# More on JellyFish cube strategy

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Jul 2, 1995, 3:00:00 AM7/2/95
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Further to the discussion on JellyFish' cube strategy: At first I thought that JellyFish simply doubles whenever the estimated (cube less) value of a position exceeds a certain point. The following two positions led me to believe, that JF would double positions with a relative equity of at least 0.411. This would correspond to a "stake adjusted" winning probability of about 71% which seems like a reasonable figure. All quoted estimates are on level 6. Position 1: 13 14 15 16 17 18 19 20 21 22 23 24 +-----------------------------------------+ | X O O | | O X | | X O O | | O | | X O | | O | | | | O | | | | | +---+ | | | | | | | | | | +---+ | | | X | | O X | | X | | O X X | | X X O | +---+ | O X X | | X X O O | | | +-----------------------------------------+ +---+ 12 11 10 9 8 7 6 5 4 3 2 1 Money game, X on roll. JF has X' equity at 0.410 and advocates no redouble and no initial double. Position 2: 13 14 15 16 17 18 19 20 21 22 23 24 +-----------------------------------------+ | X X O | | O X | | X O | | O | | X O | | O | | X O | | O | | | | | +---+ | | | | | | | | | | +---+ | O | | | | O X | | X | | O X | | X X O | +---+ | O X X | | X X O O | | | +-----------------------------------------+ +---+ 12 11 10 9 8 7 6 5 4 3 2 1 Money game, X on roll. JF has X' equity at 0.411 and judges initial double as well as redouble. Position 3, however, tells a different story: Position 3: 13 14 15 16 17 18 19 20 21 22 23 24 +-----------------------------------------+ | X X O O | | O X O | | X O O | | O X | | X O | | O | | | | | | | | | +---+ | | | | | | | | | | +---+ | | | | | O X | | X | | O X | | X X | +---+ | O X X | | X O X O | | | +-----------------------------------------+ +---+ 12 11 10 9 8 7 6 5 4 3 2 1 Money game, X on roll. JF has X' equity at 0.414 and says no redouble and no initial double. Apparently JF' cube algorithm is not a function of equity only. Perhaps the value of cubeownership is not simply a constant, and perhaps some measure of volatility is included in the algorithm. Any comments on this would be appreciated very much. Even though position 3 appears more volatile than position 2, it is not inconceivable than position 2 is a double and position 3 is not, despite the "fact" that position 3 is also slightly stronger for X (according to JF). This is, I imagine, because X does not lose his market by all that much, if at all, when he wins the fight for the 5-point. If, on the other hand, O wins the battle for the 5-point, the game is going to be a roughly even high anchor versus high anchor game, probably lasting for quite some time. This means that O will benefit greatly from owning the cube. In position 2 cubeownership may not be nearly as valuable; O will usually be forced into some kind of holding game and usually win by getting and hitting one crucial shot, when he has build his board. Consequently the cube will not help him as much as in diagram 3. Does this make sense? I seriously doubt whether any non-neural algorithm will be able to capture this difference in cube dynamics between position 2 and 3. (JF's cube algorithm is indeed, according to Kit's recent posting, non-neural.) So why the the difference in JF's cube action in position 2 and 3? I wonder if JF does distinguish between doubles and redoubles as all? Comments on JF's doubling strategy as well as on the above positions will be very much appreciated. :-)))) L. H. Madsen

### Fredrik Dahl

Jul 8, 1995, 3:00:00 AM7/8/95
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JF Cube strategy:

It does not do any volatility analysis, but that we may try to
get into a later version.

Money game:
It first estimates the value of the cube for the take side
by multiplying his winprob by a factor 0.15, giving an eq-estimate E.
If E<0.5 it takes.
If E>L it doubles, only I don't quite remember the number.
Think L was set to about 0.32.
Note that the cube action from this alg. is not a function of equity only!
In a gammonish position, the underdog will win more games (cubeless)
than in a race, assuming identical equities,
and therefor he will have more use of the cube.
From rollouts I have gotten the impression that 0.15 is a bit low,
and maybe should be about 0.2.

Match play:

It first calculates recube potental from the score as the fraction of
extra points from recube usefull (R). If the recube will be to 8, for example,
and it only needs 6 more points, only 2 of the 4 extra points put on the line
are usefull, so the recube potential from the score (R) = 0.5.
It estimates the cube value for the taker by multiplying his win prob by the factor
(1+0.15*R). It then checks if the matcheq gotten by immediately redoubling
is higher than the one the preceeding calculations give, and in that case
disregards the R.

Then it calculates the matcheq according to the corrected probabilities
using Kits table to get the double-take match eq (DT).
It then calculates the matcheq gotten from never cubing (N).
It then tabulates the matcheq from double-pass (DP).
If N>DP, it plays on automatically.
The intervall [N,DP] is the doubling window,
and it doubles if DT is bigger than a*N+(1-a)*DP.
We currently use a=0.4, which means that it doubles in the upper 40%
of the doubling window.
When either player needs more than 11 points we don't use eq charts,
but simply assume that each point is equally valuable,
and truncate the payoff when it exceeds the number of points needed.

Fredrik Dahl.

### Anthony R Wuersch

Jul 9, 1995, 3:00:00 AM7/9/95
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In article <3tm4br\$b...@gymir.ifi.uio.no>,
Fredrik Dahl <fred...@ifi.uio.no> wrote:
>JF Cube strategy:

Thanks a lot for that, Fredrik! Having an explanation of what Jellyfish
means when it says "I double" or "I pass" is very useful to help us judge
if it made a proper decision.
--
Toni Wuersch
a...@world.std.com {uunet,bu.edu,bloom-beacon}!world!arw