Shark Feeding On Newbies
David B. Sandler
Last night my wife (a newbie off to a rough start on fibs) was invited to
a 2-pointer by someone ranked in the top 80 players on fibs, with loads
of experience. She was very exited that such a good player would invite
her; I was a bit puzzled. Out of interest, I followed this person's next 5
or 6 matches using th "whois" command; they were ALL against folks rated
1420-1530 or so, and all had less than 50 experience points.
This got me thinking (often very dangerous for me). Has anyone ever
considered adding another "barometer" to a player's fibsability - the
average\mean\median (I can never keep them straight) of a player's
OPPONENT'S rating at the time the player played them. It seems obvious
that an 1850-rated player whose opponents' average rating is 1775 would be
a much stronger player (at least in theory) than an 1850-rated player who
feeds on 1450-rated players with little experience. Perhaps a rolling
average of a player's oponents' most recent 200 or 300 experience points
could be added to his rating, rank and experience at the "rating" command.
(I realize that this simple suggestion would probably require about a
zillion hours of programming by people already taxed to the hilt for
time; I'd offer to help but I can't even balance my checkbook).
I'm also aware that anything which discourages better, more experienced
players from challenging and/or accepting challenges from players trying
to learn is NOT a good thing. However, I don't believe this would be a
side-effect of my suggestion.My own experience (about 350) has been that I
invite people within 75 points of my own rating, plus and minus, and am
typically invited by players in the same range, with some exceptions of
course. (I've also invited, albeit rarely, folks 200 points above me, and
been invited by a few 100-150 above me). But about 80% of the time, I find
I'm playing someone "relatively equal". And I'm sure that the REAL
top-notch players wouldn't ignore an occasional invite by someone 200 or
300 points below them just because the opponent's rating would lower their
"OPP-RATING" a tad. However, an OPP/RATING would shed some light on sharks
and,thus,tend to spotlight the true top players on fibs, while warning
newer players about whom they're about to play.
I wondered if anyone shares my view, and whether it's feasible. Of course,
if this is the 3 or 4-hundredth time someone has made this suggestion,
please feel free to tell me to go back to sleep.
Dave Sandler (bar_ky)
Peter Fankhauser
"David B. Sandler" <westfall.ta...@worldnet.att.net> wrote:
<snip, reporting about a player playing 2pt games against newbies)>
Yes, there are some players whose ego is wacky enough to inflate
their rating by trying to steal points from newbies. The
strategy you described probably works well. (a) (I think it
was Ed Rybak who pointed out that) newbies might be overrated,
in particular newbies below 1500 with fairly small experience 20-50)
(b) there is a significant chance that newbies don't understand
the right cube-action at 2-away,2-away, which is simply doubling
at the first opportunity.This gives the "expert" some free rolls
in case things go badly, and allows him to make VERY effective
doubles. In more moderate ways quite a few players try to
gain rating by specializing on certain rating ranges or
unusual match-lengths (e.g. 4pters).
But then, what's the problem? If rating was money, one might have
to do sth. about it (e.g. adding a topic to the FAQ). But rating is
just your individual measurement (not that reliable) where about
your game stands. If you inflate your rating artificially, you've
lost that measurement.
funk
Gert de Beer
Peter Fankhauser (funk) wrote:
> Yes, there are some players whose ego is wacky enough to inflate
> their rating by trying to steal points from newbies. The
> strategy you described probably works well. (a) (I think it
> was Ed Rybak who pointed out that) newbies might be overrated,
> in particular newbies below 1500 with fairly small experience 20-50)
> (b) there is a significant chance that newbies don't understand
> the right cube-action at 2-away,2-away, which is simply doubling
> at the first opportunity.This gives the "expert" some free rolls
> in case things go badly, and allows him to make VERY effective
> doubles.
I am one of the "newbies below 1500 who don't understand
the right cube-action at 2-away,2-away".
In fact I don't even know what the expression means.
Please enlighten me and maybe other newbies too.
