Tom
First let me mention: I very often feel the same. But I am convinced, it
is just a FEELING. Let me propose an experiment: Play a - let's say -
300 point match against JellyFish using manual dice. Then tell us the
outcome. Is it better than a 300 point match with JF-generated dice?
We have this discussion very often here. But I believe, it's a phenomena
of the human brain: If you roll well, you feel lucky, if JellyFish does
roll well, it cheats.
Do you play on FIBS? If yes: Whats your rating there? JellyFish was
playing as a bot on FIBS in the Level5-version a couple of years ago. It
had a rating of up to 2000 (average of 1900). JF plays at Level 7
nowadays. I don't even want to know it's possible rating at FIBS :-( And
playing on FIBS it was using FIBS dice!
You will find some nice articles about JF-"chaeting" here:
http://www.bkgm.com/rgb/rgb.cgi?menu
Regards,
Hardy
--
You'll find me as Hardy_whv at FIBS!
So I got the dice from my game and put Jellyfish in manual mode and
rolled the dice myself and entered them. Like playing a completely
different game.
Then I found a program that creates lists of random rolls and now I use
that and set it to rollout 300 sets. Then I back out of Jellyfish and
make a new run with the program every game or two. Even then Jellyfish
hits open men much more often than it does when you manually roll dice
for each turn, but not as much as when generating the rolls itself. I
suspect Jellyfish is looking ahead when the random rolls list is loaded
and can make optimal choices knowing what you have coming. With manual
dice rolls it can't do that. But when Jellyfish is allowed to use its
own generator it can easily see where your open men are and roll what it
needs to hit them.
I've tried two or three backgammon programs and they all seem to be
looking ahead to some extent, except one called bgblitz.
I don't know how these various games are programmed but they [ shouldn't
] be allowed to look ahead at coming rolls but there is no way to know
if they do or not. But from the difference in using them in their native
mode ( rolling the dice themselves ) and importing lists and in manual
mode it would seem apparent that they certainly don't play fair because
in manual mode the level of the computers play falls about 500%.
METHOD FOR VERIFYING THAT JELLYFISH DOES NOT
GENERATE DICE ROLLS TO ITS OWN ADVANTAGE
1) Record Jellyfish's current "seed" setting.
2) Play a game against Jellyfish, recording all the dice rolls and moves for
each side.
3) Reset the seed to its previous starting value.
4) Play a new game. The initial dice roll will be the same as before. When
it is your turn to play your first move, make a completely different play from
the previous game. Do the same on your second move, then play normally.
5) Record all the rolls and moves of this second game.
Notice that although Jellyfish is now faced with completely different
positions than before, the sequence of dice rolls is exactly the same. It is
not giving itself different numbers to benefit from the changed
situations. The dice rolls are entirely determined by the opening seed!!
------------------------------------------------
METHOD FOR VERIFYING THAT JELLYFISH DOES NOT TAKE
UPCOMING ROLLS INTO ACCOUNT IN DETERMINING ITS PLAYS
Since the sequence of rolls in the game is determined by the initial seed, you
might believe that Jellyfish adjusts its plays to take advantage of upcoming
rolls. Here's how to verify that this is not happening.
1) Play a game (or several games) against JF and record the rolls and moves.
(The simplest way to do this is to save each game as a *.gam file and print it
when the game is done.)
2) Pick a game where you think JF must have cheated because of its good luck.
3) Set up each of JF's positions in the game and, using the "Best Moves"
option, query as to what it thinks the best move is for the roll it had.
Note that it always made the best which its evaluation function thought was
best, not a play tailored to take advantage of upcoming rolls.
The above text is from this site: http://effect.webbie.net/dice.htm
Ed Collins
"Hardy Hübener" wrote, in a discussion about cheating JellyFish:
> If you roll well, you feel lucky
I think it's much worse: people (all of us to some extent) are more than willing
to attribute wins to their "good play". (To notice own luck would already be one
half of a sane attitude.) And in spite of their "sophisticated play", they are
losing again and again due to JF's (or any other opponent's) "incredible luck".
And if they can't see any dice like with a bot, they locate the reason to their
losses there, where it's apparently not controllable (thanks to Ed Collins for
addressing this error).
Sorry, Steven, if I am too harsh, but it's all in your mind.
