Have the Tooth Out Right Away?
Duncan D. Robertson
Money game, O owns cube at 2, X has 3 men borne off:
+-24-23-22-21-20-19----18-17-16-15-14-13
O O O O O O
O O O O O
O
X X
X X O X X X
X X O X X X O
+--1--2--3--4--5--6-----7--8--9-10-11-12
X rolls 4-4. Should X play safely (for the moment) and move his 5s and
4s and hope all goes well with the later throws, or should he bite the
bullet and move his 6s and blot his 5 (or 4 to get one more man in,
which seems of dubious value)?
If he runs the 6s, he will leave O a second shot at him with 6-5, 6-4,
6-3, 5-4, 5-3, 4-3, or 2-2 ... 13/36 of the rolls plus some slight
chance of having to blot two rolls later as well.
It's harder to figure all of the possibilities if he clears his 5 and 4
points, but it instinctively looks as if that could open up a can of
worms that could last for several rolls.
Would your play be the same if this were the last game of a tournament
match? Thanks for the input.
Stephen Turner
Duncan D. Robertson wrote:
>
> Money game, O owns cube at 2, X has 3 men borne off:
>
> +-24-23-22-21-20-19----18-17-16-15-14-13
> O O O O O O
> O O O O O
> O
>
> X X
> X X O X X X
> X X O X X X O
> +--1--2--3--4--5--6-----7--8--9-10-11-12
>
> X rolls 4-4. Should X play safely (for the moment) and move his 5s and
> 4s and hope all goes well with the later throws, or should he bite the
I play safe at any score. Why would you want to leave a shot now? You're
unlikely to have to leave more than one shot later (unless O leaves his
anchor and you roll n3 for n >= 4), so why leave a voluntary shot now? Even
if you do get hit later, you've got more men off. Besides, you might get away
with it...
The only circumstances in which you might consider leaving a shot now are if
O's board was bad but about to get better.
In general here are the criteria to consider in "pay now/pay later" situations:
1) Are you likely to leave more or worse shots if you pay later? [NO]
2) How likely are you to get away with not paying at all if you don't pay now?
[SOME]
3) Is your opponent's board going to improve by the time you pay? [NO]
--
Stephen Turner sr...@cam.ac.uk http://www.statslab.cam.ac.uk/~sret1/
Stochastic Networks Group, Statistical Laboratory,
16 Mill Lane, Cambridge, CB2 1SB, England Tel.: +44 1223 337955
"Collection of rent is subject to Compulsive Competitive Tendering" Cam. City
Gerald Dahlin
Duncan D. Robertson wrote:
>
> Money game, O owns cube at 2, X has 3 men borne off:
>
> +-24-23-22-21-20-19----18-17-16-15-14-13
> O O O O O O
> O O O O O
> O
>
> X X
> X X O X X X
> X X O X X X O
> +--1--2--3--4--5--6-----7--8--9-10-11-12
>
> X rolls 4-4. Should X play safely (for the moment) and move his 5s and
> 4s and hope all goes well with the later throws, or should he bite the
> which seems of dubious value)?
>
> If he runs the 6s, he will leave O a second shot at him with 6-5, 6-4,
> 6-3, 5-4, 5-3, 4-3, or 2-2 ... 13/36 of the rolls plus some slight
> chance of having to blot two rolls later as well.
>
> It's harder to figure all of the possibilities if he clears his 5 and 4
> points, but it instinctively looks as if that could open up a can of
> worms that could last for several rolls.
>
> Would your play be the same if this were the last game of a tournament
> match? Thanks for the input.
If you advance from the 4 and 5 points with your 4-4,
you will have 5 off. On your next roll, any of 30 rolls do no immediate
damage (only 6-4,6-5, and 5-4 expose a single blot). Even then, your
risk is 39% (14 rolls out of 36). So your probability of being hit
after your next turn is: 1/6 x 14/36 = 6.5%. Also, you will likely
have 6 off if you do open next time.
My humble opinion is to pay later.
Greycat Sharpclaw
There is an allegation that "Duncan D. Robertson" <nw...@btigate.com>
wrote:
>Money game, O owns cube at 2, X has 3 men borne off:
>+-24-23-22-21-20-19----18-17-16-15-14-13
> O O O O O O
> O O O O O
> O
>
> X X
> X X O X X X
> X X O X X X O
>+--1--2--3--4--5--6-----7--8--9-10-11-12
>X rolls 4-4. Should X play safely (for the moment) and move his 5s and
>4s and hope all goes well with the later throws, or should he bite the
>bullet and move his 6s and blot his 5 (or 4 to get one more man in,
>which seems of dubious value)?
