X to play 6-3
David Montgomery
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| X X O O O | | X O |
| O O O | | X O |
| | | O |
| | | O |
| | | |
| | | | [1]
| | | |
| | | O |
| | | X O |
| | | X O |
| X X X | | X O |
| X X X | | X X O |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Money game. X to play 6-3.
Toni Wuersch
22-16 16-13 is my play. X's man on the 22 point has little added value
where it is, so it should be racing, not holding back.
It's important to recall that a holding game depends both on contact shots
and on racing potential.
USRobots
I'll give this one a try...
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| X X O O O | | X O |
| O O O | | X O |
| | | O |
| | | O |
| | | |
| | | | [1]
| | | |
| | | O |
| | | X O |
| | | X O |
| X X X | | X O |
| X X X | | X X O |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Money game. X to play 6-3.
The critical variable in this type of position is the status of the race.
After this roll, X will trail in the race 142 - 127. He will have some
racing chances, which is good, but may run out of timing for his holding
game, which is bad. (In general, having both racing and hitting chances
can be a bad thing. Having one or the other is often better.)
X should realize that the checker on the 3-pt is almost useless at the
moment. It doesn't significantly increase his hitting chances, and could
provide a target for O in the future. X doesn't have nearly enough timing
to try to make the 3-point and play a 7-3 holding game, so he should just
run with the useless checker, 22/13.
If O hits the blot, it may re-enter on the 1- or 2-point, a better place
than the 3-point. In any case, X will gain some timing. O has a
relatively bad attacking position, so gammon chances are small.
If O misses the blot, X will have maintained his racing chances, and
created another builder for his side of the board, to help his hitting
chances.
Thanks,
Peter Bell (USRobots)
Hugh B. McNeil
| X X 0 0 0 || X 0 |
| 0 0 0 || 0 |
| || X 0 |
| || 0 |
| || | X to move 6-3
| || 0 |
| || X 0 |
| || X 0 |
| 0 0 0 || X 0 |
| X X X || X X 0 |
+--1--2--3--4--5--6------7--8--9--10-11-12-+
[ 4,5,and 6 in X's home board are, of course, X's points. I have
no text editor here...]
Following up what I said earlier, my moves in order of selection
are (best to worst):
1. 11-5, 7-4
2. 11-2
3. 22-16, 11-8
4. 22-16, 7-4
5. 24-18, 11-8
6. 24-18, 7-4
7. 22-13
On second thought, maybe [22-16, 7-4] is better than [22-16,11-8].
Well? (to those @ JF, TDG, etc).
USRobots
+-1--2--3--4--5--6--||--7--8--9--10-11-12-+
| X | X 0 0 0 ||--X 0 |
| 0 0 0 || X 0 |
| || 0 |
| || 0 |
| || | X to play 6-3
| || 0 |
| || X 0 |
| || X 0 |
| X X X || X 0 |
| X X X || X X 0 |
___________________________________________
Hugh B. McNeil wrote:
******
Down 15 pips @ opponent on roll,
X has substantial race equity, and 0 will hit when reasonable.
Therefore instead of putting a blot into the outfield, 11-5 and
7-4, or 11-2 are preferred. In this variation, all of the large
numbers play reasonably well. 4's and 6's come out, and other 5's
make the two point.
Another posting suggested running from the opponent's 3 to the
mid point, and this must be wong because:
1) it has not improved the race;
2) it gives 0 a low cost opportunity to improve his race
chances by hitting X with few return shots;
3) a large swing on 5-1 by 0, which turns a direct shot into
an indirect shot plu gain in the race.
It is probably better to move 24-18, 7-4 than 21-13.
*******
Well, I did not consider the swing on 5-1, which may make my suggestion
inferior. I still think my move is reasonable, however. My main argument
still stands: X's racing chances are fairly lousy, 20% at most, but just
good enough to screw up his timing. It's no tragedy if X gets hit - he
loses some racing equity but gains some hitting equity. See Robertie
#201C, for example - White, 20 pips down in a 5-point holding game, is
*worse* off than if he was 50 pips down.