Gert de Beer
(playing using the name 'biltong')
John R. Grout
In article <4ttc38$m...@rs18.hrz.th-darmstadt.de> Peter Fankhauser <fank...@darmstadt.gmd.de> writes:
> The theoretically correct cubeaction at [2-away, 2-away] is to double at the
> first opportunity, that is, if your opponent has won the opening roll, you
> double immediately, and play the game for the match.
> Suppose, you win s1% singles,
> g1% gammons and you lose s2% singles, and g2% gammons.
> Your match-equity (chances of winning the match) if you do not
> double are as follows (using Kit Woolsey's Match-equity table)
>
> Score match-equity
> you win single: -1,-2 70%*s1%
> you win gammon: 0,-2 100%*g1%
> you lose single -2,-1 30%*s2%
> you lose gammon: -2,0 0%*g2%
> [funk advises a double when s1 > s2]
Thank you, funk, for the theoretical analysis.
However, don't the 70% and 30% match equity estimates understate an expert's
chances against a newbie at both (-1, -2) and (-2, -1)? A relatively small
change in those estimates would dramatically increase the single game chances
needed for an expert to double in this position (and make it all the worse for
the newbie _not_ to double).
For example, if you used 80% and 40% instead of 70% and 30%, you would get
0.8*s1 + g1 + 0.4*s2 < s1 + g1, which is s1 > 2 * s2... which means the expert
would need _twice_ the chance of a single game victory against a single game
loss before a double.
--
John R. Grout Center for Supercomputing R & D j-g...@uiuc.edu
Coordinated Science Laboratory University of Illinois at Urbana-Champaign
Cha...@terra.com
Peter Fankhauser <fank...@darmstadt.gmd.de> wrote:
>Gert de Beer <g...@ist.co.za> wrote:
>>
>
>> I am one of the "newbies below 1500 who don't understand
>> the right cube-action at 2-away,2-away".
>> In fact I don't even know what the expression means.
>> Please enlighten me and maybe other newbies too.
>>
>
>
<blah blah blah deleted>
Way to go!
You just answered a newbie's question about a thimble full of jargon by
unloading a truck-load of jargon on him.
What color is the sky in your world?
Charles
Peter Fankhauser
> However, don't the 70% and 30% match equity estimates understate an expert's
> chances against a newbie at both (-1, -2) and (-2, -1)? A relatively small
> change in those estimates would dramatically increase the single game chances
> needed for an expert to double in this position (and make it all the worse for
> the newbie _not_ to double).
>
> For example, if you used 80% and 40% instead of 70% and 30%, you would get
> 0.8*s1 + g1 + 0.4*s2 < s1 + g1, which is s1 > 2 * s2... which means the expert
> would need _twice_ the chance of a single game victory against a single game
> loss before a double.
hmmm, that is an interesting observation. I've never thought about this,
but don't see any flaw in it (btw. I think Tomas Szabo has produced
match-equity tables for players with different skill, they can be
found via Stephen Turners WWW-pages).
The whole thing might further be influenced by the volatility
of a position, that is, are there any big swings on next turn, or is
the position fairly stable. But probably r.g.b is not anymore the
appropriate place to discuss this, without getting flamed for using
elitist jargon.
funk
Peter Fankhauser
gr...@polestar.csrd.uiuc.edu (John R. Grout) wrote:
>
>
> For example, if you used 80% and 40% instead of 70% and 30%, you would get
> 0.8*s1 + g1 + 0.4*s2 < s1 + g1, which is s1 > 2 * s2... which means the expert
> would need _twice_ the chance of a single game victory against a single game
> loss before a double.
On second thought. If you are the better player, also your chances
for a position with cubeless winning percentages s1 and s2
(if played out between equally skilled players) should be better than
s1. Thus it might even out.
funk
Peter Fankhauser
> I am one of the "newbies below 1500 who don't understand
> the right cube-action at 2-away,2-away".
> In fact I don't even know what the expression means.
> Please enlighten me and maybe other newbies too.
>
Ok, here we go.
2-away, 2-away means a match-score, where both
players have to go 2pts for winning the match. For example,
for a match-length of 2, 0:0. This normalized way of denoting
match-scores is useful, because it does not matter how many
points you've won or lost already, but only how many points you need
for winning the match. Thus 0:0 for a 2pter is equivalent to
3:3 for a 5pter.