Regards,
Peter aka the juggler
(one toppost line for a reason: not moaning but looking at it in a way
I haven't seen here before :-)
> Doesn't the following two methods prove that Jellyfish does not cheat?
>
>
>
> METHOD FOR VERIFYING THAT JELLYFISH DOES NOT
> GENERATE DICE ROLLS TO ITS OWN ADVANTAGE
> ------------------------------------------------
> METHOD FOR VERIFYING THAT JELLYFISH DOES NOT TAKE
> UPCOMING ROLLS INTO ACCOUNT IN DETERMINING ITS PLAYS
> ...
> 3) Set up each of JF's positions in the game and, using the "Best Moves"
> option, query as to what it thinks the best move is for the roll it had.
Assuming they are playing with something better than the Light version,
right? And it's probably unlikely this is the case.
On a side note, I'll present something last that might be fun to
discuss (at least for cheating programmers :-).
Before that, I'm happy to announce someone I introduced Jellyfish too
has switched view from "Jellyfish cheats" to "Jellyfish probably cheats
sometimes". He has also advanced from level 2 to level 5 one pointers
(means he is about 50% in win/loss according to his own words on
statistics). That's probably too positive of him but whatever.
We did start a discussion on how Jelly SHOULD cheat. Which got rather
interesting. Although I've played thousands of matches against Jelly I
still sometimes "feel" it cheats :-). Yes, I should know better. We
both now attribute the feeling to the same thing. Quit a game before
it's played to conclusion and Jelly is likely to get a wow roll next
game. Bullocks. It's probably more that if you loose so badly that you
quit in disgust you play a bit worse the next games as you are
emotionally unstable. Or to loose that badly in the first place means
you are playing very bad today anyway :-). I actually run two Jellys
for months where I always quit when things went badly in one of them.
Yes, the quit-Jelly had worse statistics in subsequent wins after a
quit but not enough to warrant anything statistically IMHO (it was a
close call though).
Anyway, now to the issue of cheating so no one (few) would notice or be
able to prove it...
Well, my buddy did propose Jelly looks ahead which is effectively ruled
out using the approach you outlined above. Almost. If *I* would make a
computer program cheat I would make it really *really* ugly to detect.
Let's assume we can predict human behaviour somewhat. If you suspect it
cheats you will probably do certain things (not just play). Manual
dice, setting the seed (even looking at the seed :-) etc. Once a
players does *any* of these actions Jelly would revert to never looking
ahead again (or not for a long time at least). Also, when looking
ahead, use the next roll "WOW LUCKY" hits "inferior move" only if it
differs very little from the "best move". Hey, you could always say the
neural net has a certain randomness built in which makes it possible if
someone asks :-).
I would be surprised to see someone has conducted a test where all the
rolls are recorded manually on an "untouched Jelly", then compared
against another PC. Heh, if one of the "off" functions would be a
player playing slowly enough to record all rolls... or the cheat comes
into effect after your first 200 games... endless possibilities
anyway...
Anyway, my point is that if you are devious enough you probably could
make something that would be one hell of a thing to prove as cheating.
After which we fall back into the best reason I've seen. Why the hell
would Jelly cheat? Unless I buy into beneficial sales (that might
backfire anyway) I don't think so.
And finally. The programmer(s) of Jelly have my upmost respect. I got
back into backgammon in a big way because of it. If there would have
been a new version in the pipeline I would have bought it but since
Jelly versions seem dead I got Snowie Student (and a few others really
crappy programs before that). And as far as rollouts are concerned $380
*IS* too expensive so I'm happy there are alternatives.
Eskimo
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Hi Steven,
first of all, what you are feeling is perfectly normal, everyone playing
backgammon has gone through this phase before. As you improve your game
more and more, you will learn to shift your attention from dice rolls
you get (or don't get) to the errors you make during play. I am aware
that this could imply that you are not as good as you maybe think, do
you have a FIBS rating?
Secondly, I would like to put the topic of alleged cheating into
perspective. I say "alleged" because this has never been proven and it
is solely based on our "feeling". Why do you think that programmers
have to resort to cheating to implement a strong backgammon program?
