's analysis does a better job of fine tuning
things.
: My conclusion is that not a double. 59% < 61%
And quite likely a correct conclusion. This just shows how difficult
these match equities can be. If I can't get it right doing the
calculations in the comfort of my home (and I think I can immodestly
claim pretty good expertise on the subject), imagine the pressure one is
under at the table, perhaps in the finals of a big tournament with big $$
at stake. Nobody promised things would be easy! However the more adept
one is at doing these calculations, the more likely one is to make the
right decision at the table, or at the very least avoid some catastrophic
cube action which dumps gobs of equity down the drain.
Kit
Carl Nielsen
+-----------------------------------------+ X
| X O . X X X | | . X . . . X |
| X O X X X | | X |
| X | | X |
| | | | | 1 |
| |BAR| | ---
| O | | |
| O | | |
| O | | |
| X O O O O O | | . . O . . . |
+-----------------------------------------+ O
1 6 7 12
Score 0-0 (Match length 3)
O to play 5-4.
I played 23-14. X rolled 4-2 and played 17-23. I couldn't get back on and
ended up losing to a gammon. Did I play wrong? Should I have left moving my
runners till later and moved 9-4 6-2 or something like that?
Suggestions Please
Carl Nielsen (CP on FIBS)
Kit Woolsey
: 24 19 18 13
: Suggestions Please
Your play looks ok to me. You have to get moving sometime and your
opponent has plenty of time if you play the waiting game, so it is
probably best to run now before you have an accident and are forced to
lose your board by rolling too many threes and fours. You were just
unlucky. Btw, what is that cube doing in the center? You have a clear
advantage with some threats, so you have a strong double. Maybe your
opponent will pass, and maybe he should pass!
Kit
Kent Goulding
: : Suggestions Please
: Kit
Biggest error here, by FAR, is the failure to double. As is so often the
case, the cube errors are the costly ones while checker plays are no big
deal. I think your opponent should pass. As far as the checker play
goes, it looks pretty close. Running now gives your opponent a crack at
grabbing TWO of your checkers, while waiting will likely expose only
one. Your home board is actually not in great danger of breaking right
away. You can't play 5s and 6s there, and you will likely run from your
anchor the next chance you get. Also, it's nice to spread out some
builders for your ace point in case your opponent runs (either forced or
by choice). I'm inclined to sit tight and see what happens next.
--KG
Dick King
First, i would have doubled. results were what they were but it's not a
standout take for O.
Second, i would have waited one roll to break. The man on the 13 pt will
probably be gone next roll.
Third, 9-4 6-2 has the virtue that it leaves a vicious collection of builders,
making a break off the 1 point very unappetizing.
-dk
Kevin B. Purvis
: Kit Woolsey (kwoo...@netcom.com) wrote:
: : Carl Nielsen (nlsc...@uctvax.uct.ac.za) wrote:
: : : 24 19 18 13
: : : +-----------------------------------------+ X
: : : | X O . X X X | | . X . . . X |
: : : | X O X X X | | X |
: : : | X | | X |
: : : | | | | ---
: : : | | | | | 1 |
: : : | |BAR| | ---
: : : | O | | |
: : : | O | | |
: : : | O | | |
: : : | X O O O O O | | |
: : : | X O O O O O | | . . O . . . |
: : : +-----------------------------------------+ O
: : : 1 6 7 12
: : : Score 0-0 (Match length 3)
: : : O to play 5-4.
[some comments deleted]
: : unlucky. Btw, what is that cube doing in the center? You have a clear
: : advantage with some threats, so you have a strong double. Maybe your
: : opponent will pass, and maybe he should pass!
: : Kit
: Biggest error here, by FAR, is the failure to double. As is so often the
[some comments deleted]
: --KG
It seems that the above position is a clear double for O and a pass for X.
No reasons are given for why this is so, and the reasons elude me. The
position looks fairly even to me. (Both have 2 men back, O's board is
better, but X has better outfield control and a threat to build his board,
neither player will have an easy time running his back men.)
Cube play is by far the weakest aspect of my game, so I would greatly
appreciate comments (especially reasons) on cube action for the above
position. Thanks.
Kevin Purvis
kpu...@cyberspace.com
fah...@brhep1.physics.brown.edu
photocopies of P magriels book backgammon. if you know who or where, it would
be appreciated.
Jason Lee
>I have no morals
Is this common for an Ivy Leaguer?
JLee
--
| Jason Lee jp...@galaxy.csc.calpoly.edu |
| "The two most common substances in the universe are hydrogen and |
| stupidity." |
| Harlan Ellison |
Mike Howerton
: I have no morals and remeber a posting of someone that is selling
: be appreciated.
I too would be interested in this item. If I could find the book for
purchase here in town then I would buy it but Gammon books are kind of
hard to come by here in Phoenix.
Casey Forest
Those of you who are interested in obtaining this book could try what
I did. Call around to some huge used bookstores (doesn't have to be
in your area or even your state) and ask if they have it. If they don't
see if they can keep a record of your request and notify you if it
comes in.
I called a store in another city to see if they had it, which they didn't.
About a month later, they called me and had just obtained a copy. I
put it on my VISA and the UPSed to me. Total cost - one phone call and
$14.00 (which included the shipping).
Hope this helps!
Casey Forrest (ms on FIBS)
:wq
:wq!
: hard to come by here in Phoenix.
James Eibisch
ca...@news.uoregon.edu "Casey Forest" writes:
> Those of you who are interested in obtaining this book could try what
> I did. Call around to some huge used bookstores (doesn't have to be
> in your area or even your state) and ask if they have it. If they don't
> see if they can keep a record of your request and notify you if it
> comes in.
'Backgammon' is somewhat harder to find outside the US (naturally). Over three
months ago I sent a request to several major out-of-print book search companies
in London for it, but no joy so far.
Does anyone have any idea of good places to look for it in Europe (for me,
preferably the UK)? Any success stories? This book is proving very elusive,
which merely enhances its appeal, which makes one look harder, etc. etc. I know
of at least one reliable source, but the 'standard' $80 if beyond me just now.
In the case of not being able to get a copy by any means, is there any book
which will do in its place?
And now the biggie. I've heard the rumours of Magriel publishing a revised
edition of Backgammon - does anyone know anything about this?
--
James Eibisch