Point by point:
1) Hmmm ... in one sense, NO move improves the race - 9 pips are 9 pips.
But in another sense, I think my move *does* improve the race because it
tries to free a runner. If X wants to win the race, he better get in a
position in which he can break contact with 4-4 or 5-5, and that won't
happen until his runners are free. As Hugh notes, 24-18, 7-4 may be
better than my move, but I think either one is better than taking both
dice on my side of the board.
2) No argument here, but remember that X's hitting equity goes up as his
racing equity goes down.
3) Although my move is worse on 5-1, it is better on 5-5, and also avoids
later attacking possibilities on the 3-point. Again, that checker is just
useless where it is.
I, too, would be curious to see other opinions/rollouts.
Thanks,
Peter Bell(USRobots)
David Montgomery
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| X X O O O | | X O |
| O O O | | X O |
| | | O |
| | | O |
| | | |
| | | | [1]
| | | |
| | | O |
| | | X O |
| | | X O |
| X X X | | X O |
| X X X | | X X O |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Money game. X to play 6-3.
Thanks for all the responses to this problem.
This is a position from _Costa Rica 1993_.
Wilcox Snellings played 22/13.
My preference before seeing any rollouts
or analysis was for 11/5 7/4. This was also
the choice of Herb Gurland, a top Boston player.
The authors of _Costa Rica 1993_ also preferred
11/5 7/4.
Wilcox Snelling rolled two plays out by hand
108 times with the following results:
11/5 7/4 -.42
22/13 -.50
The authors rolled another play out 108 times:
11/8 24/18 -.50
I rolled all of these plays out (and several others)
3888 times on Jellyfish (no truncation, duplicate
dice, 3 sets of 1296 with seeds 2430, 2431, and 2432).
Jellyfish cubeless equities:
22/13 -.363
22/16 11/8 -.405
22/16 7/4 -.416
24/18 11/8 -.446
11/5 7/4 -.449
24/18 7/4 -.456
24/15 -.458
I wasn't really that surprised that 22/13 came out
on top, although it wasn't the play that I would
have made. But I was *very* surprised that it came
out right by so much. This mistake actually costs
about 2/10 of a point when the cube is figured in.
I would welcome any further illumination on why
22/13 is so much better than the other plays,
especially 11/5 7/4.
David Montgomery
monty on FIBS
William C. Bitting
[cut]
: Money game. X to play 6-3.
: Thanks for all the responses to this problem.
: This is a position from _Costa Rica 1993_.
: Wilcox Snellings played 22/13.
: Wilcox Snelling rolled two plays out by hand
: 108 times with the following results:
: 11/5 7/4 -.42
: 22/13 -.50
------------------------------------------
Questions:
1) Why 108 times?
2) What is respresented my the numbers -.42 & -.50?
Is this the loss in "game equity?"
3) Why aren't the numbers in 2 positive? Would a
different roll be positive?
[cut]
: I rolled all of these plays out (and several others)
: 3888 times on Jellyfish (no truncation, duplicate
: dice, 3 sets of 1296 with seeds 2430, 2431, and 2432).
Which means?
[cut]
: But I was *very* surprised that it came
: out right by so much. This mistake actually costs
: about 2/10 of a point when the cube is figured in.
2/10 doesn't look very big on a small number like .35 % ?
[cut]
: David Montgomery
: monty on FIBS
Perhaps there are some others reading this thread that only have a vague
idea about the general topic of "rollouts?" When doing 108 rollouts by
hand, how does one come up with numbers like -.42 or -.50, etc..
TIA, wcb on FIBS
David Montgomery
>David Montgomery (mo...@cs.umd.edu) wrote:
>: Wilcox Snelling rolled two plays out by hand
>: 108 times with the following results:
>
>: 11/5 7/4 -.42
>: 22/13 -.50
>------------------------------------------
>Questions:
>1) Why 108 times?
One way to eliminate some of the luck in a rollout is make
sure that the first roll follows its assumed probability
distribution. That is, play the position out some multiple
of 36 times, and for each set of 36, begin twice with each
non-double and once with each doublet.
