Gammonfever BG Quiz - Position #18
Micke Nilsson
X doubles. Take or drop for O?
Money session. Score X-O: 0-0
X on roll, cube action
+24-23-22-21-20-19-------18-17-16-15-14-13-+
| X O O | | O O X X |
| O O | | O O X |
| O | | X | S
| | | X | n
| | | | o
| |BAR| | w
| | O | | i
| | | O | e
| X | | O |
| X X X X | | O |
| O X X X X | | O |
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
Pipcount X: 131 O: 159 X-O: 0-0/Money (1)
CubeValue: 1
paulde...@att.net
It's more difficult for X to extract X's back man than for 0 to enter.
X has a marked lack of builders to attack the 1 point or fill in the 3
point. With only 2 blots, X's gammon equity is not so huge, and 0's
prime-building threats against X's man on the 24 point are quite
serious.
Passing would be a huge blunder. If you shift X's 24 man to the 21
point, then Robertie's 501 Essential... has a position similar to this
modified position. Of course, the modified position is much better for
X than the given position. However, even the modified position is
close to a take (and possibly a take).
Paul Epstein
Philippe Michel
Pass. O's prime looks pretty, but it is simply not enough.
O rolls first and can use all of his roll ; X will pass his turn half of
the time and have only one "free" dice the other half, so X will somehow
work towards improving his prime 4 times faster than O on the next roll,
and possibly on the following ones.
When it comes to escaping, X better board is a huge advantage. When X
steps up to the 21pt, what is O going to do ? Hitting loose in a 2pt vs.
4pt board is a good way to lose a gammon ; not hitting is a sure way to
lose the game. O's position would be much better if its prime were 1 pip
more advanced, from the 4pt to the 7.
paulde...@att.net
position that is incredibly biased towards X.
"When X steps up to the 21 point.." Yes, but X may need time to do
that. X does this with 7/18 probability at most, perhaps less because
21 is duplicated for safetying the 15 blot and 11 has other uses. Even
when X gets to the 21 point, X can fail to jump for 1 or 2 rolls.
There is further duplication in that the 3 is also often useful to fill
in X's three point by 6/3 or to hit 0 loose if 0 enters on the 3 point.
When X steps up to the 21 point, 0 should hit loose, and be in an
excellent position to make a 5 point prime. "A good way to lose the
gammon". That's a bit vague but 0 doesn't lose a gammon very often
even in the most extreme scenario Philippe outlines.
Yes, 0's position would be better with a more advanced prime but, as it
stands, 0 has an excellent take.
All previous postings by Philippe have been excellent. Even when his
suggested play has not been optimal, he has shown real insight and made
instructive comments.
On the other hand, many of my postings have been wildly wrong. But I
don't apologise so much because, hopefully, my misconceptions had
instructive elements.
Anyway, despite Philippe's previous good form, this is an extraordinary
blunder by him. I haven't seen the bot analysis of course, but I
really will be completely amazed if passing is not a blunder.
Paul Epstein
Raccoon
Philippe Michel wrote:
> Pass. O's prime looks pretty, but it is simply not enough.
Sounds good. O may get lucky and hit something in the outfield, but
otherwise he needs to anchor to avoid a gammon, or anchor to play a
so-so acepoint or 22-point game. And X with a 28 pip race lead doesn't
have to do anything fancy to win this game.
David C. Ullrich
wrote:
>And now the final position...
>
>X doubles. Take or drop for O?
I'd tend to suspect O should drop, although
it doesn't look all that clear to me.
Like maybe X brings a few men down, then if O
comes in it seems like O's a little behind, if
O bounces he's in big trouble.
> Money session. Score X-O: 0-0
>
> X on roll, cube action
> +24-23-22-21-20-19-------18-17-16-15-14-13-+
> | X O O | | O O X X |
> | O O | | O O X |
> | O | | X | S
> | | | X | n
> | | | | o
> | |BAR| | w
> | | O | | i
> | | | O | e
> | X | | O |
> | X X X X | | O |
> | O X X X X | | O |
> +-1--2--3--4--5--6--------7--8--9-10-11-12-+
> Pipcount X: 131 O: 159 X-O: 0-0/Money (1)
> CubeValue: 1
>
************************
David C. Ullrich
David C. Ullrich
>[...]
>
>Anyway, despite Philippe's previous good form, this is an extraordinary
>blunder by him. I haven't seen the bot analysis of course, but I
>really will be completely amazed if passing is not a blunder.
