2 away - 2 away, another aspect
Harald Wittmann
First.
As many know, I'm currently working on the doubling algorithm for loner.
Today I played a few 2-point matches and were quite satisfied with loner's
cube decisions when I wondered why to hell I programmed loner to care
about gammons at this matchscore. As we know from older postings this
should be the last game in the match because it's sure that the cube will
be turned. At the score 2 away - 2 away loner plays using a gammonprice
of 0.75. This means gammon counts 50% more than in a money game! I came
to the conclusion that this must be wrong because gammons will never count
at this match score since the cube will be always turned. So 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?
Second.
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.
And in deed ... assuming that the opponent turns the cube at the first
opportunity, a 2-point match is nothing else than a 1-point match. In fact,
turning the cube at the first opportunity seems to be the best strategy
for a weak(er) player (guarantee him/her not to throw a marketlooser when not
doubled).
So, when loner would play only 2-point matches it would win the same number
of matches like now, 58.5% against a 1700-player. This means that loner's
rating would drop 90(!) points (1-ptr vs 2-ptr, using the rating formula) ...
Did I anything wrong?
If I'm right, this seems to be the first (proofed) irregularity in the rating
formula.
Any comments are welcome!
Harald Wittmann
wittmann@fibs
witt...@fmi.uni-passau.de
Bernhard Kaiser
: 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.
: And in deed ... assuming that the opponent turns the cube at the first
: opportunity, a 2-point match is nothing else than a 1-point match. In fact,
: turning the cube at the first opportunity seems to be the best strategy
: for a weak(er) player (guarantee him/her not to throw a marketlooser when not
: doubled).
: So, when loner would play only 2-point matches it would win the same number
: of matches like now, 58.5% against a 1700-player. This means that loner's
: rating would drop 90(!) points (1-ptr vs 2-ptr, using the rating formula) ...
: Did I anything wrong?
: If I'm right, this seems to be the first (proofed) irregularity in the rating
: formula.
: Any comments are welcome!
i think the rating system is quite accurate, but of course there is a irregularity in it con-
cerning two-pointers. If you play against all opponents, its ok, i think, since most weak players
dont double soon. But if loner would play only against good opponents, he would do better to
play onepointers instead of twopointers.
But there is no way to solve this problem , i think, since you never cant say , a guy with more
then rating X doubles immediately, a guy with less not :)
one-pointer
Ron Karr
>
>First.
>As many know, I'm currently working on the doubling algorithm for loner.
>Today I played a few 2-point matches and were quite satisfied with loner's
>cube decisions when I wondered why to hell I programmed loner to care
>about gammons at this matchscore. As we know from older postings this
>should be the last game in the match because it's sure that the cube will
>be turned. At the score 2 away - 2 away loner plays using a gammonprice
>of 0.75. This means gammon counts 50% more than in a money game! I came
>to the conclusion that this must be wrong because gammons will never count
>at this match score since the cube will be always turned. So 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?
>
>Second.
>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.
>And in deed ... assuming that the opponent turns the cube at the first
>opportunity, a 2-point match is nothing else than a 1-point match. In fact,
>turning the cube at the first opportunity seems to be the best strategy
>for a weak(er) player (guarantee him/her not to throw a marketlooser when not
>doubled).
>So, when loner would play only 2-point matches it would win the same number
>of matches like now, 58.5% against a 1700-player. This means that loner's
>rating would drop 90(!) points (1-ptr vs 2-ptr, using the rating formula) ...
>
>Did I anything wrong?
>
>If I'm right, this seems to be the first (proofed) irregularity in the rating
>formula.
>
Harald--
1. I think you're right that loner (or anyone else!) should play exactly the same
in a 2-point match as in a 1-point match. This assumes that the correct doubling
action is always double-take whenever the side on roll has any market losers.
Therefore gammons will never be relevant. However, if one side waits too long to
double, the gammon price with the cube on 1 COULD be relevant in deciding whether
to play on, or whether to take. If one side plays on, checker play could be
affected by gammons as well.
As for the gammon price, I'm not sure where you get 75%. If the cube is on 1, the
gammon price is (100-70)/(70-0) = .43 (assuming equity at -1:-2 is .7). If the
cube is on 2, the gammon price is of course zero.
2. As for the ratings/win rate issue, I don't think it's really an irregularity in
the rating formula. It's more of an irregularity in backgammon match strategy--
the fact that it turns out to be correct to never lose your market in 2-point
matches, so therefore 2-pointers really are not twice as long as 1-pointers.
I think the rating formula is designed to provide an overall measure of a player's
performance against players of all skill levels and over a wide range of match
scores. As such, it seems to work pretty well. (In the tournament world, people
rarely play matches of less than 5 points anyway)
Loner is arguably the best 1-point match player on FIBS, and might be the best
2-point match player as well, even though it might have a lower rating if it only
played 2-pointers.
Ron
FIBS: ronkarr
Walter G Trice
[snip]
>So 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?
>Second.
>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.
[snip]
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
not doubling:
(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.
Walter Trice