The theoretically correct cubeaction at this score is to double
at the first opportunity, that is, if your opponent has won the
opening roll, you double immediately, and play the game for the
match.
This may seem obvious when you have an advantage
(for example your opponent has started with a nullo roll like 41
or so). Because your opponent can not redouble you (it does not
matter whether you win a 2pter 4:0 or 2:0), you simply double your
advantage, no matter how small it is.
But why should you double if the opponent has opened with a good
roll like 31? Simply, because your opponent will double next turn
anyway - if s/he follows the right cube action. So the only real
mistake you can make is failing to double.
So far the theory. In practice, when you think your opponent
does not understand the right cube action ("expert" vs. "newbie"),
you can wait with the "automatic" double. Thus, when your opponent
opens with a 31, you don't double, hoping that your opponent also
won't double next turn (which would be the proper cube-action for
moneygame on most replies - but wrong at -2,-2).
With this you get some "free turns" which might improve your
position - after which you double immediately.
More precisely, if you know about the proper cube
action, and your opponent does not, the "correct" cube action
can be determined as follows. Suppose, you win s1% singles,
g1% gammons and you lose s2% singles, and g2% gammons.
Your match-equity (chances of winning the match) if you do not
double are as follows (using Kit Woolsey's Match-equity table)
Score match-equity
you win single: -1,-2 70%*s1%
you win gammon: 0,-2 100%*g1%
you lose single -2,-1 30%*s2%
you lose gammon: -2,0 0%*g2%
If you do double this looks as follows:
you win (single or gammon): 100%*(s1%+g1%)
you lose (single or gammon): 0%
Thus you should double when: 0.7*s1+g1+0.3*s2 < s1+g1, that
is (after some simple transformations),
when your chances to win a single game are larger than
your opponent's chances to win a single game, surprise, surprise.
For zero gammons this simply means you should double as soon as you
are favorite to win. For larger gammon rates, this can have some
surprising effects. Assume you have 50% to win the game (single
or gammon), and you have 15% to win a gammon, whereas your opponent
has only 10%. s1=35%, s2=40% - you should NOT double, but play on,
although you are a favorite for money, rather your opponent
should double, and thereby switch off your gammons. But I am
not even sure such a position can be reached if you follow the
proper strategy of doubling as soon as s1%>s2%.
How long can you take a double by your opponent? If you
pass, you are at -1,-2, with a chance of 30% to win the match.
If you take, we know already that you've got s1%+g1%. Thus as long
as you can win 30% of the games (single or gammon) you should take
the double.
If your opponent plays a simple moneygame strategy
(double/take s1%+2*g1%-s2%-2*g2% between 0.45 and
0.55, below that no double, above that drop) s/he gives away
equity. Whenever s/he is favorite (and probably s2%>s1%) and
s/he fails to double s/he gives away s2%-s1%, and that might happen
more than once per game, giving you the chance to turn around the
game or to properly pass when things go badly. In addition,
s/he might give away equity by cashing, when s/he should play on for
the gammon (note that s/he probably does not lose equity by
taking, when s/he should drop, as you should still double as soon
as s1%>s2%). That adds up.
But all this should of course be theory, if both players
understand the proper cube-action and double immediately.
funk
PS.: I hope I've got the maths right here, I never really bothered
about it, as I double on s1%+g1%>s2%+g2% (at least when I think so)
immediately anyway.
beergut
David B. Sandler wrote:
>
> Last night my wife (a newbie off to a rough start on fibs) was invited to
> a 2-pointer by someone ranked in the top 80 players on fibs, with loads
> of experience. She was very exited that such a good player would invite
> her; I was a bit puzzled. Out of interest, I followed this person's next 5
> or 6 matches using th "whois" command; they were ALL against folks rated
> 1420-1530 or so, and all had less than 50 experience points.
>
Hi there.....Some people place so much importance on the " ratings " That the sharks are
of little consequence. The major problem for a few "very few" is rating manipulation.