Well, not an expert, I'll admit (and my FIBS rating will insist <g>),
but it seems to me that:
Moving the 6's in gives an immediate risk.
Leaving pieces on the 6's *may* result in a later blot, but may not...
a 6-1 or 6-2 becomes a very good roll, for instance. Yes the risk of
a delayed blot is very substantial, but not certain.
"Biting the bullet" and leaving a blot on the 6's does not prevent all
further risk... many of the "bad" rolls next time are bad either way
(6-5, for intance).
Looking at the numbers as competently as I really can seems to support
the conclusion that the intuitive arguements give:
I would play it safe, and hope for the best luck in my rolls, rather
than automatically leaving a blot now because it lessens the chances
on one later.
Greycat
Gre...@tribeca.ios.com
Does anyone have any spare tunafish??
Stein Kulseth
In article <332FB2...@cam.ac.uk>, Stephen Turner <sr...@cam.ac.uk> writes:
|> Stephen Turner wrote:
|> >
|> > In general here are the criteria to consider in "pay now/pay later" situations:
|> > 1) Are you likely to leave more or worse shots if you pay later?
|> >
|> 4) If still in doubt, pay later.
|>
Isn't 1) and 2) two sides of the same coin here?
In the magnificently annotated Woolsey-Bagai match, Jeremy quotes Kit on
pay now/later strategy, and gives the 3 main criteria as:
Is my opponent's board improving or crashing?
If I pay later will I be likely to leave more and worse shots?
If I pay now and am missed will I be home free?
Of course the answer to the 3rd question in the given situation is still
"No" as he is still more than 1/3 to leave another shot.
--
stein....@fou.telenor.no
... signature funny quote (and more) at http://www.nta.no/brukere/stein
Stephen Turner
Stephen Turner wrote:
>
> In general here are the criteria to consider in "pay now/pay later" situations:
> 1) Are you likely to leave more or worse shots if you pay later?
> 2) How likely are you to get away with not paying at all if you don't pay now?
> 3) Is your opponent's board going to improve by the time you pay?
>
I left out the final point:
4) If still in doubt, pay later.
--
Duncan D. Robertson
Gerald Dahlin wrote:
>
> Duncan D. Robertson wrote:
> >
> > Money game, O owns cube at 2, X has 3 men borne off:
> >
> > +-24-23-22-21-20-19----18-17-16-15-14-13
> > O O O O O O
> > O O O O O
> > O
> >
> > X X
> > X X O X X X
> > X X O X X X O
> > +--1--2--3--4--5--6-----7--8--9-10-11-12
> >
>
> you will have 5 off. On your next roll, any of 30 rolls do no immediate
> damage (only 6-4,6-5, and 5-4 expose a single blot). Even then, your
> risk is 39% (14 rolls out of 36). So your probability of being hit
> after your next turn is: 1/6 x 14/36 = 6.5%. Also, you will likely
> have 6 off if you do open next time.
>
> My humble opinion is to pay later.
Thanks for the input, and I am pretty well convinced that on balance
paying later is correct here. Just to complete the picture, however, I
should add that, after moving the 5s & 4s, I was anticipating O moving
one of his men on my 3-point so that I'd have to move a 3 next time.
Then a 6-3, 5-3, or 4-3 would give him a double shot at me. Never mind;
I can't be gammoned because I have men in, and the 5s and 4s will give
me a reasonable chance to score a gammon for myself. Thanks again for
your remarks.
Stephen Turner
Stein Kulseth wrote:
>
> In article <332FB2...@cam.ac.uk>, Stephen Turner <sr...@cam.ac.uk> writes:
> |> Stephen Turner wrote:
> |> >
> |> > 2) How likely are you to get away with not paying at all if you
> |> > don't pay now?
>
Er ... that's one interpretation. :) But not the way I was thinking of it.
Perhaps I would have been better to say:
1) How likely are you to get away with not paying at all if you
don't pay now?
2) If you do leave shots later, are they likely to be more or worse
thank the ones you could leave now.
--
Stephen Turner sr...@cam.ac.uk http://www.statslab.cam.ac.uk/~sret1/
Statistical Laboratory, 16 Mill Lane, Cambridge, CB2 1SB, England
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for any inconvenience this may cause" Topshop, Cambridge