In your own post you say that passing is a _huge_ blunder...
I certainly don't know what's right, but _I_ will be amazed if
either passing or taking turns out to be a huge blunder...
>Paul Epstein
************************
David C. Ullrich
Zorba
rate, it's hard to say how big. -1.1 ?
It's big for X to be on roll with O on the bar. That just gives X some
freedom to do very useful things before O is back in play. F.i. X can
diversify nicely to his 11 and 10 points with complete safety for now.
That will help a lot next turn to improve the offense. Even if X goes
to his 9, 8 or 7 points, the risk is small with O on the bar.
Another feature here is that X is in little hurry to safety the 15pt
blot, since O already needs a three to enter. So only 1-3 and 3-3 hit
for now.
X has a very strong board and O is already struggling with two
backcheckers. If O anchors on 22 he's in good shape, but he needs quite
a bit of luck to do that. More likely is that he anchors on 24 which
isn't much good here. And there's a small but significant chance that O
may get closed out, losing a gammon. X doesn't have the ammonition this
turn, but next turn X may be threatening.
O may use his prime to contain X, but the problem is that usually O
himself will also have a strong blockade in front of him, and O may
have one more checker to jump over the blockade than X will have.
--
_
/
_ orba
Peter Schneider
I share the opinion with the majority that it's a pass. Perhaps it's even a
little blunder to take. O is on the bar, and it's not unusual to dance, say,
3 times on this 4 point board -- a disaster spelled with g.
And I agree much with all of Philip's arguments.
Regards,
Peter aka the juggler
paulde...@att.net
that most (and perhaps all) others on the thread are very strong, so I
can't help moderating my certainty in the light of the countervailing
opinions. [By the way, isn't "countervailing" a great word? I just
hope it means what I think it means.]
Relying on the resources of my own knowledge and understanding, I
would expect passing to be a blunder worth about 0.3 points. So that's
why I said "huge".
Could be wrong though, with such brains stacked against me.
Paul Epstein
Grunty
X's. This gives X plenty of game plans: he can go for a gammon with a 5
with little fear of a return hit, or else spread builders over the
outfield.
O's prime has poor blocking value. Should it be one point larger, O
might try a take, in merit to the possibility that he manages to
anchor, establishing a fairly timed battle of primes. As it is, it's no
prime.
This is a clear pass to me.
Micke Nilsson
Money session. Score X-O: 0-0
X on roll, cube action
+24-23-22-21-20-19-------18-17-16-15-14-13-+
| X O O | | O O X X |
| O O | | O O X |
| O | | X | S
| | | X | n
| | | | o
| |BAR| | w
| | O | | i
| | | O | e
| X | | O |
| X X X X | | O |
| O X X X X | | O |
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
Pipcount X: 131 O: 159 X-O: 0-0/Money (1)
CubeValue: 1
3-Ply Money equity: 0,560
1,7% 32,7% 65,1% 34,9% 8,0% 0,4%
1. Double, take 0,866
2. No double 0,725 (-0,141)
3. Double, pass 1,000 (+0,134)
Proper cube action: Double, take
------------------------------ End ----------------------------------
Snowie 3-ply full rollout:
Money session. Score X-O: 0-0
X on roll, cube action
+24-23-22-21-20-19-------18-17-16-15-14-13-+
| X O O | | O O X X |
| O O | | O O X |
| O | | X | S
| | | X | n
| | | | o
| |BAR| | w
| | O | | i
| | | O | e
| X | | O |
| X X X X | | O |
| O X X X X | | O |
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
Pipcount X: 131 O: 159 X-O: 0-0/Money (1)
CubeValue: 1
Rollout Money equity: 0,629
1,1% 34,9% 67,1% 32,9% 7,0% 0,4%
95% confidence interval:
- money cubeless eq.: 0,629 ą0,025,
- live cube no double: 0,764 ą0,040,
- live cube double take: 0,970 ą0,068.
Rollout settings:
Full rollout,
324 games (equiv. 10839 games),
played 3-ply (standard), cube 3-ply,
settlement 0,550 at 16 pts,
seed 1, without race database.
Evaluations
1. Double, pass 1,000
2. No double 0,784 (-0,216)
3. Double, take 1,018 (+0,018)
Proper cube action: Double, pass
Live cube
1. Double, take 0,970
2. No double 0,764 (-0,206)
3. Double, pass 1,000 (+0,030)
Proper cube action: Double, take
------------------------------ End ----------------------------------
Grunty
> Snowie 3-ply instant evaluation:
> Proper cube action: Double, take
>
> Snowie 3-ply full rollout:
> Proper cube action: Double, pass
> Live cube
> Proper cube action: Double, take
Hmm, another not unanimous result from Snowie.
