How to play 4-away, 2-away?

[Øystein Johansen]

Hi!

How to cube at the score 4-away, 2-away?

Can anyone give me a good lesson on useing the cube at this score?
I guess the leader should not cube before he have 83% winning chanse, and
at a late position (I asume). But what about the trailer? How should he
make his cube decisions? Is it right to make a early double, and go for a
gammon, or is this a very risky strategy. (Like opening with 6-4 and move
8-2 6-2, and turn the cube in the next turn?)

I have been thinking about it for a while, but I can not figure out the
right strategy here. Please give me some hints!

Oystein

[Tom Keith]

Řystein Johansen wrote:

> Hi!
>
> How to cube at the score 4-away, 2-away?
>
> Can anyone give me a good lesson on useing the cube at this score?

Let me give this one a try ...

Leader's Strategy

At 2-away, Leader obviously would like to win a two-point game so he
can claim the match. But a one-point win is also very good because
that would put the match score at 1-away, 4-away and Trailer would
then have to win *three* consecutive single games to win the match.

Trailer's break-even point for accepting/declining Leader's double
is when Leader's chances of winning the game are 83%. To see why,
keep in mind that Trailer's strategy if he accepts will be to
immediately redouble and put the entire match on the line. The 83%
represents Leader's match winning chances at 1-away, 4-away.

Leader wants to double as close to this 83% mark as he can. He must
be careful about doubling too early because he doesn't want to give
Trailer a chance to turn the game around and steal the match.

With a significant gammon threat, Leader may wish to hold off
doubling until he sees if the gammon threat pans out.

Trailer's Strategy

When there is no gammon possibility, Leader's break-even point for
accepting/declining Trailer's double is when Trailer's game winning
chances are 80%. (If Leader drops, his chance of winning the match
is .60. If he takes, his match chances are (80% * .50) + (20% * 1.00)
= .60.)

So Trailer wants to double when his game-winning chances are
somewhere around 80%. He's also happy to double a bit earlier than
this because he is hoping Leader will accept the double and make the
game worth two points. Then Trailer will need just one more win after
this one to claim the match.

Doubling early might seem to be a dangerous tactic (because two points
is exactly what the Leader needs to win the match), but it is actually
less dangerous than a normal double because the Leader has no
effective redouble.

When gammons are a factor, Trailer has to be very aggressive with
the doubling cube. Consider the situation from the Leader's point
of view. Leader will be *very* reluctant to accept a double when
there is any kind of serious gammon threat -- he doesn't want to
lose a doubled gammon. Leader will still be ahead in the match
if he drops a single point now.

On the other hand, Trailer *really* wants to get his double in
while Leader will still accept it. So Trailer must have his finger
on the doubling trigger right from the start of the game. As soon
as Trailer has even a modest lead in the game, he should consider
doubling. And if the lead is accompanied by an increase in gammon
chances, then Trailer should double immediately.

At this score, gammons are worth a lot more for Trailer than they
are for Leader. So Trailer will be playing towards gammonish
positions and Leader will be trying to avoid them.

Tom

[Chuck Bower]

>Řystein Johansen wrote:
>
>> How to cube at the score 4-away, 2-away?
>> Can anyone give me a good lesson on useing the cube at this score?
>

In article <32A1F4...@io.org>, Tom Keith <tak...@io.org> wrote:

>Let me give this one a try ...
>
>Leader's Strategy
>

(snip)

>Trailer's break-even point for accepting/declining Leader's double
>is when Leader's chances of winning the game are 83%.

(snip)

>Leader wants to double as close to this 83% mark as he can. He must
>be careful about doubling too early because he doesn't want to give
>Trailer a chance to turn the game around and steal the match.
>With a significant gammon threat, Leader may wish to hold off
>doubling until he sees if the gammon threat pans out.

Good qualitatively and quantitatively so far... CRB

>Trailer's Strategy
>
>When there is no gammon possibility, Leader's break-even point for
>accepting/declining Trailer's double is when Trailer's game winning
>chances are 80%.

Right here, too... CRB

(snip)

>When gammons are a factor, Trailer has to be very aggressive with
>the doubling cube.

(snip)

>At this score, gammons are worth a lot more for Trailer than they
>are for Leader. So Trailer will be playing towards gammonish
>positions and Leader will be trying to avoid them.
>
>Tom

Correct advice, but a tad on the vague (non-quantitative) side.
This table should help make things clearer:

match match
trailer's gammon trailer's "last match leader's
win fraction roll" dbling pt drop point

0 46% 80% (as Tom said...)
1/6 26% 69%
1/4("typical game") 23% 64%
1/3 20% 60%
1/2("typical blitz") 17% 53%
2/3 14% 48%

NOTE: Except for the first line of this table (where I assumed no
gammons for either side), I have assumed LEADER's gammon fraction = 0.27.
This translates to the trailer having about 6% winning chances if s/he
doesn't win this game. NOTE: THIS INCLUDES THE LEADER'S GAMMON CHANCES, SO
IT IS LOWER THAN THE 8.5% - 9% NUMBER MOST PEOPLE ARE THINKING. Jellyfish
level 6 cubeless rollouts say that from the starting position (before
opening roll) 27% of all games will end in gammons. In other words,
each player has a gammon fraction of 0.27. THIS MEANS THAT THE MATCH
TRAILER IS ALREADY IN THE DOUBLING WINDOW! (But, of course, s/he can't
double before the opening roll.)

Can we find some market losers? Suppose LEADER opens 41 and plays
13/9, 24/23. TRAILER rolls 55 (making two inner board points) and
LEADER then fails to enter. What does JF level-7 (cubeless) evaluation
give for the likely outcome of this game? TRAILER wins 61.6% total
games with a gammon fraction of 0.48. Checking the about table, we
see that TRAILER has missed his/her market by about 8% (53% is drop/take
point compared to the ~61% winning chances).

This example probably doesn't justify TRAILER's double after the
opening roll, since the sequence 55 followed by wiff is TRAILER's best(?)
and even then the market isn't missed by a huge amount. Still, it indicates
that the TRAILER at this match score should have a "hair trigger" when
gammon wins are in the air. It also shows that TRAILER should steer the
games towards gammonish positions (and, of course, LEADER should be steering
away from them).

Chuck
bo...@bigbang.astro.indiana.edu
c_ray on FIBS