Gnubg: reading dice rolls from text file
Scott Steiner
since there are continous discussions going on about gnubg's dice rolls,
I wanted to ask if there are any plans to build an option that reads
dice rolls from a text file like in Jellyfish. I think this is a good
and relatively easy option to implement and it should convince the
skeptics finally that dice rolls are not manipulated, or? Comments any
one?
Jim Segrave
You can select your rolls from the generator supplied by
www.random.org. That's as independant of the gnubg code as one could
want. You can use manually supplied rolls. What's the point in wasting
programmer's time on those who simply find it easier to believe that the
software cheats somehow, instead of accepting that it probably plays
backgammon better than them? It makes as much sense as arguing about
the earth being flat or whether man has walked on the moon.
--
--
Jim Segrave j...@jes-2.demon.nl
Jørn Thyssen
gnubg cheats in two ways: (1) by rolling incredible good dice for itself
and extremely bad dice for the human opponent; and, (2) by "looking"
ahead in the dice sequence, and choosing it's moves based on the
knowledge of future rolls.
By using a file you'll only rule out (1). gnubg will still cheat by
looking ahead.
The only true way to avoid gnubg's cheating is by using the manual dice
option.
Also, several places in the gnubg code there is code like:
if( RollDice ( ms.anDice, rngCurrent ) < 0 )
return -1;
Although RollDice /appears/ to be defined in dice.c it's really a macro
that evaluates to:
( ap[ fMove ].pt == PLAYER_HUMAN && gnubgIsF*****() ) ?
RollAntiJoker ( ms.anDice, rngCurrent ) :
( ap[ fMove ].pt == PLAYER_GNU && gnubgIsF*****() ) ?
RollJoker ( ms.anDice, rngCurrent ) :
RollNormalDice ( ms.anDice, rngCurrent );
I hope this clarifies things!
Jørn
jason.darling
Not once when shut out has it rolled a set of 7's from the bar.
I've never seen it slip off extra checkers during bearoff either.
And it only ever moves 4 times the number on a double, not 5.
And you know what? I've never seen it place a die carefully in a cup, hold
it there with a finger, distract my attention and then let them slip out the
cup after i've heard the reasurring rattle.
By human standards this thing is a f*** saint so who are we to judge it? :-)
Frank Berger
The scepticals will argue, that the bot will look at the next rolls
and so avoid jokers and so on......
They don't want believe it that the bots are stronger. On the
jellyfish side are two tests, to check whether the bots cheat. Or they
could use manual dice? They could look at the source of GNU? Nothing
helps to stop that complaints,
I believe that stupid "xyz cheats" will stay forever.
ciao
frank
Scott Steiner
Hi Joern,
I hope you didn't understand me wrongly - I wasn't implying that gnubg
is cheating, I never did and I never will because I think such
accusations are ridiculous to be honest. I'm a big fan of gnubg, I
think it's great and actually I had hoped that this was evident
considering my continuous positive postings in this newsgroup over the
past months that I've been here.
The reason I asked about dice rolls from a text file is because I'm sick
myself of always coming across posts that accuse gnubg, or any other
respectable bot for this reason, of cheating. I thought that such
skeptics don't bother to use manual dice because it's bothersome and
distrubs flow of play when you always have to roll the dice and sway to
the computer back and forth. That's why I thought maybe a text file
would be an alternative that quiets the skeptics down. But after
reading your post I noticed that not even the text file is a solution
because of the alleged 'lookahead' feature of gnubg that you so
humourously described, a 'feature' that I didn't even think of which
actually shows again that I'm not one of those skeptics because if I
were then I probably would have thought of it. So in conclusion I
actually now do see that the only solution is the manual dice option,
which kind of startles me though that skeptics still accuse gnubg of
cheating since that surely should clear things up.
Well, I hope I could clear things up now ;-). Please let me say again
that I think gnubg is a great software and I'm certainly _not_ one of
those people who accuse it of cheating. Such accusations have no
grounds IMO. Thanks for your effort and that of your colleagues for
supplying the backgammon community with this outstanding software! I am
confident that I can speak not only for myself but for many others
regarding my gratitude and appreciation.
thx!
Pete
Preamble:
I believe that Lee Harvey Oswald killed John Kennedy. I don't believe that
there is a Tripartite Commission secretly running the world. Etc, etc, etc.