Maybe 3888 games and GNUBG "Supremo" are in order here too.
Whatever the final results be, this would suggest the decision is not
so clear-cut as I thought. I felt as I'd very gladly play X part in a
prop.
I call the tough guys to roll this one out...
Raccoon
Grunty wrote:
> Micke Nilsson wrote:
>
> > Snowie 3-ply instant evaluation:
> > Proper cube action: Double, take
> >
> > Snowie 3-ply full rollout:
> > Proper cube action: Double, pass
> > Live cube
> > Proper cube action: Double, take
>
> Hmm, another not unanimous result from Snowie.
> Maybe 3888 games and GNUBG "Supremo" are in order here too.
Micke reports TWO evaluations and ONE rollout result.
eval one: DT 0.866
eval two: DT 1.018
rollout: DT 0.970 ±0,068
The problem is not that the evalutions and rollout disagree. The
problem is that the 324-trial rollout result is not informative. DT
0.970 with a 95% confidence interval of ±0.068 -- well, might a longer
rollout say DT 0.902? Or might it say DT 1.038? We don't know.
Often enough, you can do a very long rollout and still not have a
significant result. And that's fine -- now you might conclude that the
decision doesn't matter much or matter enough to bother taking the time
to make a long rollout a lot longer. But if you want to know what
Snowie 'thinks' about this position, and want to compare Snowie to
GNUBG, 0.970 ±0.068 doesn't cut it. You need at least 1296 trials and
probably more.
Generally, quadrupling the number of trials cuts the 95% confidence
interval in half. So if the result after 324 trials has a 95% CI of
±0.068, then 1296 trials will have a 95% CI of about ±0.034. If after
1296 trials the DT equity is closer to 1.000 than 0.034, yet more
trials will be needed.
paulde...@att.net
I thought".
At this point, it is fairly probable that I am the only one who got the
action right here (although my track record across all 18 problems
might not be so good.) Not only does double/take pass 2 of the 3 tests
(evaluation + live cube rollout), but I think the double/pass verdict
comes from a less realistic model, and the average of the two rollout
verdicts is also a take.
Could someone explain the difference between the two types of rollout?
Anyway, I give kudos to three people -- Zorba and David for explicitly
indicating that the decision is marginal; myself for (with the best of
the current evidence) getting the action right.
I'll give myself 3rd place because "marginal pass" is a better answer
than "very clear take" even though my answer happens to lead to the
correct action (with best current evidence.)
501 Essential covers this type of position very well.
It seems to me that a world-class professional would probably say
"Hmmm, this is extremely marginal either way. Looks like a toss-up."
This leads to the interesting question of how to act on that
uncertainty.
A position which is theoretically exactly marginal is a practical take
(unless there is no skill left in the position.) The reason is that
the possibility of future errors (by both players) increases the
volatility which gives extra equity to the underdog. For a clearer
analogy, if the playing conditions at a tennis event are pathologically
bad with lots of bad bounces etc. [which inject an additional element
of chance or volatility], then that favours the weaker players at the
expense of the stronger players.
If you prefer a backgammon analogy, which shows why human error
transforms marginal pass/takes to takes: Imagine a completely marginal
position. Then add the following rule: an observer randomly selects a
number from 1 to 1000 before every future roll. Whenever the number 1
is picked, a player is legally required to make a checker play blunder.
Then this rule (attempted to model human error more rigorously)
clearly transforms marginal decisions into takes.
On the other hand, the rake transforms an exactly marginal decision
into a pass (see previous threads).
Which of these 2 factors is more important? My judgment is to give
more weight to the rake factor, because it's more tangible than the
volatility factor. General Conclusion: In online money backgammon, a
cube should be passed if you can't decide between taking and passing.
A final observation: We've had a debate about how Snowie 3 ply
compares with the top professionals. I would imagine that a top
professional would handle this type of position extremely well. It's a
very standard type of position. However, note that Snowie's initial
assessment of 0.866 seems seriously wrong. Whatever the final answer
is, I'd bet that Robertie/Woolsey/Kazaross etc. would give a much more
accurate evaluation than Snowie-non-rollout.
So I'm now more willing to accept Gregg's opinion that top ten players
are better than Snowie.
Paul Epstein
David C. Ullrich
>[...]
