Cube Action
Silverfox
| Courtney Foster (X) vs. (O) |
| 5 point Match |
--------------------------------------------------------------------
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
| X O O | | O X |
| X O O | | O X |
| O | | X | S
| O | | | n
| | | | o
| |BAR| | w
| X | | O | i
| X | | O | e
| X | | X O |
| O X X | | X O |
| O X X | | X O |
+24-23-22-21-20-19-------18-17-16-15-14-13-+
Pipcount X: 151 O: 163 X-O: 3-1/5 (1)
CubeValue: 1
Jerry Weaver
2-away O's doubling window is 33-62 for "gammonish" positions, which
this would be. If this is true, then O is certainly within the
doubling window here, since he looks to be at least at 50%.
The question is, should he double now or wait? For that we ask, does O
have a market-losing sequence, a combination of rolls by O an X that
will cause you to drop next time? Certainly 6-6 by O would cause you
to drop after a poor roll by you, and perhaps even a 6-1 by O followed
by a poor roll by you. Consequently, it seems correct by O to double
here, odd as that looks.
Note that if there is no chance of a gammon, as in a straight race,
then 0's doubling window is a much more normal-looking 61-80.
Jerry
Douglas Zare
Jerry Weaver wrote:
It's not right, but it is not a huge error. Gnu is prone to this type of mistake, making
overly aggressive doubles and redoubles when the cube will be dead. Doubling immediately
trailing 2-away 4-away is not always right, but on average it only gives up perhaps 1-2% mwc
(the difference between Crawford 2-away and 2-away 4-away in the MET), and most of that is in
positions where you have a clear disadvantage, such as when your opponent has opened by
making a point, or has hit you.
That both players have made their 5 points increases the gammon rate, and that is precisely
what you don't want to see as the leader. So, it is more reasonable to double, but it is
still wrong.
> >
> According to Hugh's doubling table, posted here on 2/6/98, at 4-away,
> 2-away O's doubling window is 33-62 for "gammonish" positions, which
> this would be. If this is true, then O is certainly within the
> doubling window here, since he looks to be at least at 50%.
It is usually better to look at the take point rather than where the doubling window opens.
The expections happen when the volatility is extreme. This is not a tremendously volatile
position. Actually, I don't think it is very gammonish, just slightly more so than normal.
> The question is, should he double now or wait? For that we ask, does O
> have a market-losing sequence, a combination of rolls by O an X that
> will cause you to drop next time? Certainly 6-6 by O would cause you
> to drop after a poor roll by you, and perhaps even a 6-1 by O followed
> by a poor roll by you. Consequently, it seems correct by O to double
> here, odd as that looks.
No, the recipe for doubling is not to have market losers and to be in the doubling window,
even if the cube will be dead. It's not 2-away 2-away. You might make better use of the cube
later. If you double now, you double a lot of your own losses. By waiting for an improvement,
you avoid doubling as many losses while doubling almost as many wins.
If you lose your market, that's not a bad thing. Losing you market by a lot is a bad thing.
An efficient double in is just as good as an efficient double out.
> Note that if there is no chance of a gammon, as in a straight race,
> then 0's doubling window is a much more normal-looking 61-80.
Why should that be normal? The money doubling window opens at 50%, not 61%, so this indicates
that when there are no gammons, the trailer might want to be more conservative with the cube.
The leader would love to see an incorrect double with checkers on the 5&2 against a 1 roll
position.
In positions in which the gammon rate is low to normal, you should double more aggressively
trailing 2-away 3-away than 2-away 4-away. For fun, compare 2-away 4-away with 3-away 4-away.
Douglas Zare
Chase
<za...@math.columbia.edu> wrote:
|In positions in which the gammon rate is low to normal, you should double more aggressively
|trailing 2-away 3-away than 2-away 4-away.
I've been spending time on these two scores, trying to figure out the
differences in doubling strategy, both for gammonish and non-gammonish
positions, so I appreciate your comment here. Can you say a bit more
about this?
Thanks.
Chase
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Douglas Zare
Chase wrote:
> On Tue, 12 Mar 2002 17:39:00 -0500, Douglas Zare
> <za...@math.columbia.edu> wrote:
>
> |In positions in which the gammon rate is low to normal, you should double more aggressively
> |trailing 2-away 3-away than 2-away 4-away.
>
> I've been spending time on these two scores, trying to figure out the
> differences in doubling strategy, both for gammonish and non-gammonish
> positions, so I appreciate your comment here. Can you say a bit more
> about this?
The racing take point is very high at 2-away 3-away (say 28%), and gammons on a 2-cube have
about the normal value, a gammon price of about 0.5. At 2-away 4-away, the racing take point is
unusually low (say 18%), but the gammon price is 1. If the absolute gammon percentage is greater
than 20%=(28%-18%)/(1-0.5), then you should be more conservative taking a 2-cube at 2-away
4-away than 2-away 3-away.
5-2 split 5-5 6-2 double: Snowie says there are 26% gammons, and that this is a close take at
2-away 3-away but a big pass at 2-away 4-away. I haven't rolled it out, though, and I would not
be surprised if it were a pass at 2-away 3-away against a very strong opponent.
5-point holding game, both midpoints, 8 with spares, 20 pip deficit: Big pass at 2-away 3-away,
and a big take at 2-away 4-away, as one wins about 25% and only gets gammoned a couple percent
of the time.
That's about taking. The doubling points are different, but more complicated.
Douglas Zare
Chase
<za...@math.columbia.edu> wrote:
Thanks for the explanation, Douglas. I'll spend some time digesting
it. One question: when you use the term "racing take point," is this
the simple risk/(risk+reward) calculation done from a match equity
table, or is it adjusted from that (or possibly calculated
differently)?
Douglas Zare
Chase wrote:
>
> Thanks for the explanation, Douglas. I'll spend some time digesting
> it. One question: when you use the term "racing take point," is this
> the simple risk/(risk+reward) calculation done from a match equity
> table, or is it adjusted from that (or possibly calculated
> differently)?
In this case (2-away n-away), it is simply the risk:reward calculation assuming no gammons. That's
because the cube will be dead. More generally, I think of the racing take point to take into account
some recubes, and I try to adjust for recube efficiencies that might be higher or lower than normal.
Douglas Zare