>2) What is respresented my the numbers -.42 & -.50?
> Is this the loss in "game equity?"
-.42 here means that after playing 11/5 7/4, X on average
lost 0.42 points per game during the 108 trials. You might
see -.42 refered to as the equity of the position, or the
points per game (ppg) won or lost. For example, if I played
a position out 4 times with the following results: +4, -4, -4, -8
then I lost 12 points in 4 games, for an equity of -3.0ppg.
This is still a little ambiguous, because the equity depends
on the cube level. When humans roll out a position, they will
generally do so with the cube in play, and so rollout results
are commonly given in terms of a 2-cube, if either side owns
the cube, or a 1-cube if the cube is centered. The equities
above were based on a centered 1-cube.
Computers, especially when rolling positions out at high speed,
are less proficient at using the cube, and so computer rollout
results are commonly given as though the position were cubeless
(i.e., no doubling is allowed, and the cube level is set at 1).
The Jellyfish numbers in my post were of this sort.
>3) Why aren't the numbers in 2 positive? Would a
> different roll be positive?
The numbers are negative because X is losing. When you give
numbers in terms of ppg, you are talking about the *net* average
points, so even though you will win some games, if on average
you lose more than you win, you have a negative equity. The
numbers were given from X's point of view since we were talking
about X's play; O's equity is the negative of X's, since whatever
X loses, O wins, and vice versa.
>: I rolled all of these plays out (and several others)
>: 3888 times on Jellyfish (no truncation, duplicate
>: dice, 3 sets of 1296 with seeds 2430, 2431, and 2432).
>
>Which means?
Jellyfish allows you to truncate rollouts -- that is,
not play them out until the end, but rather stop them after
each side has made so many moves, and let the computer
settle (estimate an equity) for the position at that point.
I didn't do this. I had the games played out until the end.
I'm not sure that it is documented in the manual, but it
is my understanding that Jellyfish will use "duplicate dice"
for rollouts if you give it the same random number seed for
different positions. For our purposes, a random number seed
is a magic number that you can type into Jellyfish when setting
up a rollout, such that if you type the same number in for
different positions, the same dice rolls ("duplicate dice")
will be used. This is very desirable when you are doing
play vs play comparisons, because often duplicate dice will
reduce the relative luck in rolling out different plays.
Incidentally, Jellyfish does *not* do this if the random
number seed is 0, the default. You have to enter some other
number, the same for each of the plays.
By duplicate dice, I mean that the same sequences of numbers
will be used for two or more positions. So, for example,
for game one the rolls might be
1-1 6-3 5-4 4-2 3-3 1-2 ....
These rolls would be used in order for rolling out the
position after 11/5 7/4, the position after 22/13, etc.
I only put the comment in because some people like to be
able to replicate others' results. The most important thing,
in my opinion, is the sample size (3888), whether or not
there was truncation (because in some situations this can
produce different results) and whether duplicate dice/random
number seeds were used (because this makes the differences
found more reliable).
>: But I was *very* surprised that it came
>: out right by so much. This mistake actually costs
>: about 2/10 of a point when the cube is figured in.
>
>2/10 doesn't look very big on a small number like .35 % ?
Well, what's big? Most checker play errors are less than
.05, cubeless. Most of the checker play errors I've seen
that are bigger than .10 are either blunders (like, I didn't
see I could hit), or positions in which you can choose between
two dramatically different approaches to the position, at
least one of which accomplishes something very significant
(like hitting, building a point, etc.). To me this position
didn't fit either of these categories.
>
>Perhaps there are some others reading this thread that only have a vague
>idea about the general topic of "rollouts?" When doing 108 rollouts by
>hand, how does one come up with numbers like -.42 or -.50, etc..
>
>TIA, wcb on FIBS
Hope this helped.
Kit Woolsey
:
: +24-23-22-21-20-19-+---+18-17-16-15-14-13-+
: | X X O O O | | X O |
: | O O O | | X O |
: | | | O |
: | | | O |
: | | | |
: | | | | [1]
: | | | |
: | | | O |
: | | | X O |
: | | | X O |
: | X X X | | X O |
: | X X X | | X X O |
: +-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
: Money game. X to play 6-3.