>
>I'll give myself 3rd place because "marginal pass" is a better answer
>than "very clear take" even though my answer happens to lead to the
>correct action (with best current evidence.)
Yes, assuming that it is in fact an extremely marginal take
(which is not so clear to me based on what I've seen) then
"marginal pass" is in fact a _much_ better answer than
"very clear take". Because the evaluation of the person who
said marginal pass was pretty close - although he makes the
wrong decision here he's giving up very little, and if he
evaluates things this closely in other positions he will
give up very little in those other positions. On the other
hand the evaluation of the "very clear take" guy was way off -
if his evaluations in other positions are just as far
off he's going to be making the wrong decision in positions
where it gives up a _lot_.
That may be a little harsh. But really - simply talking
about the _backgammon_ might be a better idea than going
on about who was right and who was wrong.
Really. Here I'm just an advanced beginner, but, say, on
sci.math I'm an expert on many topics. There are a lot of
very smart guys there who say a lot of very interesting
things about math - sometimes they get something wrong and
they just say oops, that was wrong, sorry, without trying
to explain how the fact that they got it wrong doesn't mean
they're stupid. On the other hand there are a lot of people
there who talk a lot about how good they are at math. Their
posts are generally much less interesting to read, because
they typically don't have much to say about non-trivial
problems.
Just a thought...
************************
David C. Ullrich
Grunty
> The problem is not that the evalutions and rollout disagree.
Ok, that is just the first symptom that the position is tricky/close,
and deserves a deeper test.
> The problem is that the 324-trial rollout result is not informative.
That's what I asked for -- a more extensive rollout.
(Same way as position #16 was re-evaluated.)
paulde...@att.net
On the one hand, I do make interesting and relevant comments about the
backgammon.
Yet, on the other hand, I (perhaps unfortunately) get competitive and
hope to show that my evaluations are better than those of others.
I don't particularly like this posting of yours because it seems that
you're comparing me to those who "don't have much to say about
non-trivial problems." However, I don't believe this is a fair
judgment (although you didn't explicitly make it).
On this particular thread, the pure backgammon content of my postings
is good. In particular I mentioned that X might have difficulty
getting to the edge of 0's prime and several other pertinent comments.
However, your posting gives the distorted impression that I didn't talk
about "the _backgammon_" at all. And you're a bit hypocritical because
your own postings (e.g the one I'm responding to) are not always filled
with glorious backgammon insights.
You criticise me (justifiably) for the negative aspects of my postings,
but say nothing to acknowledge the positive content. When criticising
others, it's important to balance the criticism by saying what the
person did well.
I was going to say "My comments were just as interesting as anyone
else's" thereby being unnecessarily competitive and amusingly
demonstrating your point about myself. Some habits die hard!
Raccoon
paulde...@att.net wrote:
> At this point, it is fairly probable that I am the only one who got the
> action right here
You may have gotten it right, but the best evidence -- the Snowie
rollout -- said: "DT 0.970 ±0.068." I believe this comparison is
analogous:
The latest election poll has Candidate X ahead of Candidate Y
51.5%-48.5%, with a (95% confidence interval) margin of error of 3%.
Based on this evidence, how can we say that either candidate's victory
is "fairly probable?"
> Anyway, I give kudos to three people -- Zorba and David for explicitly
> indicating that the decision is marginal;
But they didn't. While David wrote that it didn't "look all that
clear," Zorba wrote: "it's hard to say how big. -1.1 ?" For Zorba,
0.100 errors are blunders. See
http://www.bkgm.com/rgb/rgb.cgi?view+1273
Elsewhere you defined a blunder as "worth about 0.3 points" -- oof! --
that's like taking a dead cube with only 17.5% gammonless winning
chances. Well sure, we don't want to be making that size error!
> A position which is theoretically exactly marginal is a practical take
> (unless there is no skill left in the position.) The reason is that
> the possibility of future errors (by both players) increases the
> volatility which gives extra equity to the underdog. For a clearer
> analogy, if the playing conditions at a tennis event are pathologically
Your argument seems to assume backgammon players of equal skill equally
likely to make outcome-influencing errors. But then in your tennis
analogy you use "underdog" to mean not positional underdog but less
able player.
Why would you or I be more likely to beat Serena Williams if the court
were uneven, or more likely to outshoot Michael Jordan if the hoop were
bent, or more likely to beat a pool hall champion if you both played
with warped cue sticks?