HOWEVER, every time I play gnubg (it seems), it comes up with
near-miraculous rolls. It may very well play at a world-class-plus-plus
level. It, however, also has a world-class wrist. Because I am not talking
about "choosing the min-max best move 10 rolls down the line". I am talking
about the number of times it hits a 17-1 shot to turn a game around, just as
one example. Or the number of pure races it wins. Or the number of times I
roll a 2-1 or 3-1 trying to get off a gammon. IOW, these are cut-and-dry
positions and situations that require no Deep Blue-type analysis.
I wish I had the time to play out a match to some significant length with
manual dice, but I don't, right now. As I said, I have no problem with the
program in terms of its analysis powers - they are great. But I just shake
my head at some of the numbers it comes up with at crucial times. As I have
said in a previous post, if a human opponent were to have come up with some
of these rolls as consistently as gnubg does, I would simply refuse to play
the opponent at the earliest opportunity.
To reiterate: I am not accusing the program of cheating. I don't know what
is going on. I do know what I do see, however.
Thanks,
Pete
jthyssen
> To reiterate: I am not accusing the program of cheating. I don't know what
> is going on. I do know what I do see, however.
I'm a bit confused: you not accusing gnubg of cheating but you think
it gets dice above average!?
What can I do to convince you that gnubg does cheat?
Jørn
Larrikin
Hi Jørn,
Re: PROGRAMMING IDEA INSTEAD OF MANUAL DICE
Personally, I have never thought that any of the Bots cheat in any way
and therefore I would never actually use what might be termed the
"change dice" programming option I propose here.
My idea is to not have one dice text file but several, perhaps 5 or
more, files which store (say) 1000 rolls each in them. A paranoid user
can simply toggle between the 5 pre-determined dice text files anytime
he wants to, as he sees fit. The Bot can hardly be accused of looking
ahead at the dice rolls when the user may have selected any of the
dice files quite at random.
A couple of silly examples on how it might work:
1) Cheating_Scumbag_Bot has broken contact and is making a race of it.
It's 25 pips down and must see sets of 5's and 6's coming up for it
and 1-2's for me. No way, I'm "changing dice" to stop that nonsense!
2) Cheating_Scumbag_Bot has hit me with 2 open blot's in it's home
board. It must see double 6's, 4's or 6-4 as my next roll to keep me
on the bar. I'll upset that little plot, I'm "changing dice"!
I am not a programmer but I don't think it would be very hard to set
this up. The "change dice" UI could probably be a simple keypad
arrangement which would display close to the board and be clicked on
just before or just after you've rolled.
Jørn, I'm sure you have better things to do with your programming
time than worry about a few paranoid "dice cheat" uers but maybe one
of the GNUBG development volunteers might like to think about it
for some future update? Is it viable?
Regardless of this, keep up the good work on GNUBG :)
Ian Dunstan.
Albert Silver
Hi Pete,
Here are a few cut-and-paste posts from the past. I have reduced them
to the minimum so as to not make this reply longer than necessary.
They were obtained from the wonderful RGB archive kept at the
Backgammon Galore! site at http://www.bkgm.com
It's just so you know you're not alone by one iota in your complaint.
Whenever you see a (...) it is some editing I did to shorten the
original.
Albert Silver
----------------------------------------------------------
Does TD-Gammon Cheat?
=========================================================================
Date: 29 JAN 97 07:52:06 CST
Subject: re: TD-Gammon
To: Gerry Tesauro
Thank you for the reply. Although I have only played one game (in
Grandmaster mode) with the new program, I would like to relate the
following incident to you, (...) I rolled 6,2 and the program followed
with 2,2. I think the odds of that happening are almost 60-1,
certainly not in the realm of the impossible, but even after only one
game, it is a little suspicious.
Thanks for the fine work, and if I'm convinced my luck is no good
after several weeks, I am going to attempt to document my 'bad luck'
with some statistical proof, which I will forward to you.
Thanks again,
Doug Metcalf
=========================================================================
Date: 30 JAN 97 06:53:37 CST
Subject: re: TD-Gammon
To: Gerry Tesauro
Mr. Tesauro,
My apologies. TD-Gammon wins even if it lets me roll the dice! The
manual
entry convinced me! Of course, now I'm wondering why I play so badly.
(...)Thanks, and once again, my sincere apologies sorry for doubting
your
program's integrity.
Doug Metcalf
------------------------------------------------
Does David's Backgammon Cheat?
Date: 17 Jun 98
Subject: Davids Backgammon
I would appreciate anyones thoughts on Davids Backgammon from
Wingammon.