It seems there are a few "very few" players on fibs that have friends who logon with new
names and then intentionally lose to their friend. This usually happens in the early
morning and is quite funny to watch. I know this happens as I was asked if I wanted to
do it. Needless to say I no longer play with that person. Everyone likes to win..but my
ego doisn't need big numbers to feed it :) BG for fun!! not a way of life !!!
beergut
David B. Sandler
I agree with most of what you say. But the fact is that the cube is what
makes bg so much fun, and rating points serve as a substitute for money,
money usually being the motivating force behind using the cube properly (I
say usually because there certainly ARE other good substitutes - take
strip bg, for example :-))
I'd guess that, if ratings were eliminated from any of the bg servers,
play would fall to a fraction of what it is because the cube would become
meaningless. SO, given that the world won't fall apart if highly rated
players feed off folks with 1450 ratings and 4 matches worth of
experience, I'd still be interested in whether it's feasible to have an
additional barometer of a player's skill - his/her opponents' combined
average rating.I(for one) enjoy playing higher rated people pretty
frequently and would be interested to know whether an 1850-rated player's
opponents had average ratings of 1500 or 1800. Then I'd be in better
position to know whether I'm about to get a bg clinic (from people like
woolsey) or whether it's a chance to pick up more points than I normally
would from someone who's probably a pretty average player, depending on
what kind of mood I'm in (such as, am I in the mood for a chance at a
bunch of points, or am I in the mood to get my brains beat in ?).
I know that this isn't the most worrisome issue currently facing the bg
community, and that bg's for fun,etc.,etc. But I'd like to know if there
are others who'd prefer to know,while trying to learn from a better
player, that the opponent IS a better player, rather than one who built up
his ranking to the top 100 on Fibs (or NG, GG, etc.)feeding off people who
are still having trouble learning how to move their checkers.
Dave Sandler (bar_ky)
Lou Poppler
On 2 Aug 1996 22:16:30 GMT, Peter Fankhauser (fank...@darmstadt.gmd.de) wrote:
: gr...@polestar.csrd.uiuc.edu (John R. Grout) wrote:
: > However, don't the 70% and 30% match equity estimates understate an expert's
: > chances against a newbie at both (-1, -2) and (-2, -1)? A relatively small
: The whole thing might further be influenced by the volatility
: of a position, that is, are there any big swings on next turn, or is
: the position fairly stable. But probably r.g.b is not anymore the
: appropriate place to discuss this, without getting flamed for using
: elitist jargon.
I certainly hope Peter is joking. This seems to me _exactly_ the sort of
topic that is appropriate in r.g.b. It is of great interest to
intermediate players such as myself, and ought to be of interest to new
players as well. Let's all try to learn one new word of Jargon each day.
-- Spider
Peter Fankhauser
I don't think that the average rating of ones opponents says
very much about ones bg-skills (with the exception of players
playing ONLY likely overrated newbies).
The rating formula on fibs evens out rating (not necessarily=skill)
differences anyway. And it seems to work quite well. I've once
analysed the over 2500 matches in Mark Damish's BigBrother database
(rating differences up 200 pts), and it turns out that no matter
how much the ratings differ, the average number of rating
points won by the higher rated player is about 0 (in fact it is
slightly below 0 most of the time). The same holds for different
match-lengths. Ed Rybak once ran a few Monte-Carlo simulations
(virtual players of different skill playing 1000s of virtual
matches against each other), and reported similar results, though
this might be also a case of selffulfilling prophecy, as he probably
used the rating formula to determine the outcome of a match.
So to gain and keep a high rating against lower rated players
you need to win a much higher percentage of matches, and thus
play good bg too, as long as you don't apply
some very specific cheats.
In addition, an unwelcome sideeffect of your suggestion might be
that higher rated players refuse to play lower rated players, in
order to keep their opponent-rating-factor high.
funk
John Quinnelly
Peter Fankhauser wrote:
>
> > For example, if you used 80% and 40% instead of 70% and 30%, you would get
> > 0.8*s1 + g1 + 0.4*s2 < s1 + g1, which is s1 > 2 * s2... which means the expert
> > would need _twice_ the chance of a single game victory against a single game
> > loss before a double.