There are a large number of chess programs out there that give the best
chess players in the world a very strong competition, I never heard
anyone accuse a chess program of cheating though. Chess is a far more
complicated game to implement than backgammon which has much more of a
predictable nature to it which can be calculated. If people can create
strong chess bots then surely they can create strong backgammon bots
too. Obviously this is no proof that backgammon bots don't cheat and
this posting isn't meant to be a proof of anything, it should just put
cheating allegations into perspective - backgammon bots are simply
neural net computer programs that play strong backgammon, they are not
sophisticated reusable rockets that fly to the moon...
BTW, humans cheat too. If they didn't, do you think I'd EVER lose to
one of them?
If JF were to cheat - in ANY way - it would look "lucky" to a Snowie
analysis.
For example, splitting and slotting an opening 2-1 are close plays.
JF always splits. Suppose it were to 'look ahead." There are 15
rolls with a 4. Suppose it were to randomize, and slot 25% of the
time when a 4 is coming up and 20% otherwise. Slight advantage to JF.
But........
Let's say that someone decided to play 1000 25-point matches, analyze
them in Snowie, and add them to account manager. One of two things
would happen:
a) The cheating built into Snowie would be so slight and subtle that
it wouldn't show up statistically - but also - JF wouldn't get a
meaningful advantage.
b) The cheating would be statistically significant, and basically
impossible for the JF programmers to deny
I'll discuss reasons people think it cheats in another post soon.
JF has been around for donkey's years, and I can't remember one top player
complaining about it cheating :-)
Michael
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"Hank Youngerman" <red...@redtopbg.com> wrote in message
news:i48n4vsp4boq4b6kp...@4ax.com...
Jellyfish cheats only when it knows that it can. When it feels that
the human is catching on, it doesn't cheat so much. As you get
better and start to understand more on how it cheats, you will find
it only cheats occasionally. If you get really good, you can keep it
from cheating, but that takes years of studying the odds involved.
1/2 :-)
Jerry
Michael
"Jerry Donovan" <jerry....@hp.com> wrote in message
news:3e4bc56c$1...@usenet01.boi.hp.com...
When my daughter was playing Jellyfish on one of the lower levels,
it was cheating her left and right. But when I started watching (and
offering some advice), it didn't cheat as much.
The part I haven't figured out is why Jellyfish feels the need to cheat
11 year olds. It isn't like they are much of a threat to the program.
The Jellyfish programmers must be cold hearted.
Whether it is some neural net thingy, so some other technology,
I wouldn't know, but it is clever and devious.
Jerry
"Michael Crane" <michael.a.c...@ntlworld.com> wrote in message
news:hBP2a.1105$Cb.1...@newsfep1-win.server.ntli.net...
> often than it does when you manually roll dice for each turn, but not
> as much as when generating the rolls itself. I suspect Jellyfish is
> looking ahead when the random rolls list is loaded and can make
> optimal choices knowing what you have coming.
This is an illusion. In reality, Jellyfish makes good moves because it
considers not what it's *going* to roll, but instead *all* the
*possible* rolls for its next few turns and it averages the results from
the *possible* rolls. Jellyfish does this as part of its trained neural
network (i.e., its neural network is trained to know that certain
checker spacings are bad, like having your blot six away from your
opponent) and with its n-ply look ahead (which considers all of the
possible reasonable rolls and move combinations, making it a much
stronger tactical player). If you did this, looking at all the possible
rolls and all your opponent's possible and figure out which result in
good positions, you'd make good moves too. So it shouldn't be a suprise
that Jellyfish looks like it's lucky.
According to: http://jelly.effect.no/dice.htm ,
*
In our experience, many people who complain about Jellyfish's "luck" have
never had the experience of playing a truly strong opponent. Those who
play well appear lucky because they create positions where more of their
own rolls play well, while more of their opponent's rolls play badly. The
effect of this is that the strong player appears to roll better.*
> ===========
That's all well and good, however if you get some dice and put Jellyfish
in manual mode and roll the dice for each turn you will find that
Jellyfish doesn't play anywhere near the game it does on automatic. It's
vaunted neural network doesn't work nearly as well when it can't see
what rolls both you and it have coming up.
==========
By " anywhere near the game " I just mean it is much easier to beat or
at least not get whomped so bad you think you are playing blindfolded.