I have had several discussions with the Author who states that the
dice
are random, but I find that hard to believe. It will keep me on the
back
for 4 to 5 throws with 4 points open. I will have 5 points blocked and
he will enter in 1 maybe 2 throws. Consistantly every blot of mine is
taken while his blots are rarely taken. (...)
-------------------------------------------------
Does Gammontool cheat?
Date: 24 Sep 91
Subject: Computer cheats, was - Information on gammontool.
> One of my friends claims that [gammontool] cheats ...
I always felt it cheated, but I have access to the source code and
it has no bias to the side rolling. (...)
I have another computer gammon game and the instructions state that
many
people feel it cheats, but that it uses a very good randomizer, so
don't blame it!
--
Jim Hurley --> ji...@ultra.com ...!ames!ultra!jimh (408) 922-0100
Ultra Network Technologies / 101 Daggett Drive / San Jose CA 95134
---------------------------------------------------
Does Hyper-Gammon cheat? (a program specialized in the BG variant
Hypergammon)
Date: 29 Jun 96
Subject: Re: Can't trust computer Bg
(...) I have this game
> called Hyper-Gammon, a backgammon derivative in which one plays 3 pieces
> against the opponent's three. Its a CD game, and the author purports to
> have hooked up his PC for two years to solve every single possible position
> involved with three backgammon pieces. 32 million positions he claims his
> computer solved, and there is this massive 172 megabyte data file on the
> CD, yet the damn thing still cheats!! For some odd reason, the only
> doubles it has ever rolled were double-6's.
-------------------------------------------------------
Does Jellyfish cheat? (I left this as is, since the post is perfect
in its clarity and conciseness)
Date: 6 Jun 97
Subject: Re: Deleted Jellyfish
> While I do not consider myself an AUTHORITY on backgammon, I do know enough
> to finally have had enough with this program.
>
> I put up with some really strange and off the wall wins. Sometimes only
> occuring after hitting some really very hard combinations. Now, I now that
> it does happen in real life, but on a consistent basis!?
>
> I got really curious after somebody had mentioned on this newsgroup on how
> jellyfish behaves after doubling or being doubled, because I noticed the
> same thing. Over a three day period I played probably over a hundred games
> on the hardest level and doubling every single time. JF3 won every single
> one of them.
>
> Enough said.
I guess I'm repeating myself, but you can PROVE to yourself that it
doesn't cheat with the dice. The two numbers SEED and COUNTER
(settings
menu) defines the state of the dice generator. If you like, you can
write down these number before starting the game. Before starting the
next game, do 'Swap sides' and reset SEED and COUNTER. You will then
see
that you get the same sequence of rolls with you getting JFs dice and
vice versa. Swapping sides is done to make the other player win the
opening roll, otherwise you'll get the same sequence exactly. It does
not take a lot of work to see that the dice rolls are independant of
who
is rolling, what the score is, what the position looks like etc.
When you start the program, it uses the system time of you pc to set
the
seed, while the counter is zero.
--
Fredrik Dahl
(Author of Jellyfish)
-------------------------------------------
Does MVP Backgammon cheat?
Date: 28 Oct 96
Subject: Re: MVP Backgammon question
Armin wrote:
> I bought a copy of a shareware game called MVP Backgammon and I'm
> wondering if anyone has had any experience with it.
> It seems to me that the rolls are not very random.
Art Buell wrote:
> I bought the same program, and I certainly agree. I know the tendency
> is to subjectively blame the dice, especially with computer programs, but
> I'm convinced that MVP is definitely biased in its rolls. (...) I'm ready to give up on this program.
Hi, Art. I'm the author of MVP Backgammon, and I'd like to respond to
your
points. I'll take the rolls issue first.
(...) it is _flatly impossible_ for my program to bias its rolls in
favor of the computer. (...)
I'd like to make it perfectly clear: the AI in MVP Backgammon does not
cheat; it has no invisible advantages over the human player, (...)
Thanks for your thoughts.
Mark Betz
(Author of MVP Backgammon)
------------------------------------------
Does Motif cheat? (Detecting a pattern by now?)
Date: 12 Oct 96
Subject: Re: motif
> I once read this newsgroup in search of an on-line backgammon game to
> play and read someone's posting about a rigged game that always seemed
> to roll the right roll, defying all odds, the game being the "motif"
> listing. And of course assuming that the posting person was not as
> good as I, I accepted the challenge and went there to play. He was
> right. It is rigged BIG TIME. Am through with it.