>
>Could you explain this in plain english? Is it better for a more experienced player to
double a less experienced player at 2-away, 2-away? And if so why? Sorry, but the
equation means absolutely nothing to me!
screwtape
John R. Grout
In article <32047E...@ntr.net> John Quinnelly <jo...@ntr.net> writes:
I wrote:
> > > For example, if you used 80% and 40% instead of 70% and 30%, you would get
> > > 0.8*s1 + g1 + 0.4*s2 < s1 + g1, which is s1 > 2 * s2... which means the expert
> > > would need _twice_ the chance of a single game victory against a single game
> > > loss before a double.
> >
> >Could you explain this in plain english?
[Since it was my follow-up comment to funk's which you quoted, I'll answer it]
When two evenly matched players are playing a relatively long match, and one
is closer to winning (but not yet 1-away), the one who is ahead needs more
before a double (or redouble) than he/she would normally because his/her
opponent has more to gain from the cube being at large values.
A simple example of this is at 2-away, 4-away. The player who is 2-away has
to realize that an initial double (to 2) gives his/her opponent the
opportunity for an immediate recube (to 4), making this game for the match.
So, the player who is 2-away will not double in many situations where he/she
would if (say) the match were at 4-away, 4-away.
Now, back to your question:
> Is it better for a more experienced player to double a less experienced
> player at 2-away, 2-away? And if so why?
First, as funk pointed out, a less experienced player should double themselves
at 2-away, 2-away... the whole question is what a more experienced player
should do if the other person (for whatever reason) fails to double.
The "match equities" funk used (which are in Kit Woolsey's "How to Play
Tournament Backgammon"... available from Gammon Press) say that someone has a
70% chance to win if they are up 1-away, 2-away (e.g., 4-3 in a 5 point
match), and still have a 30% chance to win if they are down 2-away, 1-away
(e.g., 3-4 in a 5 point match). My comment was that an expert probably has
more chance against a beginner in each of those situations than two evenly
matched players would, making it more risky to double and let one's less
experienced opponent roll lucky dice in this game and win the match.
John R. Grout
In article <4tu1l4$1t...@rs18.hrz.th-darmstadt.de> Peter Fankhauser <fank...@darmstadt.gmd.de> writes:
> gr...@polestar.csrd.uiuc.edu (John R. Grout) wrote:
> >
> >
> > For example, if you used 80% and 40% instead of 70% and 30%, you would get
> > 0.8*s1 + g1 + 0.4*s2 < s1 + g1, which is s1 > 2 * s2... which means the expert
> > would need _twice_ the chance of a single game victory against a single game
> > loss before a double.
>
> On second thought. If you are the better player, also your chances
> for a position with cubeless winning percentages s1 and s2
> (if played out between equally skilled players) should be better than
> s1. Thus it might even out.
Sometimes they probably would... but if this particular game is (or can
become) a straight running game, this game's probabilities would not
accurately reflect the overall skill differential.
Joe Dwek's comments on running games (from "BG for Profit"):
"Rate your opponent. If you are the much better player try to avoid races
like the plague. If not, keep the running game in mind and play for it at
every opportunity."
Walter G Trice
The question raised was "what is the correct doubling strategy in
a 2 point match when the players are not equal in skill?"
The answer is that, assuming perfect cube action by both players,
it is still correct for either player to double at his first
opportunity. This is actually quite simple. Suppose, for instance,
that A can beat B 62% of the time in a single game. Then if A doubles
immediately his match winning chance is 62%; if B doubles immediately
HIS match winning chance is 38%. Now suppose A has some strategy that
makes his match winning chance some higher number, say 63%. Then B
can still use the 38% strategy, which would result in A having a
101% probability of either winning or losing. Which is impossible.
Hence A has nothing better than the 62% produced by the immediate
double.
Of course it is often true in practice that A WILL have a better
strategy because B WON'T turn the cube when he should.
-- Walter Trice
David B. Sandler
Peter Fankhauser <fank...@darmstadt.gmd.de> wrote:
>"David B. Sandler" <westfall.ta...@worldnet.att.net> wrote:
>>
><snip ... suggesting to display the average rating of opponents>
>
>I don't think that the average rating of ones opponents says
>very much about ones bg-skills (with the exception of players
>playing ONLY likely overrated newbies).
