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Whatever you think of JellyFish 3.0's style of play and precise level
of skill (better, as good as or almost as good as the best), overall
JF3.0 has proved to be competitive with expert human players. Playing
with the handicap of a short "search for best move" time factor,
JellyFish sits at or near the top of the ratings lists on FIBS and, in
private play against some of the world's best players, holds its own
or better.
JellyFish gets good results despite complete ignorance of its
opponents, and despite (or because of -- let's avoid that argument for
now) a marked preference for steering games into nonvolatile,
nongammonish and relatively simple advanced anchor, minimal contact
racing positions.
JF does this, generally, by splitting instead of slotting, and working
very hard in the opening to make an advanced anchor. JF tends to avoid
prime versus prime battles and backgames -- the weakest parts of its
game -- when it can. But JF3.0 plays priming and backgames well, and
when aggressive play is required, JF can blitz with the best of them.
In published positions, JF has occasionally shown experts why the
blitzing play is better than the obvious, so-called "pure" priming
alternative.
Curiously, despite (or again, because of) its style, when JellyFish
plays against itself it wins and loses gammons more frequently than
human players do. Against average to expert human opponents, JellyFish
wins gammons with a frequency most humans should envy but, by avoiding
deep anchor games, backgames, and bad takes, proves rather difficult
for its opponents to gammon.
Bad takes -- positional judgement and cube strategy are the most
challenging aspects of modern backgammon. It's not easy to learn to
play the checkers competitively, but it's much more difficult,
especially in match play, to double neither too soon nor too late, and
to drop or take correctly. Among advanced and even expert players,
errors with the cube tend to be much more costly than mistakes in
checker play.
Perhaps this -- cube handling -- is JellyFish's biggest advantage over
human players, including experts. How much easier it is *not* to have
to think! JellyFish plugs a position into its neural net and out pops
a decision. Sometimes JellyFish is wrong, but it's hardly ever wrong
by much. If "I laugh at that cube" was part of JellyFish's
programming, there's no question who would be laughing the most, and
most often, last.
TO ERR IS HUMAN?
Occasionally, though, JellyFish makes a mistake -- not a question of
style but a clear error, and sometimes an out and out laugher. I'd
like to look at some positions where JellyFish goes wrong now, because
there's a lot to learn from JellyFish, even from its mistakes.
On Jan. 3, 1998 in the newsgroup rec.games.backgammon, Donald Kahn
described one match situation and five related positions in which
JellyFish fails to double when it should. Donald also described one
match situation in which JellyFish makes a bad play on the first roll
of the game. Another reader contributed a money play bearoff position
in which JellyFish does not double, but should.
Those positions turned out to be even more interesting than they
appeared at first glance. I'd like to discuss them a bit more and then
add five more bearoff situations where JellyFish's cube action is
incorrect.
For match equity estimates I used Kit Woolsey's match equity table.
For precise positional equity values, I used Hugh Sconyers' 4 checker
vs. 4 checker database, one of two databases included in Hugh's
downloadable BG Interface for Windows for his CD-ROM library of
bearoff and backgame positions.
In all positions, JellyFish is X and bears off to the lower left.
POSITION 1:
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O | | |
| O | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| X | | |
| X | | |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Match to 4, Jellyfish 2, Opponent 0, Centered cube
Cube Action?
In this "last-roll" position, JellyFish has 26 winning and 10 loses
rolls -- a huge double and a marginal take. For money, JellyFish
correctly doubles, and takes for the other side.
In match play it's a different story.
Donald wrote:
> Leading 2-0 in a 4 point match, with two pieces on the 2-point
> against 2 pieces on the 1-point, JellyFish recommends "no double". It
> does not recognize that this is a last roll situation, and the double
> offers 17-10 odds: you should actually double with a piece on the 5
> point and a piece on the 3 point.
At this match score, JellyFish does not double, although it has an
opportunity to win the match on the roll with little risk by doubling
now -- if Opponent takes. Actually, the correct cube action is
double/pass!