No. I truly doubt that Tom Keith, the programmer of
http://www.bkgm.com/motif.html
has any motivation to have Motif cheat. I have not
ever noticed anything out of the ordinary. The disasterous
and opportunistic rolls seem to occur at random for both
players. It just plays some parts of the game very well,
arranging its checkers to take best advantage of future rolls.
(...)
--
Robert D. Johnson (rjohnson) rjoh...@cvbnet.cv.com
http://www.cv.com/
Pete
It's not possible to prove a negative, J, so don't set yourself up for an
impossible goal. My gut feeling is that you and your group are honest, and
that you have created a very strong engine (thoug the user interface needs
work). Of course, as UNIX-based programmers, you would think that's
secondary :).
In the poker newsgroups people complain all the time about their opponents
"rivering" them. IOW, coming up with a very improbable joker to win. The
general consolation is that THEY river you because more often THEY are in a
long-shot position; YOU on the other hand, being the better player, are
generally the favorite, and therefore, YOU tend to river THEM less often.
This analogy should work here also. Since gnubg is the stronger player than
me, it is I who should be rivering it. Instead, way, way too often it is
gnubg rivering me, as I have noted before. I mean it is tough enough to get
this beast to accept my doubles when it has a potential backgame, but I know
it has gotten more jokers than it should.
Douglas Zare
Pete wrote:
> > What can I do to convince you that gnubg does [not] cheat?
>
> It's not possible to prove a negative, J, so don't set yourself up for an
> impossible goal. My gut feeling is that you and your group are honest,
Great. Do you realize that your accusations of cheating are insulting?
You are not a strong player. (Your posts have demonstrated this.) You are in no
position to judge what is normal when you play one of the strongest players in
the world. You are making the same tired allegation that has been made against
every single backgammon program (and server) I've ever heard of, and which will
be made against future ones. Do you think that _all_ of them cheat, that _all_
of them have failed to implement a decent random number generator or make use of
hidden information? Well, if not, then people are quite capable of saying that
honest programs cheat. If you have intellectual integrity, you will be convinced
that you are wrong, but next month another basement player will be whining in
your place, just as others were before you.
That it is tough to prove that even an open source program like gnubg never
cheats does not mean that your allegations cannot be refuted. Carefully state
your patterns and test them. Suppose you think you can predict that some joker
in certain situations is only 10:1 rather than 17:1. If you honestly believe
that, offer to bet as though the odds were 15:1. You will find many people
willing to bet against you. If you don't believe enough to bet, then you don't
believe the accusations enough to publicize them. If you actually find that
certain random number generators used by gnu produce humanly detectable
patterns, it would be shocking to those familiar with random number generators.
It would be the most noteworthy discovery of the year in that part of computer
science.
Douglas Zare
s.w.a....@hccnet.nl
Jørn wrote:
>What can I do to convince you that gnubg does (not) cheat?
>>
>>
Easy....implement a genuine cheat mode as extra accesoire in the next
version....that will show them all how much they will lose against a
top of the shelf bot that really cheats.....
I for one would love to play it, I'm a masochist.....:-)
p
Gus
The psychology is interesting. It is quite difficult, psychologically, to
be objective when it comes to looking at luck. When I get the 6-6 5-5 to
win, it isn't luck, but a recovery or evening out of the bad luck I
suffered earlier in the game -- I deserved it. And, of course, I know I
didn't cheat and control the dice. On the other hand when my opponent gets
6-6 5-5 to win, he must be controlling the dice in some way.
It doesn't matter whether one plays against a program or a live opponent.
You can't imagine how often my opponents have demanded to check my dice in
live tournaments. I have had my opponent growl at me that I am not rolling
the dice properly -- they don't roll enough but drop out of the cup and
land flat. I am apparently too lucky. (One way I get around this is to
have them roll for both of us. Much to their chagrin they roll jokers for
me!)
When I play on FIBS, zone.com, VOG, Gamesgrid, and so on, I have been
accused of having a program that controls the dice. I am apparently too
lucky.
Actually, there was a way (bug now fixed) on VOG where you could preview
the upcoming dice. OOOPS! But this was a mis-design by the programmers
that they fixed when detected. The programmers made a mistake, but it was
the players who found a way to find the upcoming sequence of dice who
cheated.
To those who are firmly convinced that a given program cheats: GET OVER
IT! The programmers of those games have absolutely no motivation to
provide other than truly random dice.
