> > Even more striking, the percentage for (2away,4away) differs by a
> > whopping 9% from the figure in Woolsey's table.
> > ...
> > Mark Damish, whome I have sent the table a few days ago, suggested
> > that this indicates that the fibs experts double way too late when
> > being behind 4away/2away.
One of the purposes of the Big_Brother program was to look at matches
played by players of different strengths and to find areas where
play is inefficient, along with the results of such play.
Although the B_B data for 4a,2a is certainly within 2 standard
deviations, I believe the current bias towards 4a winning more
than he/she (referred to as he heretofore) theoretically should,
is correct, in spite of theoretically inefficient doubles
(doubling too late) and is explainable.
I don't have a copy of the original post, but for the record, Kit's
table shows that that 4a,2a wins about 32% of the time, while observed
matches between the top 150 players on FIBS yield about 38% wins through
December. Kit's table assumes a gammon rate in the low 20's.
> I don't understand Mark's explanation. Trailer did better based on
> Big Brother results than Kit's table predicts, so this means trailer
> plays better than we might have expected. Did he perhaps mean that
> players 5 years ago doubled too late when losing 4a 2a?
I've never tried to explain this. I summarize what I believe with:
1) At 4a,2a it seems that 4a doubles too late which is technically
inefficient.
2) At 4a,2a it seems that 2a takes doubles which are technically
drops at this score. This is also technically inefficient.
3) The two technically incorrect plays DO NOT cancel out, and the
result is a beautiful equity finesse which favors the 4a
player.
4) This brings up some ramifications where the technically correct
play might be the wrong play.
It is particularly important to note that the 4a player should be
the weaker player "on average", because the stronger player should
reach 2a more often than the weaker player. Given the wide range
of ability using the top 150 players on FIBS, it is on average
the weaker player who appears to be gaining from errors at this score.
1)
Why do I believe that 4a,2a doubles occur too late? Take a look at this
position. You (4a) roll a 31: 8/5 6/5. Your opponent (2a) rolls a
41: and slots with 13/9 6/5. Would you consider doubling this position?
Would you consider dropping this position? The built in money reflex
of money play would usually see the dice shake without a second thought.
But, lets evaluate the position. Some relative numbers. Assuming that
4a is considering turning the cube. The take point for 2a is 0.2.
The gammon price for 4a is 1.0. the gammon price for 2a is 0.0.
The recube vig for 2a is 0.0.
Since the gammon price is 1, there is a cute shortcut to compute
the percent of games the 2a needs to win in order to take:
min_%winning_games(2a) = 20% + %gammons(4a)
In the above example (from memory) after 4a made the 5pt and 2a
exposed extra blots, 4a will gammon 2a more than in the starting
position. How much? If I assume that the starting position yields
1112% gammons of total games for me, then I can estimate that about
1720% of the total games are gammons for 4a given the above position.
2a needs (20+17=37%) to be able to win about 3740% of the time to
have a take in this position. Does he? It's close, and is probably
correct for a stronger player to drop a weaker player at this
score from that position after the first roll!!!
The key to understanding 4a,2a double/takes is to be ability to
assess 4a's gammon chances, and 2a's winning chances. It is important
to look at the position every roll. There are other doubles at
4a,2a to be aware of. It truly is the most amazing score in backgammon.
2)
Once you start estimating the winning_game% for 2a, look at games
played at this score played by players at all levels. I've heard
some world class players recently comment that they would never have
considered some of the doubles that JF/Mloner make at this score,
but after study, they conclude that if correct, they have been
doubling too late. Since quite a few strong players fail to
consider to double at the technically optimal time, it is very
safe to assume that they (and weaker) players also fail to correctly
analyze this score and take positions that are technically passes.
3)
Assuming that the results are not some cruel statistical abboration,
(we're still within 2 standard deviations here), then the Big_Brother
program is indicating that when 4a doubles late, and 2a takes, then
4a will win more than his share of games, as dictated by match equity
tables. It makes sense: If one takes positions which are drops, then
he looses equity. This is true for money, as well as the 4a,2a score,
where correct cube action is often misjudged.
4)
Consider another score that has had a lot more analysis, 2a,2a.
What is the proper doubling strategy at this score?
 Double with ANY single market losing sequence, no matter how remote.
 Double when you approach your opponents take point (30% cubeless).
 Double the first chance you get.
 Double exactly the same as a money game.
If you chose ANY of the above, you are not getting maximum equity at the
2a,2a score, UNLESS you are always playing the same class of player all
of the time.
If two players are utilizing Kits Woolsey's advice and making the
optimal technical play of doubling at the first market loser, then the
correct play corresponds to the correct technical play.
What if you're opponent has never heard of Kit Woolsey and you know it?
Doubling at the first market losing sequence will be the incorrect play,
as your opponent will ALWAYS (give or take 1 market loosing sequence)
take next roll. I won several extra matches last year because I knew
my opponent would not double at 2a,2a, and by waiting to approach his
personal drop point, I managed to lose the game, but not the match, which
I would have lost using the technically correct strategy.
The point of this is that optimum play might not always the
the technically correct play. If 2a is taking too much, then it looks
like it is correct to bypass the technically correct doubling point
for 4a,2a. If 2a is making optimal takes based on calculating his
winning chances Vs your gammons, then not doubling at the optimum
"early" time will end up costing him equity. It looks like the
decision to double at this score is largely based (as usual) on your
opponent. The optimal strategy at 2a is to only take positions that
where game_winning% > 20 + gammons(4a). By "taking only the takes"
you don't give away equity as the Big_Brother data indicates, and can
gain equity if your opponent is doubling theoretically late, which he
probably is.
Peace...
..Mark
damish@ll.mit.edu