To decide if doubling is right, we need to know how often JF wins this
game. We need to know how often JF rates to win the match at the match
scores reached after double/take and win, double/take and lose, no
double and win, and no double and lose. Then, we need to fill in the
blanks in this equation:
(Game winning chances) times (match equity after winning the game),
plus (game losing chances) times (match equity after losing the game)
equals (total match equity)
Finally, we need to complete the equation twice -- once for doubling,
once for no double, and see which equation gives JellyFish the better
chance to win the match.
The relevant numbers are:
JellyFish bears off both checkers on 26/36 rolls, or 72.22%.
JellyFish doesn't double and wins -> score 3-0, match equity 83%
JellyFish doesn't double and loses -> score 2-1, match equity 60%
JellyFish doubles and wins, -> score 4-0, match equity 100%
JellyFish doubles and loses, -> score 2-2, match equity 50%
If JF doubles and Opponent takes, JF wins the match immediately 72% of
the time, and 28% of the time starts the next game with 50% winning
chances. So our equations looks like this:
Double/take: 0.7222 x 1.00 + 0.2778 x 0.5 = 86.11% match equity
(Over the board, you might compute this as 26/36 (the 26 numbers that
win the match) + 5/36 (half of the 10 numbers that lose the game) =
31/36 = 86%
No double: 0.7222 x 0.83 + 0.2778 x 0.6 = 76.61% match equity.
(Over the board, this one´s a little tougher but you might compute
this as 80% and a bit more of 26/36, plus 60% of 10/36 = about 27.5/36
= about 76%.)
What about the take? Oh, here's a shortcut to determining match equity
for both sides! Opponent needs 4 points to win the match. If Opponent
drops, he has 17% match equity at the score 0-3 Crawford. Since
take-and-win only happens 10/36 of the time, after which Opponent
should win the match half the time from the score 2-2, Opponent's
match winning chances after taking are half of those 10/36 rolls, or
13.88%. Opponent does much better by dropping.
To recap:
Correct double, incorrect take: JF has 86.11% match equity
Correct double, correct pass: JF has 83.99% match equity
JF does not double: JF has 76.61% match equity
JellyFish errs on the other side of the board also. If we reverse the
position and scores:
POSITION 2
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O | | |
| O | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| X | | |
| X | | |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Match to 4, Jellyfish (still X) 0, Opponent 2, Centered cube
If Opponent doubles, JellyFish takes, giving up about 2% match equity.
RELATED LAST ROLL POSITIONS
As Donald indicated, the leader of a match in a last roll situation
(where there´s no fear of a redouble) can sometimes double even when
not a favorite to win the game.
Let´s take Position 1, move JellyFish's checkers to create positions
in which JellyFish's game winning chances become increasingly worse,
and determine the correct cube action.
Here again are the relevant match equities:
No double/win or double/drop -> score 3-0, match equity 83%
No double/loses -> score 2-1, match equity 60%
Double/take/win -> score 4-0, match equity 100%
Double/take/lose -> score 2-2, match equity 50%
POSITION 3
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O | | |
| O | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| | | |
| X X | | |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Match to 4, Jellyfish 2, Opponent 0, Centered cube
JellyFish bears off both checkers on 25/36 rolls, or 69.44%.
Double/take: 0.6944 x 1.00 + 0.3055 x 0.5 = 84.71% match equity
No double: 0.6944 x 0.83 + 0.3055 x 0.6 = 75.96% match equity.
Take: 0.3055 x .05 = 15.27% match equity
Drop: 17.00% match equity
Correct cube action: double/drop. JellyFish says no double/take.
POSITION 4
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O | | |
| O | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| | | |
| X X | | |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Match to 4, Jellyfish 2, Opponent 0, Centered cube
JellyFish bears off both checkers on 23/36 rolls, or 63.88%.
Double/take: 0.6388 x 1.00 + 0.3611 x 0.5 = 81.93% match equity
No double: 0.6388 x 0.83 + 0.3611 x 0.6 = 74.68% match equity.
Take: 0.3611 x .05 = 18.05% match equity
Drop: 17.00% match equity
Correct cube action: double/take. JellyFish says no double/take.
