May 17, 2011

Doubling in races

Last week there were some technical problems with Blogger service, but now it seems everything is OK. I've manually returned the missing comments.

There were some very good comments by ah-clem and pthalo about two methods for converting pip count to doubling action - Trice count and Keith count.

If you didn't read them yet, I recommend you to read the comments from the last time.

Today we'll discuss cubes in races without the contact, in positions where both players have started to bear-in without opposition.



This is our position from the last time:

is Player 2

score: 0
pip: 111
Unlimited Game
Beaver
pip: 100
score: 0

is Player 1
XGID=----BCD-CB-Ac---ab-dcb----:0:0:1:00:0:0:2:0:10
on roll, cube action?


It is a pure race, neither of the players have any wastage (many checkers on lower points - 1pt, 2pt and 3pt), so most important factor in these positions is a pip-count.

Probably the easiest rule for converting pip-count to cube action is 8-9-12 rule. I use slightly modified version as I think it is more accurate than original. Here is it:

Calculate 10% of your pip-count. It is easy as you just have to divide your pip-count by 10.
- if you lead by 10% - 2 pips - correct cube decision is double/take (but no redouble)
- if you lead by 10% - 1 pips - now it is correct to redouble
- if you lead by 10% + 2 pips or more - correct cube decision is (re)double/pass

In our original position we're leading 100 pips to 111.
It is easy to calculate 10% of 100. Our opponent trails by 11 pips, that is 10%+1 and he can still take.

Analyzed in Rollout No double Double/Take
Player Winning Chances: 76,76% (G:0,00% B:0,00%) 76,81% (G:0,00% B:0,00%)
Opponent Winning Chances: 23,24% (G:0,00% B:0,00%) 23,19% (G:0,00% B:0,00%)
Cubeless Equities +0,535 +1,072
Cubeful Equities
No double:+0,836 (-0,082)±0,004 (+0,832..+0,840)
Double/Take:+0,918±0,005 (+0,913..+0,923)
Double/Pass:+1,000 (+0,082)
Best Cube action: Double / Take


If you weren't sure about doubling, then you're too shy with the cube and you're probably doubling too late when positions become double/passes. You're winning one point by one, instead of winning two points.

If you passed this, try to remember the 8-9-12 rule.
The race is long and you'll have plenty of time to come ahead and win this game (probably with redouble to 4).




The exercise for more experienced players was to guess doubling decision in this position if White was leading 1-0 in a 3pt match.

To know how to answer this, it is important to know how big is the match winning chance (MWC) for Black if he passes this cube, and then try to see how many times Black can win the game in this position, based on the pip-count.

As this blog is called backginners I don't want to go into details about that.
If you want to know more, check ah_clem's comment to the previous post. He answered correctly, with very good explanation.




Here are some exercises for your homework.
If you apply the 8-9-12 rule, there shouldn't be any problem finding correct cube decisions:

1.
is Player 2

score: 0
pip: 119
                         
Unlimited Game
Beaver
                          pip: 110
score: 0

is Player 1
XGID=----BBC-CBABc---bc-dba----:1:1:1:00:0:0:2:0:10
on roll, cube action?


2.
is Player 2

score: 0
pip: 91
Unlimited Game
Beaver
pip: 80
score: 0

is Player 1
XGID=---BCCCCA-----a-aaaddc----:0:0:1:00:0:0:2:0:10
on roll, cube action?


3.
is Player 2

score: 0
pip: 75
Unlimited Game
Beaver
pip: 70
score: 0

is Player 1
XGID=--ACCCD-A--------aadccc---:1:1:1:00:0:0:2:0:10
on roll, cube action?



4 comments:

  1. i wrote a really long comment but my browser ate it.

    using your formula:
    1. double take
    2. double pass
    3. double take

    using a Keith count (formula I am most used to) the results are a little different:

    1. no double, take
    2. double, pass
    3. double take


    In practice, though I don't think it matters too much which formula you use because using any formula gives you a huge advantage over an opponent who doesn't use a formula and it is usually better to double than not double.


    For the intermediate-advanced player who is interested in a comparison of different formulas, there's a really good article here: http://www.bkgm.com/articles/CubeHandlingInRaces)

    -pthalo

    ReplyDelete
  2. As I see it: In positions 1 and 3 the cube has already been turned, so they should both be no redouble.

    2 is double/pass.

    ReplyDelete
  3. I agree with Frede, 1 and 3 are borderline double with centered cube but no redouble.

    2 is double pass.

    ReplyDelete
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