Match Play at 2-away/2-away|
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Match Play at 2-away/2-away
Harald Wittmann asks:
> Why should loner care about gammons? I think it should play like in
> 1-point matches (playing for the highest entire winning probability).
> Is this correct? Any comments?
> I thought a little bit longer and did some calculations. Assuming that
> loner's rating is 2000 and it wins 58.5% of the 1-point matches against
> a player with rating 1700, I got (using the rating formula) loner has to
> win 61.9% of the 2-point matches to held its rating.
> I was surprised! Never possible, I thought.
In practice most players do not double on time in a 2 point match
and you can win more 2-pointers than 1-pointers against a
substantially weaker player. There are 3 ways to gain equity from
(1) Opponent loses his market;
(2) he takes a drop;
(3) he drops a take.
I would not forgo these opportunities for equity theft just to
pick up small gains that only occur 2% of the time, which is
usually the situation if you make the first 'optimal' double.
My practical rule is that I prefer not to double until I get
to a position in which an error is possible, and against a
weak opponent such positions are very common!
It is also worth considering that take-points are very different
when one player can win an even position 58.5% of the time. Gammon
rates will also be different -- gammons might be something like
30% of the stronger player's wins but only 15% for the weaker
player. This means that at 2-away/1-away the stronger player
would still have about a 40% chance of winning the match but for
the weaker player it would only be 20%. Thus some racing positions
that are drops for money would still be takes for the underdog.
But positional complexity is also a factor, and there are
conceivably positions so difficult to play that the weaker
player would have to drop at this score though they would be
easy takes between equal opponents.
In short, it becomes marvelously complicated when your weaker
opponent doesn't know when to double. The investment needed
to discover this fact is very small because the weaker player
should ABSOLUTELY double as soon as he thinks he MIGHT have
a market losing sequence.
Match Play at 2-away/2-away
- Basic strategy (Darse Billings, Feb 1995)
- Counterexample? (Jim Williams+, Mar 1998)
- Do you need an advantage to cube? (Keene Marin+, Feb 2006)
- Double immediately? (Chuck Bower, Oct 1998)
- Ever too good to double? (Kit Woolsey, July 1995)
- Minimum game winning chances to double (Walter Trice, Mar 1999)
- Practical strategy (Walter Trice, July 1995)
- Practical strategy (Albert Steg+, Feb 1995)
- Proof for doubling immediately (Robert Koca+, May 1994)
- Proof of doubling with market losers (Walter Trice+, July 2001)
- Sample game (Ron Karr, Dec 1996)
Backgammon Galore :
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