>
>The rating formula on fibs evens out rating (not necessarily=skill)
>differences anyway. And it seems to work quite well. I've once
>analysed the over 2500 matches in Mark Damish's BigBrother database
>(rating differences up 200 pts), and it turns out that no matter
>how much the ratings differ, the average number of rating
>points won by the higher rated player is about 0 (in fact it is
>slightly below 0 most of the time). The same holds for different
>match-lengths. Ed Rybak once ran a few Monte-Carlo simulations
>(virtual players of different skill playing 1000s of virtual
>matches against each other), and reported similar results, though
>this might be also a case of selffulfilling prophecy, as he probably
>used the rating formula to determine the outcome of a match.
>
>So to gain and keep a high rating against lower rated players
>you need to win a much higher percentage of matches, and thus
>play good bg too, as long as you don't apply
>some very specific cheats.
>
hard to believe that an 1800-rated player who plays 1450-average players
is as capable as an 1800-rated player who plays 1800-average people as a
steady diet. I still think it would be an interesting factor to know, and
would certainly influence my decisions on who to challenge, since I'm
looking to learn.
>In addition, an unwelcome sideeffect of your suggestion might be
>that higher rated players refuse to play lower rated players, in
>order to keep their opponent-rating-factor high.
>
>funk
My initial post recognized the slight possibility that this could happen,
but I think the main result would be to point up very significant
differences in ratings of players and their opponents, rather than stop
people from playing most players who invite them.I, for one, would
continue to seek out higher rated players like you, but would continue to
accept invitations from just about anyone, regardless of rating, because
it's more fun that way. I guess the bottom line for me is that everyone
knows that a Notre Dame football team with a 6-4 record is still a better
team than an undefeated Dipstick State team, due to strength of schedule.
I'm simply suggesting that, while Fibs ratings take the opponent's rating
into effect in recalculating a player's new rating, the additional
barometer I'm urging might simply shed even more light on the situation.
Of course, that's just my opinion - I'm usually wrong.
Dave Sandler (bar_ky)
Peter Fankhauser
w...@world.std.com (Walter G Trice) wrote:
>
> The question raised was "what is the correct doubling strategy in
> a 2 point match when the players are not equal in skill?"
Nah, the question was indeed "what is the correct doubling strategy
for a player with higher skill who knows about the correct
strategy against someone who does NOT know
about the correct strategy - but for example, follows a "simple"
moneygame strategy".
>
> Of course it is often true in practice that A WILL have a better
> strategy because B WON'T turn the cube when he should.
>
Indeed, that case appears to be more complex than I originally had
anticipated.
funk
TuggyBear
Peter Fankhauser <fank...@darmstadt.gmd.de> wrote:
(snip)
>The whole thing might further be influenced by the volatility
>of a position, that is, are there any big swings on next turn, or is
>the position fairly stable. But probably r.g.b is not anymore the
>appropriate place to discuss this, without getting flamed for using
>elitist jargon.
>funk
Newbie here...
I disagree. It seems to me that r.g.bg. should be a place for discussions about
any level of backgammon. People have been very kind to me in answering my newbie
questions, and I have read your "elitist" stuff with interest. How else will I
learn except by challenging myself to understand complex information? Please
continue....
Tuggy
Fredrik Dahl
Hi all,
I've been through this before in here, but ok...
At (-2,-2) or 2-away-2-away (like 5-5 in a 7pt match)
it is not an error to double right away.
If someone thinks this is wrong, he should be willing to
prop it against me, giving me a small money compensation
for making this error every time.
Now THAT would be silly, as each match is obviously 50-50,
because I double him in right away every time.
Fredrik Dahl.
Tim Mirabile
John Quinnelly <jo...@ntr.net> wrote:
>Peter Fankhauser wrote:
>>
>
>> > For example, if you used 80% and 40% instead of 70% and 30%, you would get
>> > 0.8*s1 + g1 + 0.4*s2 < s1 + g1, which is s1 > 2 * s2... which means the expert
>> > would need _twice_ the chance of a single game victory against a single game
>> > loss before a double.