POSITION 5
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O | | |
| O | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| | | |
| X X | | |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Match to 4, Jellyfish 2, Opponent 0, Centered cube
JellyFish bears off both checkers on 19/36 rolls, or 52.77%.
Double/take: 0.5277 x 1.00 + 0.4722 x 0.5 = 76.38% match equity
No double: 0.5277 x 0.83 + 0.4722 x 0.6 = 72.13% match equity.
Take: 0.4722 x .05 = 23.61% match equity
Drop: 17.00% match equity
Correct cube action: double/take. JellyFish says no double/take.
POSITION 6
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O | | |
| O | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| x | | |
| X | | |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Match to 4, Jellyfish 2, Opponent 0, Centered cube
With checkers on the 3 point or on the 3 and 4 points, JellyFish bears
off both checkers on 17/36 rolls, or 47.22%.
Double/take: 0.4722 x 1.00 + 0.5277 x 0.5 = 73.60% match equity
No double: 0.4722 x 0.83 + 0.5277 x 0.6 = 70.85% match equity.
Take: 0.5277 x .05 = 26.38% match equity
Drop: 17.00% match equity
Correct cube action: double/take. JellyFish says no double/take.
POSITION 7
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O | | |
| O | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| | | |
| X X | | |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Match to 4, Jellyfish 2, Opponent 0, Centered cube
JellyFish bears off both checkers on 14/36 rolls, or 38.88%.
Double/take: 0.3888 x 1.00 + 0.6111 x 0.5 = 69.43% match equity
No double: 0.3888 x 0.83 + 0.6111 x 0.6 = 68.93% match equity.
Take: 0.6111 x .05 = 30.55% match equity
Drop: 17.00% match equity
Correct cube action: double/take. JellyFish says no double/take.
And now for something different...
POSITION 8:
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| X O | | O X |
| X O | | O X |
| O | | O X |
| O | | X |
| O | | X |
| | | | 64
| X | | O |
| X | | O |
| X | | X O |
| O X | | X O |
| O X | | X O |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Match to 4, Jellyfish 2, Opponent 3, Post-Crawford
JellyFish rolls 21 and plays 13/11 6/5.
Donald wrote:
> Post-Crawford, behind 3-2 in a 4 point match, JellyFish Level 7
> recommends playing an opening 2-1: 13/11 6/5. Slotting the 5 point
> against an opponent with a free drop is a well-known no-no.
There's been lots of discussion of slotting versus splitting with the
opening rolls 21, 41, and 51. JellyFish usually prefers to split, and
there are good reasons for both slotting or splitting -- either as a
matter of style, or to create or avoid gammonish or unclear positions
at certain match scores or in money play.
However, none of the usual arguments apply to *this* score -- 2-away
1-away post-Crawford -- when the *trailer* rolls 21, and JellyFish´s
slot is a mistake.
At this score, the trailer can't gain by slotting because he will
never be able to cover the blot and start priming the leader. Why?
Because on the next roll the leader will either hit the blot or miss
it. Either way, the trailer will then double. But if the leader hits
the blot (or rolls 33 or 66) he's a clear favorite and has an easy
take -- all the hitting rolls give the leader 60% or more winning
chances. After all other rolls, the leader is an underdog, uses his
"free drop," and starts the next (and last) game with 50% winning
chances.
A look at JellyFish´s evaluation of the position following its 21 play
reveals why it makes a bad play here. JellyFish gives itself only
49.6% winning chances but a positive 0.244 equity, because JF
correctly ignores its opponent's gammon chances but incorrectly counts
its own potential gammon wins twice. But at this score with the cube
coming next roll, JellyFish can't use gammons, and its "look-ahead"
fails to realize that JF will be doubling at its next opportunity,
annulling its own gammon chances.
MORE POSITIONS
The rest of these positions (9-14) are money game bearoff positions in
which JellyFish makes the wrong cube decision. For each position I'll
tell you:
(a) the correct cube action;
(b) what JellyFish does;
(c) how many points per game JellyFish wins with correct
and incorrect cube action; and
(d) how many points per game JellyFish gives up by making
the wrong decision.
The next position is in many beginning books on backgammon, but
JellyFish isn't much of a reader.
