Maybe Mloner knows something
Kit Woolsey
RainerBirkle earlier today:
1. He started with 5-4, playing 24/20, 13/8
2. I rolled 2-1, playing 13/11, 6/5*
3. He rolled 6-6, flunking
Having seen some of the positions mloner has been flinging cubes over at
this match score, I figured if it is good enough for mloner it is good
enough for me, so I doubled.
As Rainer scooped it up, it occurred to me that maybe I didn't mind this
too much. After all I was a clear favorite, had some decent gammon
chances, and that would win the whole match for me. As it happened
everything went my way, I pinned him back to an ace-point game and
gammoned him for the match.
Afterward, I started wondering if he even was supposed to take, since I
had realized that I didn't mind his taking. If he passes, according to
my equity table his winning chances in the match are 60%. I fed the
position to jellyfish for 10368 rollouts (this certainly should be
enough, and it is hard to imagine any major bias in this position). The
results were (backgammons not included):
Rainer won gammon: 10.0%
Rainer won single: 29.5%
Woolsey won single: 40.4%
Woolsey won gammon: 20.1%
These certainly look about what one might expect. Now, let's turn them
into match equities. If Rainer wins the game (gammon or not) he wins the
match. If I win a single game we are tied. If I win a gammon, I win the
match. Thus, Rainer's match equity if he takes the double according to
the rollouts is:
39.5% X 1.00 +
40.4% X .50 +
20.1% X 0
This comes to 39.50 + 20.20 = 59.70%. This is less than the 60% he would
have had if he passed, so it looks like he actually has a bare pass!
Look at the implications. While this was a very small market loss for me,
there were clearly much bigger ones available -- I might have crushed him
with 1-1, 3-3, 4-4, or 5-5 and then if he had flunked the market loss
would have been big. This is not to suggest that I should have doubled
after his opening 5-4 -- I'm not even a favorite yet, so the cost when I
lose a single game and lose the match (instead of being behind 4-1 for 17%
equity) appears to be greater than the potential gains from doubling.
What it does show is just how little an edge one might need to double at
this score, provided there is some decent volatility and gammon potential.
Looks like mloner's early doubles at this match score aren't so foolish
after all.
Kit
bobk
>I had the following sequence when behind 3-1 in a 5-point match vs.
>RainerBirkle earlier today:
>
>1. He started with 5-4, playing 24/20, 13/8
>2. I rolled 2-1, playing 13/11, 6/5*
>3. He rolled 6-6, flunking
>
>enough, and it is hard to imagine any major bias in this position). The
>results were (backgammons not included):
>Rainer won gammon: 10.0%
>Rainer won single: 29.5%
>Woolsey won single: 40.4%
>Woolsey won gammon: 20.1%
>
Don't know if it is significant or not but I can certainly imagine
a possible major bias. After the double it is a one way gammon
position for kit but the JF cubeless rollout plays as though it
is a normal money game. Is one side hurt more by this?
Not sure why but my guess is that failing to play gammon safe for
Rainer hurts him more than failing to play gammon agressive for Kit hurts
Kit. Anyone have a guess about the size of such a bias? (or even if I
have gotten the direction right.)
On a related note is this a good idea for neural nets?:
Train separately for double match point and for one way gammon
positions. Seems like it should not be too much extra effort
since previously obtained weights for money play could be
used as the starting point and difference will not be huge.
I think the gain in playing ability near the end of a match
could be substantial.
,Bob Koca
bobk on FIBS
ko...@bobrae.bd.psu.edu
Kit Woolsey
: kwoo...@netcom.com (Kit Woolsey) wrote:
: >I had the following sequence when behind 3-1 in a 5-point match vs.
: >RainerBirkle earlier today:
: >
: >1. He started with 5-4, playing 24/20, 13/8
: >2. I rolled 2-1, playing 13/11, 6/5*
: >3. He rolled 6-6, flunking
: >
: >....
: >position to jellyfish for 10368 rollouts (this certainly should be
: >enough, and it is hard to imagine any major bias in this position). The
: >results were (backgammons not included):
: >...
: >Rainer won gammon: 10.0%
: >Rainer won single: 29.5%
: >Woolsey won single: 40.4%
: >Woolsey won gammon: 20.1%
: >
:
: Don't know if it is significant or not but I can certainly imagine
: a possible major bias. After the double it is a one way gammon
: position for kit but the JF cubeless rollout plays as though it
: is a normal money game. Is one side hurt more by this?
: Not sure why but my guess is that failing to play gammon safe for
: Rainer hurts him more than failing to play gammon agressive for Kit hurts
: Kit. Anyone have a guess about the size of such a bias? (or even if I
: have gotten the direction right.)
I agree there might be a bias. However the fact that you aren't
confident which way the bias is should indicate that it probably isn't
going to affect things much. Keep in mind that I wasn't trying to be
exact -- I was just trying to illustrate that Rainer probably had a close
take-pass decision in a position the rest of us would be wondering if
I even had a double.
: On a related note is this a good idea for neural nets?:
: Train separately for double match point and for one way gammon
: positions. Seems like it should not be too much extra effort
: since previously obtained weights for money play could be
: used as the starting point and difference will not be huge.
: I think the gain in playing ability near the end of a match
: could be substantial.
I don't think this is really necessary. Keep in mind that now the nets
give equity estimates for backgammons, gammons, and simple wins for each
side. Thus, to play accurately at double matchpoint or in one-way gammon
situations all they have to do is modify the weights they give to the
various outcomes and they should do quite well. In fact, if my
understanding is correct both jellyfish and mloner do that now when
playing matches.
Kit
Stephen Turner
>
> I don't think this is really necessary. Keep in mind that now the nets
> give equity estimates for backgammons, gammons, and simple wins for each
> side. Thus, to play accurately at double matchpoint or in one-way gammon
> situations all they have to do is modify the weights they give to the
> various outcomes and they should do quite well. In fact, if my
> understanding is correct both jellyfish and mloner do that now when
> playing matches.
>
This isn't clear to me. They train cubeless, so the percentage of gammons
represents the percentage of gammons GIVEN a cubeless strategy. The percentage
of gammons if you were to follow a different strategy might be quite different.
It's not just a matter of weighting the different cubeless percentages
according to the relevant match equities.
--
Stephen R. E. Turner
Stochastic Networks Group, Statistical Laboratory, University of Cambridge
e-mail: sr...@cam.ac.uk WWW: http://www.statslab.cam.ac.uk/~sret1/home.html
Gerry Tesauro
>
> On a related note is this a good idea for neural nets?:
>
>Train separately for double match point and for one way gammon
>positions. Seems like it should not be too much extra effort
>since previously obtained weights for money play could be
>used as the starting point and difference will not be huge.
>I think the gain in playing ability near the end of a match
>could be substantial.
>
This seems like a potentially good idea, because the regular
neural net trained for money play will give you win and gammon
estimates *assuming money-type plays are made* by both sides.
Thus it's conceivable that if we trained a win estimator
under conditions of double match point where gammons don't
count, then such a win estimator might be different from
the win estimator that comes out of money-condition training.
However, this appears not to be the case empirically. I once
trained a double match point version of TD-Gammon, and compared
it to regular TD with the gammon estimates turned off.
There seemed to be no measurable advantage in playing ability
of the DMP version, at least at the 1-ply level. One-way
gammons I don't know about, but I'd have to guess that you
get reasonably correct play just by taking the regular
money-play net and re-weighting the win and gammon outputs
appropriately. Perhaps Fredrik or Harald could contribute
further to the discussion.
-- Gerry Tesauro (tes...@watson.ibm.com)