Perhaps the tennis analogy can be salvaged by assuming equally skilled
players with one player up two matches to none when Hurricane Felicity
hits. Is the trailing player now more likely to win than she would have
been if the skies had remained clear? Why would she be?
You continue:
> transforms marginal pass/takes to takes: Imagine a completely marginal
> position. Then add the following rule: an observer randomly selects a
> number from 1 to 1000 before every future roll. Whenever the number 1
> is picked, a player is legally required to make a checker play blunder.
> Then this rule (attempted to model human error more rigorously)
> clearly transforms marginal decisions into takes.
But in backgammon errors in checker play do not occur randomly; a
superior player is less likely to err than his opponent; one side or
the other of a position may be more difficult to play; and the
likelihood of either player making an error playing on from a given
position may be great or small or nonexistent.
One can't decide whether one has positive equity in taking a marginal
(1.000) cube without considering how likely either player is to make
mistakes that will swing the perfect-play equity one way or the other.
A superior player, it seems clear, can gain equity taking marginal
cubes against less than perfect opposition in positions where skill
still matters. Why the inferior player would gain equity by taking in
the same position isn't clear at all, at least not to me. In fact it's
easy to imagine, is it not, a 1.000 cube proposition with positive
equity for the superior player no matter which side of the proposition
she plays.
> compares with the top professionals. I would imagine that a top
> professional would handle this type of position extremely well. It's a
> very standard type of position. However, note that Snowie's initial
> assessment of 0.866 seems seriously wrong.
But does this mean Snowie doesn't play as well as a player (or other
bot) with a more accurate evaluation? If double/take is correct, the
inaccuracy of Snowie's evaluation doesn't cost Snowie a thing; it
correctly takes.
On the other hand, it might be a pass. We're still waiting for Snowie's
considered opinion, among those of other world class players.
Grunty
> Whatever the final answer is, I'd bet that Robertie/Woolsey/Kazaross
> etc. would give a much more accurate evaluation than
> Snowie-non-rollout.
You made the key distinction there: "non-rollout".
Top players *evaluation* would still be less accurate than a bot
rollout.
Top players can *assess* certain positions better than a bot.
Top players can *play* certain positions better than a bot.
But it isn't fair comparing t.p. assessment with a bot's rollout.
Ideally, to achieve ultimate certainty in such border positions, we
should be asking a top player to do a *manual rollout* (not an
assessment), in order to put into account his bit-superior skill all
along those games.
Unfortunately, no player can reach, in a practical timeframe, the
n-thousand games mark bots can, nor has their consistency in level of
play.
Raccoon
Cube analysis
Rollout cubeless equity +0.6196
Cubeful equities:
1. Double, pass +1.0000
2. Double, take +1.0161 ( +0.0161)
3. No double +0.8124 ( -0.1876)
Proper cube action: Double, pass
Rollout details:
Centered 1-cube:
0.6691 0.3424 0.0109 - 0.3309 0.0690 0.0030 CL +0.6196 CF +0.8124
[0.0013 0.0017 0.0005 - 0.0013 0.0009 0.0003 CL 0.0033 CF 0.0079]
Player White owns 2-cube:
0.6801 0.3415 0.0093 - 0.3199 0.0645 0.0030 CL +1.2870 CF +1.0161
[0.0017 0.0024 0.0007 - 0.0017 0.0011 0.0005 CL 0.0089 CF 0.0129]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 981169792 and
quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
paulde...@att.net
Keep doing more and more rollouts until you get the verdict that you
previously argued for.
Could someone explain the deeper aspects of what these rollouts mean?
For example, there seem to be two sorts of rollouts: live cube and
another type.
What are the distinctions between the two? And what type of rollout is
this one? And where are the error bounds indicated at a 95% level?
O.k. that's a lot of questions for sure. But if anyone does have the
time/willingness/energy to give a deeper understanding of rollouts, or
to give an online reference, I'd really appreciate it, and I'd bet
others would too.
I did look into this briefly with a google search, but still came away
a bit baffled.
Thank you.
Paul Epstein
Raccoon
paulde...@att.net wrote:
> This seems a bit like the Florida recount.
>
> Keep doing more and more rollouts until you get the verdict that you
> previously argued for.
Argued? Come on. I gave my opinion, right or wrong. If you intended to
imply that I'm doing "more and more rollouts" until I get one that
agrees with me, I'd resent it. I've only done one rollout.