Regards...
"Albert Silver" <silver...@hotmail.com> wrote in message
news:f9846eb9.02120...@posting.google.com...
Zorba
Actually I think this is a GREAT idea! Maybe it'd be a nice challenge
for some puzzlers/programmers to try and create a cheating bot, where
the cheating is hard to identify, let alone prove! This cheating bot
would win very often though, and look like an extra-extra-terrestrial
player just based on the results of games and matches.
Setting the bot to manual dice would stop the cheating (assuming one
enters 'random' dice of course!), unless someone can come up with a
way to still cheat in those occasions!
--
_
/
_ orba (who wonders what kind of rating such a bot could achieve!)
s.w.a....@hccnet.nl
zo...@chello.nl (Zorba) wrote:
Maybe it'd be a nice challenge
>for some puzzlers/programmers to try and create a cheating bot, where
>the cheating is hard to identify, let alone prove! This cheating bot
>would win very often though, and look like an extra-extra-terrestrial
>player just based on the results of games and matches.
>>
>>
That is not exactly what I had in mind. Why should it operate in a
covert way ? Doesn't make sense. I have followed the discussion here
lately, read the older messages on the archive website, and it seems
to be an ungoing problem. And it does not make any sense. I have
played half a dozen shareware and freeware bots the last couple of
months on a daily basis, and I don't think that they 'cheat'. I admit
that I thought so the first couple of days I played Jellyfish, and the
same goes for GNU. But I found that if you really do some serious
testing there is no truth in it,. The bots have lucky rolls, sure, but
so has the human player. Both Jellyfish and GNU are extremely
difficult to beat for an average player, and probably more so when
their roots go back to 1970's 'dark ages' game strategies. Personally
I think the 'cheat' discussions are boring. As has been explained here
recently, it is extremely difficult to prove that a bot does not
cheat. So, to look at it from a slightly different angle, why not
include a 'cheat' mode in GNU as an extra ? GNU already has the name
to cheat in certain circles. It is a no lose position for the
developers...the people who do not believe that it cheats now won't
change their mind, but there is a slight chance that some of the
'believers' are converted.
What I had in mind is thus more a demonstration tool, a gimmick. You
could probably implement several levels, like a Murat level with a
target of 60% win average (for beginners :-) ), a Hardcore level with
a target of 80% win average, and a Mission Impossible level with a
target of 100% win average.
Although I am not a programmer, nor good at math, or even very good at
bg.....in regards to the highest cheat level possible, I estimate
that a bot with the playing strength of a Jellyfish or a GNU, one that
looks ahead 1 or 2 ply, and fiddles with the rolls all the time, must
be able to score -very- close to 100% against any human player....or
any 'honest' bot for that matter.
P.
Volsano
>HOWEVER, every time I play
> gnubg (it seems), it comes
> up with near-miraculous rolls.
I'm willing to believe that the bots have better dice than I do for a very
simple reason -- they are better players and get into better positions.
Look at it this way. Maybe typically when I am on roll, I have:
* 1 really good number
* 10 good numbers
* 10 indifferent numbers
* 12 bad numbers
* 3 really bad numbers
So on an average roll I am going to throw below average.
My bot opponent typically has a different set of numbers -- make some up
yourself --and they are going to be weighted towards better numbers. The bot
will on average throw above average.
What would be interesting -- and maybe telling -- would be a post-match
analysis that shows the joker-potential of each player.
If the bot has (on average as always) 2.5 joker numbers on each roll, and I
only have 2.0 then then it will produce more miraculous rolls without having to
have a miracle happen.
Colin
Zorba
> zo...@chello.nl (Zorba) wrote:
>
> >Maybe it'd be a nice challenge
> >for some puzzlers/programmers to try and create a cheating bot, where
> >the cheating is hard to identify, let alone prove! This cheating bot
> >would win very often though, and look like an extra-extra-terrestrial
> >player just based on the results of games and matches.
>
> That is not exactly what I had in mind. Why should it operate in a
Just to be clear: I don't mean GNUBG should cheat without telling the
user; I just meant that it might be a nice idea that IF and WHEN the
user activates this cheat mode, the actual cheating is somewhat
sophisticated, so that it would be hard to prove the bot actually
cheats in this mode. This mnight be even more impressive I think, and
certainly more frustrating (a cheat mode that just rolls repeated
6-6's and 2-1's for you to win any race seems pretty boring).