With manual dice rolls I saw many fewer instances of JF getting exactly
what it needed to hit open men. When allowed to generate the rolls
itself, JF hardly ever failed to hit any open man within 12 spaces, it
almost always comes up with just the right combination.
And the whole thing is just my subjective opinion. I didn't write
anything down. Just general observations and only based on a few games
maybe 20 or so.
Not statistically valid I know, but it seemed very apparent that things
were very very different when it wasn't allowed to roll it's own. Using
a list from an external generator was somewhere in between rolling it's
own and the human rolling the dice each turn.
It couldn't give itself exactly what it needed to hit your open men (
although it did as much as would be expected ) but it still could look
ahead and see what rolls were coming. Only the programmers, or people
capable of reverse engineering the program could ever tell us if JF can
look ahead or not. If it can, it should be reprogrammed to prevent it.
If it can't it's hard to understand the difference in play when you use
manual dice.
Doing multi-play evaluation is fine, but knowing what is coming is a bit
too much of an edge.
Then too, I've wondered about the neural net stuff. The program has
different levels of capability and I wonder how that is controlled. Is
the neural net given an exact number of megs of ram to work with at each
level or a percentage of available memory?
If a percentage it would explain why I see very little difference in JF
beween level 1 and level 5 or higher since I have over 700 megs of ram
available and if the neural net was designed to work with a computer
with 128 megs then giving it 700 would allow even the lowest level of
ability to be quite awesome because it would have more memory on the
lowest level of play on a high memory machine than the highest level of
play would have on a low memory machine.
Anyway just my opinions and wonderings .... YMMV.
Now, this kind of a roll has nothing to do with some deep analytical
analysis of a position where the machine is looking ahead 15 and a half
plies or whatever and making the best possible move. It is simply a
magic roll. And I don't remember it giving me this kind of a magic roll
even once during these matches.
Just my 2 cents worth.
Pete
PS Note that I am not even bringing up a game where gnubg was behind by
44 pips in a race against me, including two men on my six point, and it won.
"Pete" <m...@here.net> wrote in message
news:v4om499...@corp.supernews.com...
> Pete
>
> PS Note that I am not even bringing up a game where gnubg was behind by
> 44 pips in a race against me, including two men on my six point, and it
won.
Same thing happened to me. Only I had a closed board and the two checkers
were on the bar. My first bearoff roll was 6-4. I had two men on my 6 point,
took one off and moved the other to the 2 point. Then she rolled 6-6 and
proceeded to win leaving me with a single checker on my 1 point. She smiled.
I was flabbergasted and stood up to give my place to the next person on the
chouette team.
In another incident, at the start of a live tournament, I watched Player 1
toss 6-2 on the opening roll. He played the usual 24/18 13/11 move. Player 2
rolled 6-3, hitting on the 18 with the 6 and moving 24/21 with the 3. Player
1 then rolled 6-6 to dance. Player 2 then rolled a 4-1 and made the 20
point. Player 1 then rolled 6-6 again. Then player 2 rolled a 3-1 and made
his 5 point and Player 1 rolled 6-5 to dance again. Player 2 doubled, Player
1 dropped and they started the next game. I felt bad for Player 1, a World
Champion, and this certainly was a good sign of things to come. I turned
around walked over to the next table directly behind me and watched another
player, miles behind in a race, win by rolling 5-5 four times in a row.