But do note that the rollout for this position is the only rollout that
has any meaning. The Snowie rollout was simply too short. I've already
explained why. The GNU Backgammon rollout tells us that when both
players are GNUBG with supremo checker play and world class cube
settings, the cube decision is a marginal pass/take. The Snowie rollout
after only 324 trials doesn't tell us anything.
> to give an online reference, I'd really appreciate it, and I'd bet
http://www.bkgm.com/rgb/rgb.cgi?menu+rollouts
http://www.bkgm.com/rgb/rgb.cgi?menu+gnubackgammon
http://www.bkgm.com/rgb/rgb.cgi?menu+snowie
> Thank you.
Any time.
paulde...@att.net
I'd like to say that I intended "argue" in its non-confrontational
sense of "present a case."
According to this definition, anyone who says that a cube should be
passed or taken, and gives reasons for that opinion, is arguing. So
you certainly did "argue" and you were right to do so. In fact, all
who gave pass/take opinions argued, including myself.
I am British. I do not know if a transantlantic difference in the
definition of "argue" is at work, but this is a standard British
definition.
Maybe my Florida recount joke was in poor taste. I certainly didn't
intend to imply anything negative whatsoever about anybody. In fact, I
believe your latest rollout is a good contribution to the discussion.
To me, the situation was somehow reminiscent of the Florida recount in
the way the assessments changed and the way the pass/take decision
appears to be so close. In fact, the situation is very reminiscent of
the Florida debacle, and some jocular reference to it seemed almost
begging to be made.
I guess that my posting could be taken in the wrong way, and so I
apologise for that
Paul Epstein
Micke Nilsson
also just for comparison. I started this rollout now and should hopefully
have it done when I get home from work tomorrow. I will try to run #16
tomorrow.
/Micke
"Raccoon" <racg...@yahoo.com> skrev i meddelandet
news:1129645785.6...@o13g2000cwo.googlegroups.com...
Micke Nilsson
X on roll, cube action
+24-23-22-21-20-19-------18-17-16-15-14-13-+
| X O O | | O O X X |
| O O | | O O X |
| O | | X | S
| | | X | n
| | | | o
| |BAR| | w
| | O | | i
| | | O | e
| X | | O |
| X X X X | | O |
| O X X X X | | O |
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
Pipcount X: 131 O: 159 X-O: 0-0/Money (1)
CubeValue: 1
Rollout Money equity: 0,641
1,1% 34,7% 67,7% 32,3% 6,8% 0,3%
95% confidence interval:
- money cubeless eq.: 0,641 ą0,012,
- live cube no double: 0,796 ą0,020,
- live cube double take: 1,029 ą0,031.
Rollout settings:
Full rollout,
1296 games (equiv. 43492 games),
played 3-ply (standard), cube 3-ply,
settlement 0,550 at 16 pts,
random seed, without race database.
Evaluations
1. Double, pass 1,000
2. No double 0,794 (-0,206)
3. Double, take 1,047 (+0,047)
Proper cube action: Double, pass
Live cube
1. Double, pass 1,000
2. No double 0,796 (-0,204)
3. Double, take 1,029 (+0,029)
Proper cube action: Double, pass
------------------------------ End ----------------------------------
Grunty
Better late than never...
As the original proponent of this series, I just wanted to say thanks,
again, to you and your fellow players in Sweden, for letting us discuss
these interesting problems.
We've got lots of insight from them.
Micke Nilsson
for sure some were. If you now consider that this player got every single
one of these correct (or rather exactly like Snowies 3-ply instant
evaluation) you must wonder how many players would do that at the table.
Then if you take in consideration that this player didn't make any other
single cuber error during the 32 matches it seems very fishy.
The player has still not said anything to his defense in public. From other
players I have heard though that he has said that it's not a big deal,
because almost everyone on TMG uses Snowie. As I said, this is not official,
but either way you gotta wonder...
/Micke
"Grunty" <grunti...@yahoo.com> skrev i meddelandet
news:1130210651.4...@g44g2000cwa.googlegroups.com...
Walt
I'd also like to say thanks, even though I never weighed in with my
(fairly worthless) opinion on any of them. Read 'em all, though,
including all the responses.
I'd like to see more quizs like this. I definitely learned something.
//Walt
Grunty
> I'd like to see more quizs like this. I definitely learned something.
Hi Walt,
there's a new one running these days, labelled "GNUBG 2-ply or BG
GIANT", just a few problems old.
QuizMaster is Zorba.
Its theme is to contrast top-bot vs top-player vs top-fish (us)
decisions in given situations of a match.
Good luck.