>>
>>Could you explain this in plain english? Is it better for a more experienced player to
>double a less experienced player at 2-away, 2-away? And if so why? Sorry, but the
>equation means absolutely nothing to me!
Let me take a shot at this. I'm not that experienced at match play, so if I
can put this into words that I can understand, then you should be able to
understand them too. :)
If it were not for the Crawford rule the 2-away, 2-away game would be almost
meaningless. Each player needs only to avoid a gammon, even at the cost of
giving away the single game. And if one player gets an edge and tries to
double, the other will simply drop. In either case, the player who is behind
after this game will immediately double in the following game, forcing a single
game for the match anyway.
The Crawford rule prevents this double, meaning that the player who goes down
to 2-away, 1-away needs to win the next two games, or gammon in the first, with
both games going all the way down to the last roll without any help from the
cube.
Now I think you have it backwards up there. At 2-away, 2-away, the weaker
player in a mismatch should double immediately and take his chances in a single
game for the match, hoping that he gets good dice. The immediate double here
takes some of the skill out of the game - no more cube handling, no more
worrying about getting gammoned, so it becomes somewhat of an equalizer.
The stronger player should prefer to try to grind out two points, knowing that
if he wins the first, he only needs to win one point out of the next two. And
if he gets bad dice and loses a single, he still has a fair chance to try to
win the next two anyway. By holding off with the cube, if he does get a strong
game as he is favored to do anyway, he will then double and either go to the
Crawford game if dropped, or play a much more favorable game for the match if
taken.
By waiting to double, the weaker player opens himself up to a situation where
he might gets a few good rolls and a good position. Now if he tries to double,
the opponent has the option of dropping, where if the weaker player had doubled
immediately, where the stronger player would be practically forced to take, and
then he would not have this option.
The same problems hold to a lesser extent when the players are evenly matched.
By not doubling, you give the opponent a chance to see what your roll is before
deciding to toss out the cube himself. Each time either player waits to
double, he gives the other the option to do so with better information.
+-----------------------------------------------------------------------------+
| Tim Mirabile <t...@mail.htp.com> http://www.angelfire.com/pg9/timm/ |
| TimM on FICS. TheSentinel on FIBS. PGP Key ID: B7CE30D1 |
+-----------------------------------------------------------------------------+
Gerald Dahlin
Peter Fankhauser wrote:
snip..
> The whole thing might further be influenced by the volatility
> of a position, that is, are there any big swings on next turn, or is
> the position fairly stable. But probably r.g.b is not anymore the
> appropriate place to discuss this, without getting flamed for using
> elitist jargon.
>
> funk
I appreciated your sharing the concept of doubling early when at
-2, -2. Although I'm not a newbie, I had not recognized this
before. Thanks for the posting, Peter.
Jerry Dahlin
mpls on FIBS
michael rochman
Peter Fankhauser <fank...@darmstadt.gmd.de> wrote:
[much snipped]
>> Of course it is often true in practice that A WILL have a better
>> strategy because B WON'T turn the cube when he should.
>Indeed, that case appears to be more complex than I originally had
>anticipated.
Funk,
Am I missing something here?
It would appear to me that were I to consider you to be
better than me, and were I ahead , I'd want the action as
large as possible. I must maximize my cash management to
beat you...win more when I do win. Or I must depend upon
sheer luck.
Were you a lesser opponent than me, I'd want to drag out the
action in order that you'd have sufficient time to hang
yourself. I would want to minimize cash management as a tool
and have skill become the denominator.
As a rule, the above is simple to follow and usually
correct. I know there are a myriad of exceptions, but if
ignored, the policy is still pretty sound; perhaps more so
in a money game than in a match. But, sound either way.
mike
John Quinnelly
(clipped the math lesson)
> >>Could you explain this in plain english? Is it better for a more experienced player to
> >double a less experienced player at 2-away, 2-away? And if so why? Sorry, but the
> >equation means absolutely nothing to me!