The following sequence is from a live match that was recorded (text boards
should appear below, if you do not see them properly and you are using
Outlook, go up to the top of the program and click on "View" and from the
dropdown menu items choose "Test Size" and then go to the right dropdown and
click on "Fixed") :
-------------------------- Move 47 O -------------------------
O to play (2 1)
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
| O | | |
| O | | |
| | | | S
| | | | n
| | | | o
| |BAR| | w
| | O | | i
| | | | e
| X | | |
| X X X X X | | |
| X X X X X | | |
+24-23-22-21-20-19-------18-17-16-15-14-13-+
Pipcount X: 32 O: 29 X-O: 0-1/11 (2)
Men Off X: 4 O: 12
CubeValue: 2, X owns Cube
O: (2 1) Can't move
-------------------------- Move 48 X -------------------------
X to play (4 2)
+24-23-22-21-20-19-------18-17-16-15-14-13-+
| O | | |
| O | | |
| | | | S
| | | | n
| | | | o
| |BAR| | w
| | O | | i
| | | | e
| X | | |
| X X X X X | | |
| X X X X X | | |
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
Pipcount X: 32 O: 29 X-O: 0-1/11 (2)
Men Off X: 4 O: 12
CubeValue: 2, X owns Cube
48. X: (4 2) 4/off 2/off
-------------------------- Move 48 O -------------------------
O to play (4 1)
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
| O | | |
| O | | |
| | | | S
| | | | n
| | | | o
| |BAR| | w
| | O | | i
| | | | e
| | | |
| X X X X | | |
| X X X X X | | |
+24-23-22-21-20-19-------18-17-16-15-14-13-+
Pipcount X: 26 O: 29 X-O: 0-1/11 (2)
Men Off X: 6 O: 12
CubeValue: 2, X owns Cube
O: (4 1) bar/21* 2/1
-------------------------- Move 49 X -------------------------
X to play (1 1)
+24-23-22-21-20-19-------18-17-16-15-14-13-+
| O O | | |
| | | |
| | | | S
| | | | n
| | X | | o
| |BAR| | w
| | | | i
| | | | e
| | | |
| X X X X | | |
| X X X O X | | |
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
Pipcount X: 47 O: 24 X-O: 0-1/11 (2)
Men Off X: 6 O: 12
CubeValue: 2, X owns Cube
49. X: (1 1) bar/24*/23* 5/4*(2)
!Alert! Joker (0.886)
-------------------------- Move 49 O -------------------------
O to play (4 3)
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
| X | | |
| | | |
| | | | S
| | | | n
| | | | o
| |BAR| | w
| | O | | i
| | O | | e
| | O | |
| X X X X | | |
| X X X X | | |
+24-23-22-21-20-19-------18-17-16-15-14-13-+
Pipcount X: 43 O: 75 X-O: 0-1/11 (2)
Men Off X: 6 O: 12
CubeValue: 2, X owns Cube
O: (4 3) Can't move
-------------------------- Move 50 X -------------------------
X on roll, cube action
+24-23-22-21-20-19-------18-17-16-15-14-13-+
| X | | |
| | | |
| | | | S
| | | | n
| | | | o
| |BAR| | w
| | O | | i
| | O | | e
| | O | |
| X X X X | | |
| X X X X | | |
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
Pipcount X: 43 O: 75 X-O: 0-1/11 (2)
Men Off X: 6 O: 12
CubeValue: 2, X owns Cube
50. X: Double
O: Pass
---------------------------------------------------------------------------
So there you have some examples of some very lucky and unlucky moments in
real life backgammon. If they did not happen when you play against a bot
like Snowie, JellyFish or GNU, then I would say whatever you are playing
with these bots is not the game of a backgammon. Luck is an element of the
game and part of what makes it so fascinating. We all have streaks of good
and bad luck, some say a bad streak can last for months, even years, so be
prepared, your luck might not change tomorrow but then again, you never
know.
Michael
Michael
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"az-willie" <scl...@npole.com> wrote in message
news:TaW2a.845$zL6...@news2.central.cox.net...
I have a worthy anecdote too. A true story. In my very first stakes
game ever online (at Gamesgrid) I opened with a simple 32 split (24/21
and 13/11), my opponent rolled 42 and pointed on my head. I danced
with a 64, he doubled, I took, and I never played another move until I
was solidly gammoned. He didn't even cover his board all that fast
either. It took him 3 more rolls to make another point in his board,
but I obligingly rolled 64 three consecutive times and a 66 to boot. I
finally got in when he had already borne off half his checkers. I'll
never forget it.
Albert
Live tournament (crawford game, so no cube action):
I need 5 4 from the bar to get in on the 5 and hit the only open blot in the
outfield. I got it! BUT
He needed a 2 6 from the bar to hit my man. He got it! BUT
Later I needed a 5-5 from the bar to hit him again. I got it! BUT
Later he needed a 5 3 from the bar to hit my last blot in the outfield. He
got it! BUT
That wasn't enough for him to win the game. He got that last man in and
started bearing off. BUT
I rolled 5 5, 6 6 and 5 5 to catch up. And eventually won.
________________
"Albert Silver" <silver...@hotmail.com> wrote in message
news:f9846eb9.0302...@posting.google.com...
