# JellyFish Early Double at 2-away,2-away.

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### micha...@yahoo.com

May 25, 1998, 3:00:00 AM5/25/98
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Earlier this year I had a discussion with Mr JellyFish Fredrik Dahl about
Jelyfish always doubles at 2-away,2-away positions. The subject was that JF
doubles right after the first move, whether it's ahead or not. Here is the
discussion: Michael Bo Hansen Wrote: Hi F. Dahl I've been playing a lot
with the JellyFish 3.0 player shareware version. I have encountered that
when JF and I both are two points away from victory, and I open with 4-2 (or
3-1 in fact), JF doubles! I must say I was quite surprised the first time it
happened. I know that an early double is necesarry when the score is 2-away
2-away, but doubling when you are underdog, that can't be correct. I'll will
be glad if you can come up with an explanation. Yours truly Michael Bo
Hansen, Denmark. F. Dahl replyed: This is in the FAQ in the JF users
manual :-). If you start the game with the plan of doubling right away,
the game will surely be played to the end with the cube on 2. So the game
will decide the match. Obviously this means that you should win 50%.
Because the score 2-away, 2-away is symmetric, it's clearly worth 50%, so
using the strategy of always doubling right away does not cost any equity,
and therefor is not wrong. Another way to look at it: If it's wrong for
JF to jack up the cube, then it must be right for you (because you win what
it loses). So if it doesn't double, you should, and then it must take. The
result is the same, the cube ends on 2. A third way to look at it: If you
say it's wrong to always double, you must think it costs equity. Then you
should be willing to pay your opponent some small amount (less than the
size of the error) to make this error. But this is clearly stupid, as you
pay him money to play an even game. A fourth way: Always doubling
transforms 2-away,2-away to 1-away,1-away, which cannot be wrong.
Michael Bo Hansen: Hi again Fredrik Dahl. I've been playing a lot with
the JellyFish 3.0 player shareware version. I have encountered that when JF
and I both are two points away from victory, and I open with 4-2 (or 3-1 in
fact), JF doubles right after! I must say I was quite surprised the first
time it happened. Here is an explanation of why I thinks it's wrong. After
I have rolled 31 in the opening roll, JellyFish (JF) is underdog of winning
the following game (distinguish from winning the total match). The
probability of JF wins the game is therefore P{JF wins game} < 0.5 We
have that the probability for JF winning the total match when doubling is
P{JF wins match by doubling} = P{JF wins game} < 0.5 because there is only
one game left. On the other hand, the probability for JF to win the match
when JF does not double is (while not taking gammons into account) P{JF
wins match by no doubling} = P{Opponent doubles} × P{JF wins game}
+P{Opponent doesn't double} × P{JF wins game} × EQ{1-away,2-away}
+P{Opponent doesn't double} × P{JF loses game} × EQ{2-away,1-away} where
P{Opponent doubles} is the probability that your opponent doubles right away
(or at least while you still can take the cube), and EQ is equity of winning
the game at that score. Of course you have P{Opponent doubles} = 1 -
P{Opponent doesn't doubles} P{JF wins game} = 1 - P{JF wins game}
EQ{1-away,2-away} = 1 - EQ{2-away,1-away} >From Equity tables, such as the
one made by Tom Keith (http://www.bkgm.com/articles/met.html):"How to
Compute a Match Equity Table", we get EQ{1-away,2-away} = 70 % Let's
say you are playing against a horrible player, who doesn't know the doubling
cube. From that P{Opponent doubles} » 0 and therefore P{JF wins
match by no doubling} = P{JF wins game} × 0.7 + (1- P{JF wins game})× 0.3 =
0.3 + 0,4 P{JF wins game} which, in the interval [0, .5 [, always is
higher than P{JF wins game} itself. Therefore P{JF wins match by
doubling} < P{JF wins match by no doubling}. The same calculations can be
made for different values of P{Opponent doubles}, and only for P{Opponent
doubles} = 1 (he always doubles) it's the same whether you double or not.
But you never know, do you? Therefore the correct action must be not to
double when you are an underdog in a 2-away,2-away situation. Yours Truly
Michael Bo Hansen, M.Sc Denmark. F. Dahl: This sounds plausible, but is
not quite correct. If JF doesn't double, then you can. So nothing can be
gained by 'trying to keep the cube down'. If you think it's wrong to
promise always to double at this score, try playing it as a proposition: I
always double, you don't. Who has the advantage? Noone, obviously, as all
games will be doubled early. So I can't ba making any error, ok? Michael
Bo Hansen: OK. I know that I will always double after I have rolled 31 or 42
in my opening roll, because I'm a favorite to win ( Not much...but enough),
but not all people do. JF should wait until I double, because there is no
reason for JF to double. If I'm stupid enough NOT to double, JF should take
an opponent who is willing to risk losing his market, you can do better by
waiting with the cube. I believe JF does this if it wins the opening roll
and the opponent responds with a crushing doublet. Michael Bo: I haven't
investigated your proposal, but shouldn't it also wait doubling when the
opponent rolls 31 and 42? F. Dahl: Against a good opponent it makes no
difference, as the cube will be turned evenually. But you could wait till
the first point where you risk losing your market, and I agree that there
is no such risk after 31 or 42. -- - Fredrik Dahl

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### ches...@feist.com

May 25, 1998, 3:00:00 AM5/25/98
to

In article <6kbc66\$8uk\$1...@nnrp1.dejanews.com>,

micha...@yahoo.com wrote:
>
> Earlier this year I had a discussion with Mr JellyFish Fredrik Dahl about
> Jelyfish always doubles at 2-away,2-away positions. The subject was that JF
> doubles right after the first move, whether it's ahead or not.Here is the
This is not just an academic issue. In my experience opponents frequently do
*not* double right away when ahead at 2-away 2-away. Therefore, it is a clear
error for Jellyfish to make the assumption that opponents will play 100%
correctly. IMO it is a clear glitch in Jellyfish, one which it would seem
could and should be easily corrected.

Jerry Weaver