: Thanks for all the responses to this problem.
: This is a position from _Costa Rica 1993_.
: Wilcox Snellings played 22/13.
: My preference before seeing any rollouts
: or analysis was for 11/5 7/4. This was also
: the choice of Herb Gurland, a top Boston player.
: The authors of _Costa Rica 1993_ also preferred
: 11/5 7/4.
: Wilcox Snelling rolled two plays out by hand
: 108 times with the following results:
: 11/5 7/4 -.42
: 22/13 -.50
: The authors rolled another play out 108 times:
: 11/8 24/18 -.50
: I rolled all of these plays out (and several others)
: 3888 times on Jellyfish (no truncation, duplicate
: dice, 3 sets of 1296 with seeds 2430, 2431, and 2432).
: Jellyfish cubeless equities:
: 22/13 -.363
: 22/16 11/8 -.405
: 22/16 7/4 -.416
: 24/18 11/8 -.446
: 11/5 7/4 -.449
: 24/18 7/4 -.456
: 24/15 -.458
: I wasn't really that surprised that 22/13 came out
: on top, although it wasn't the play that I would
: have made. But I was *very* surprised that it came
: out right by so much. This mistake actually costs
: about 2/10 of a point when the cube is figured in.
: I would welcome any further illumination on why
: 22/13 is so much better than the other plays,
: especially 11/5 7/4.
: David Montgomery
: monty on FIBS
While Jellyfish rollouts are usually accurate and quite informative,
occasionally they can give us wrong information. One the dangers is that
the program is simply misplaying the position, and this affects one of
the plays being rolled out more than the other one. Keep in mind that
for the rollout the program is playing with only 1-ply (that is the same
as level 5). This is necessary for speed purposes -- to use 2-ply in the
rollouts would make the rollouts take far longer. The program still
plays pretty well at 1-ply, but not nearly as well as 2-ply and therefore
is more likely to be doing something wrong in the play. Most of the time
this will not matter (particularly in play vs. play problems), since
these errors in play tend to cancel out and generally are not huge
anyway. Occasionally the two plays being tested lead to different types
of positions, where one play gives the program a chance to make an error
which the other play doesn't.
When I saw David's results, I thought this might be happening. I thought
after playing 11/5, 7/4 the program might be making the defensive three
point if it rolled a two. I also thought this might be the wrong
strategy -- hanging back on the ace point with the back man and springing
the other checker could be better. So, I decided to run a test. I had X
play 11/5, 7/4 with the 6-3, and gave O a 6-1 (played 13/6). This left
the following position:
13 14 15 16 17 18 19 20 21 22 23 24
+------------------------------------------+
| O X | | O O O X X |
| O X | | O O O |
| O | | O |
| O | | |
| | | |
| | | |
| O | | |
| O X | | X X |
| O X | | X X X |
| O X | | X X X |
+------------------------------------------+
12 11 10 9 8 7 6 5 4 3 2 1
Now I gave X a 4-2 to play, and looked at Jellyfish's 1-ply opinion. I
also rolled out the three logical plays 2952 times each, duplicate dice.
These were the results:
Play 1-ply Rollout
24/22, 7/3 -.428 -.514
7/3, 5/3 -.501 -.486
22/18, 5/3 -.510 -.412
These results confirmed my suspicions. Jellyfish was thematically
misplaying the position in its rollouts after playing 11/5, 7/4 with the
original 6-3. However after playing 22/13 with the 6-3 the program
didn't have the opportunity to make this sort of misplay, since there was
no way to make the 22 point so there was no incentive to move the back
checker. This misplay might be sufficient to turn the rollout results of
the 6-3 around, and certainly explains why 22/13 came out so much better
than 11/5, 7/4 in David's rollout.
Any time you are suspicious about the results of a rollout, it is vital
to examine how the program is playing at least the next couple of rolls
before accepting the results of the rollout as gospel. The rollouts are
good, but we still have to keep our eyes open or we may fall into some
unexpected traps.
Kit