Peter Schneider
> I'm willing to believe that the bots
> have better dice than I do for a very
> simple reason -- they are better
> players and get into better positions.
>
> Look at it this way. Maybe typically when I am on roll, I have:
> * 1 really good number
> * 10 good numbers
> * 10 indifferent numbers
> * 12 bad numbers
> * 3 really bad numbers
>
> So on an average roll I am going to throw below average.
>
Hmmm... as I have said in another thread, I think that this kind of
reasoning is not correct. The crucial point is the definition of "[really]
good number". The term "joker" as used by the bots is defined as a roll
which gives you (when you move correctly) an equity gain of x millipoints
*above average* equity of all rolls. (x is 500 in the Snowie defaults). In
other words, a "joker" is *relative* to your position and the other possible
rolls.
Even if the bot plays well and blocks many good rolls, this just decreases
the equity of your position; interestingly, the average number of jokers is
not affected! As a result of the bots good play, some rolls which would have
been only average in a better position may now become jokers. You may even
have *more* jokers because your equity *de*creases!
As a trivial example, let's consider a late dmp bear-off, your turn. The bot
has born off properly and needs only 1 more move, while a bad player would
have mis-played it and thus would need 2. You need 2 moves as well, or a
double roll; now, because of the bots proper play, all your double rolls
(suddenly your only chance to win) turn into huge jokers, while they would
have been only just nice against the bad player (you'd win 5/6 of all games
without one anyway).
It is important to realize that your equity in a given position already
incorporates the impact of all the possible rolls. Therefore, on average,
even very bad players have as many potential jokers as anti-jokers when they
are rolling; but those jokers may then just save them from losing gammon
;-).
Regards,
Peter aka the juggler
s.w.a....@hccnet.nl
Zorba wrote:
I just meant that it might be a nice idea that IF and WHEN the
>user activates this cheat mode, the actual cheating is somewhat
>sophisticated, so that it would be hard to prove the bot actually
>cheats in this mode. This mnight be even more impressive I think, and
>certainly more frustrating (a cheat mode that just rolls repeated
>6-6's and 2-1's for you to win any race seems pretty boring).
>>
>>
taste...:-)
p.
Pete
Allow me to add my two cents to this discussion. You seem to be
concentrating on looking at jokers at any point in a game or a match, to
measure the general equity increase of a given dice roll. I prefer to
concentrate on the key situation in a game, such as bearing off, hitting a
shot in a backgame, etc.
By way of an analogy, go to rec.gambling.poker. There, people are constantly
complaining about how somebody drew out on them, i.e. hitting a long shot
card on the river, aka "getting rivered". The normal response to these
complaints is to say that, look, the patzer is more likely to get into a
long-shot situation than the "good" player, and logically, theredore, the
patzer will draw out more often than the good player.
By extension, my position is that since gnubg is the better player, gnubg
should be drawing out on a player less often than the converse. However, in
my experience, this is clearly not true, in fact, the very opposite seems to
be the case.
Your example of a late bearing-off situation highlights my point. gnubg has
played better than the user and has gotten into a single-roll situation. The
user has not played optimally and he needs a double to win. In this case, as
well as most cases, it is the user who should be rolling more jokers since
he generally will be in the underdog position.
Do you believe that you get a). more jokers, b). the same number of jokers,
c). less jokers than gnubg in the crucial situations?
Pete
Peter Schneider
> You seem to be
> concentrating on looking at jokers
> at any point in a game or a match, to
> measure the general equity increase
> of a given dice roll. I prefer to
> concentrate on the key situation in
> a game, such as bearing off, hitting a
> shot in a backgame, etc.
That would, if I understand correctly, be reflected by changes in cumulated
match equity. I would believe that it is not dependent on a player's skill
either.
> Your example of a late bearing-off situation
> highlights my point. gnubg has
> played better than the user and
> has gotten into a single-roll situation. The
> user has not played optimally and he
> needs a double to win. In this case
Yes...
> , as
> well as most cases,
No ;-) ...
> it is the user who should be rolling more jokers since
> he generally will be in the underdog position.
Oh my. This was a (counter-)example for Volsano, not a general rule. I tried
to explain carefully my point why both parties should in average roll the
same amount of jokers.
> Do you believe that you get a). more jokers, b). the same number of
jokers,
> c). less jokers than gnubg in the crucial situations?
Also in crucial situations, I believe b. These "crucial situations" may just
more often be gammon-saves for the bad players than for gnubg.