POSITION 9:
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O | | |
| O | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| | | |
| X X | | | 2
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Money game
DJ wrote:
> Money game: Jellyfish on roll holding the cube. Jellyfish has a piece
> on his 5 point and 2 point. Opponent has a piece on his own ace point.
> Jellyfish does not double, tho favored in this final roll bearoff.
Correct cube action: double/take, redouble/take.
JellyFish does not double, does not redouble.
ppg if cube is centered, no double: 0.0555
ppg if JellyFish doubles: 0.1111
By not doubling, JellyFish gives up 0.0555 points per game.
ppg if JellyFish holds a 2-cube: 0.1111
ppg if JellyFish redoubles to 4: 0.2222
By not redoubling, JellyFish gives up 0.1111 points per game.
POSITION 10
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O O | | |
| | | |
| | | |
| | | |
| | | |
| | | | 64
| | | |
| X | | |
| X | | |
| X | | |
| X | | | 2
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Money game
Correct cube action: double/take, redouble/take (but only barely a
double and redouble).
JellyFish does not double.
ppg if cube is centered, no double: 0.0925
ppg if JellyFish doubles: 0.1481
By not doubling, JellyFish gives up 0.0555 points per game.
ppg if JellyFish holds a 2-cube: 0.2407
ppg if JellyFish redoubles to 4: 0.2962
By not redoubling, JellyFish gives up 0.0555 points per game.
These last four positions I found while playing with Hugh Sconyers'
nifty 4x4 database.
POSITION 11
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O O O O | | |
| | | |
| | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| | | |
| | | |
| X | | |
| X X X | | | 2
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Money game
Correct cube action: double/take, no redouble/take.
JellyFish doubles and redoubles.
ppg if cube is centered: 0.3531
ppg if JellyFish doubles: 0.4060
ppg if JellyFish holds a 2-cube: 0.844158
ppg if JellyFish redoubles to 4: 0.812140
By redoubling, JellyFish gives up 0.032018 points per game.
POSITION 12
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O O O O | | |
| | | |
| | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| | | |
| X | | |
| X X X | | | 2
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Money game
Correct cube action: double/take, no redouble/take.
JellyFish doubles and redoubles.
ppg if cube is centered: 0.2967
ppg if JellyFish doubles: 0.2981
ppg if JellyFish holds a 2-cube: 0.694150
ppg if JellyFish redoubles to 4: 0.596228
By redoubling, JellyFish gives up 0.097922 points per game.
POSITION 13
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O O O O | | |
| | | |
| | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| | | |
| | | |
| | | |
| X X X X | | | 2
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Money game
Correct cube action: double/take, no redouble/take.
JellyFish doubles and redoubles.
ppg if cube is centered: 0.320975
ppg if JellyFish doubles: 0.325056
ppg if JellyFish holds a 2-cube: 0.785603
ppg if JellyFish redoubles to 4: 0.650112
By redoubling, JellyFish gives up 0.135491 points per game.
POSITION 14
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O O O | | |
| O | | |
| | | |
| | | |
| | | |
| | | | 64
| | | |
| | | |
| | | |
| X | | |
| X X X | | | 2
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
Money game
Correct cube action: double/take, no redouble/take.
JellyFish doubles and redoubles.
ppg if cube is centered: 0.282335
ppg if JellyFish doubles: 0.288788
ppg if JellyFish holds a 2-cube: 0.730276
ppg if JellyFish redoubles to 4: 0.577576
By redoubling, JellyFish gives up 0.1527 points per game.
NOTES
Kit Woolsey's match equity table is on Stephen Turner's WWW Backgammon
Page at:
http://www.statslab.cam.ac.uk/~sret1/backgammon/equities.html#table
Hugh Sconyers' BG Interface and information about his CD-ROM databases
is at:
http://www.realtime.net/~sconyers/
Thanks to Kit Woolsey for reading an earlier draft of this article and
to David Montgomery for suggesting that "JellyFish laughs" would be an
infuriating addition to JellyFish's repertoire.
_______________________________________________
Daniel Murphy http://www.cityraccoon.com
Raccoon on FIBS: http://www.fibs.com
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