When the leader is 2 away doubling strategy?
mi...@depreli.demon.co.uk
Could somebody please explain to me what the doubling startegy should
be when you are trailing in a match and the leader is 2 away.
My understanding so far of doubling theory is that once you are within
the doubling window should consider doubling if the equity gained by
doubling and not missing your market is more than the equity lost by
giving your opponent sole access to the cube.This can happen right at
the bottom end of the window in last roll situations i.e when you have
a checker on your 2 and 5 points and your opponent has 2 checkers on
his 1 point you should double because the game ends after this roll
so just being a tiny favourite you should double.Of course its ideal
to double right at the top of your window as this is the most
effecient time but in theory its better to double slightly earlier
than later if your have market losing sequences as this would cost you
equity if you dont.
Now onto my main point.I have read articles explaining doubling theory
at the match score of 4 away 2 away.A good example is :
Leader 5-4 plays 13/8 24/20
Trailer 2-1 plays 13/11 6/5*
Leader dances
Trailer doubles trailer takes equity for leader (.297)
or if trailer points on the blot with 3-1
its a double drop equity .337
I can see whats happening here as the high gammon rates make it very
advantageous for the trailer to double and for the leader to be
cautious of taking.
Now I want to get ont the general subject when the leader is 2 away
At this score the leader gets no benefit from owning the cube as there
will never be any equity lost by doubling early WITHIN THE DOUBLING
WINDOW as the cube is dead.So does this mean that if you have even a
single market loser you should double?
Lets take a look at an example:
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O O X O O O | | O |
| O X O O O | | O |
| | | O |
| | | O |
| | | O |
| | | |64
| | | |
| | | |
| | | |
| X | | |
| X X X X X X | | |
| X X X X X X | |O |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Score is X 6 away O 2 away
at this score doubling window opens at 58.8%
Jellyfish evaluation is as follows.
wins g/bg
O 40.9 5.8
X 43.4 9.9
So using the match equity tables we get the following
X nodouble wins single equity 81.4x25=20.35
X nodouble wins gammon equity 18.6x32= 5.95
====
26.30
X doubles wins single equity 81.4x32=26.05
X doubles wins gammon equity 18.6x50= 9.30
====
35.35
X nodouble lose single equity 87.6x10= 8.76
X nodouble lose gammon equity 0.00
====
8.76
X doubles loses equity 0.00
so x is risking 8.76 to gain 9.05 and because the gammons are much
more valuable to the trailer he needs 50.8 in raw winning chances,
which he has.
Now the BIG QUESTION is should X double with 1 huge market loser
(5-5) plus some others 6-6 and 4-4 followed by a poor reply from O.
Can someone explain to me whether it's correct to double or not
because according to the criteria whether I'd be better off in equity
terms doubling or not doubling, I'm oviously better off doubling as I
can't be worse off as there is no lost equity as the cube is dead.
Or should I be assuming that sometime in the future of this game I
must have a better opportunity to double i.e nearer to my opponents
drop point but that may of course never happen?
In this position O won,t be doubling until his position reaches 89.3
pct because of X's massive recube.
So what if this were a money game and someone said to you:
A. You can double only when you are above 58.8 pct winning chances and
the benefit of this is that your oponent can't redouble and as an
added bonus if you lose a gammon you wont have to pay double.
or....
B. You can wait for a better winning percentage still above 58.8 pct
to double and again your opponent can't redouble but if you get
gammoned before you double it will cost double and also your opponent
has the opportunity to double you out if his winning percenatge goes
above 89 pct.
What would be the right tactic ??
So in general when the leader is 2 away if I'm in the doubling window
and have some market losers what is the correct strategy?
David Montgomery
In article <348a95d4...@news.demon.co.uk> mi...@depreli.demon.co.uk writes:
>Now I want to get ont the general subject when the leader is 2 away
>At this score the leader gets no benefit from owning the cube as there
>will never be any equity lost by doubling early WITHIN THE DOUBLING
>WINDOW as the cube is dead.So does this mean that if you have even a
>single market loser you should double?
No. Although you are not giving your opponent a cube they can
use as a weapon, you are still doubling your opponent's wins.
For this reason, you shouldn't double until you have significant
chances of big market loss.
If you don't have significant chances of a big market loss, then
there are two things that can happen:
1) Things can go your way. Now you can double, and you won't
have given up much by waiting since you only rarely lose your
market by a lot.
2) Things can go against you. Now you are glad that you haven't
doubled, since doubling still doubles your losses.
When your opponent needs 2 points, scenario 2) is less scary, since
a) if you double your opponent cannot use the cube against you,
b) if you don't double, your opponent still could use the cube, and
c) doubling doesn't double your opponent's gammon wins --
but this doesn't mean that you can double with any market loser.
For example, at -4:-2, in a gammonless low wastage medium length race,
you still need to be around 73% to offer a profitable double. You need
roughly a 10% lead in the pipcount, even though if the count were
even you would have a number of large market losers.
David Montgomery
monty on FIBS
mo...@cs.umd.edu