On the basis of your deep analysis, we will send the Bot Police to arrest
the GNUBG programmers. However, we will need all the records you kept of the
games in order that we may confirm your analysis. Now, was it six times GNU
cheated with 44 or was it twelve times? Perhaps some number in between? Are
you positive you aren't simply remembering only the times you lost badly or
suspiciously and forgetting the good games you had? We assume also, of
course, that you have played several thousand games in the period you
mention so that the statistics you will provide will be meaningful. You have
played several thousand games against GNUBG, haven't you? As soon as you
provide the evidence and it is confirmed by our crack statistical squad,
we'll break into the strongholds of those vicious, conspiring GNU
programmers in New Zealand, Norway, Sweden, Denmark, and wherever else they
are hiding their cheating, cowardly butts, and we will arrest them and throw
them into deep dungeons where, until their trial when the bot wars are over
sometime in the future, they will have to play Jellyfish, which we all know
cheats without shame.
For a more rational discussion of these matters, please examine all the
posts of our favorite troll, Murat K. He will no doubt enlighten you with
his calm, rational, intelligent, and reasonable approach. Perhaps someday
you could become a protégé of his and further enlighten us on all matters
pertaining to cheating bots.
Happy Valentine's Day! ;-)
Ric
"Pete" <m...@here.net> wrote in message
news:v4om499...@corp.supernews.com...
Dear Ric,
Thanks for the Valentine's Day greetings -- from you and the others you
represent as "we, we, we...". I did not realize you were the appointed
lead poobah of the Defenders of the Faith of the GnuBG Anti-Defamation
League.
On a lighter note, no I do not keep accurate statistics of my play
against the bots. I don't even keep inaccurate ones. I make mental
notes. I am simply a reporter of facts as I see them. If your experience
is different, fine, so be it.
Let me just tell you that I have played probably 300 matches (normally
to 11) against gnubg in the past few monts. Between 1974 and 1982 I
played thousands of money games in clubs in Michigan, Illinois, Ohio,
California, and Nevada. The sheer number of great rolls that gnubg comes
up with in precisely the situation I described in my initial post is
close to mind-boggling.
I don't know who this Murat character is. I have read several of his
posts and I consider him to be either a lunatic or someone who just
likes to yank the chain of this newsgroup.
Yours truly,
Pete
Ric
"Pete" <m...@here.net> wrote in message
news:v4qblu7...@corp.supernews.com...
Not according to my brand new EE CUMMINGS spell checker. :)
>It couldn't give itself exactly what it needed to hit your open men (
>although it did as much as would be expected ) but it still could look
>ahead and see what rolls were coming.
>>
>>
You're wrong....you can check it out yourself....
-jot down the rolls and moves of a game starting on a certain
seed/counter number on a piece op paper
-start a new game while entering the same rolls manually and make
exactly the same moves as you did the first time
You will see that JF will always answer your moves in exactly the same
way.
You can try this out as many times as you want..the result will always
be the same, that is, at the same play level.
1) About two months ago, I discovered Motif backgammon on the Internet
(before I knew about gnubg, JF, snowie, etc). I got soundly trounced
every time I played it, and was sure it was cheating because of it's
ability to roll doubles for itself, especially when it needed them. So
I kept a log of all the doubles rolled by both sides in 50 games -- I
rolled more than Motif did!
2) Since then, I've downloaded gnubg, and play it mostly in tutor
mode. What floored me are the open gnubg blots that I could hit with my
rolls, but don't see, until the tutor points them out. So maybe the
problem isn't so much that gnubg amazingly hits your blots, but that you
don't see all of his that could be hit.
Billie
PS. I can now play Motif nearly even, so even if gnubg cheats, it's
helping MY game!
I agree completely that Jellyfish, et al, do not cheat. But one question.
How in the world COULD a chess robot cheat??
Gregg C.
Hi Gregg,
I think you misunderstood my point or I didn't express myself properly.
A chess bot does NOT cheat, that was my point. Nobody complains about
chess bots cheating (and how could they?) and chess is much more
difficult to implement than backgammon so if it is possible to program
world class chess bots then why shouldn't it be possible to program
world class backgammon bots? I just wanted to make the point clear that
backgammon bots are no world wonders and having to resort to cheating to
play well is not necessary. I hope I was clearer now ;-)
Regards
Scott