(clipped lots of good stuff)
> The stronger player should prefer to try to grind out two points, knowing that
> if he wins the first, he only needs to win one point out of the next two. And
> if he gets bad dice and loses a single, he still has a fair chance to try to
> win the next two anyway. By holding off with the cube, if he does get a strong
> game as he is favored to do anyway, he will then double and either go to the
> Crawford game if dropped, or play a much more favorable game for the match if
> taken.
Thanks for the explaination. (thanks also to the others who tried to render it in a way
I could understand). Your statement here illustrates part of the reason I didnt' follow
it. I have been led to understand that a stronger player wants longer matches so that
his skill will be more of a factor then luck( as you stated here), but the equation
_seemed_ to say (or at least the first commentary on it) that the stronger player should
double immediately. That seemed contrary to what I knew and I became confused.
Thanks again.
screwtape
'Intelligence guided by experience', Nero Wolfe.
Bill Taylor
fred...@ifi.uio.no (Fredrik Dahl) writes:
|> At (-2,-2) or 2-away-2-away (like 5-5 in a 7pt match)
|> it is not an error to double right away.
|>
|> If someone thinks this is wrong, he should be willing to
|> prop it against me, giving me a small money compensation
Yeah yeah. If you can get over your truculence you might learn something.
It is not exactly "wrong", in that it is an optimal strategy, as you say.
However, it is still inferior, in that there are other optimal strategies
that do better when the opponent plays *less than* optimally. If you'd
bother to read what other folk have taken a lot of trouble to write up,
you might get the point.
Here is a simplified situation, from a much simpler game.
OPPONENT:
OC1 OC2 <---- opponent's choices
------------
Choice 1 || 4 4 ||
YOU: Choice 2 || 2 3 || <--payoffs to you.
Choice 3 || 6 4 ||
------------
It's the payoff matrix for a simple one-(simultaneously, hidden)-choice-each
zero-sum game.
Your choice 1 is optimal, and you can play it with a clear conscience.
You will win 4.
Your choice 2 is just plain wrong and bad, you will win only 3, (maybe only 2).
But your choice 3 is "the best", making choice 1 just a little bit wrongish.
Choice 3 will still only win you 4; unless the opponent goes mad and plays OC1.
A sensible opponent will always play OC2, so it doesn't matter if you pick 1
rather than 3. But every so often there is a stupid oponent who plays OC1,
and you don't know exactly who they are, (though you can bet Kit & Patti
are excluded!) So; you may as well play the "best" choice 3, and win more.
Please keep your silly remarks about props to yourself. Of course they're
correct legalisticly, but you will make less than the rest of us against
the bunnies.
True, there are no hidden moves in BG; but it is still very similar.
Instant doubling is like choice 1. Careful occasional waiting is like choice 3.
----
But in spite of all my arrogant remarks I still play choice 2 myself,
occasionally, by oversight, and even OC1....
-------------------------------------------------------------------------------
Bill Taylor w...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
The answer may be right but it's not the answer I want.
-------------------------------------------------------------------------------
John Graas
Peter Fankhauser <fank...@darmstadt.gmd.de> wrote:
[snip]
>(btw. I think Tomas Szabo has produced
>match-equity tables for players with different skill, they can be
>found via Stephen Turners WWW-pages).
[snip]
I have a question about this. What is everybody's opinion about which
table is most practical to use over-the-board??
I curious whether it is your experience that it is easier to use Kit's
table and do the calculations on-the-fly, or is it easier to memorize
one of the published expansions of the base table for use during a
match??
John
"Have Laptop -- Will Travel"
Standard Disclaimers Apply
Oz Childs
Bill Taylor (mat...@math.canterbury.ac.nz) wrote:
: fred...@ifi.uio.no (Fredrik Dahl) writes:
:
: Instant doubling is like choice 1. Careful occasional waiting is like choice 3.
:
: ----
:
: But in spite of all my arrogant remarks I still play choice 2 myself,
: occasionally, by oversight, and even OC1....
:
: -------------------------------------------------------------------------------
: Bill Taylor w...@math.canterbury.ac.nz
: -------------------------------------------------------------------------------
: The answer may be right but it's not the answer I want.
: -------------------------------------------------------------------------------
Ha! I do it to, by oversight or plain curiosity. But it makes sense
that the weaker player should double. Say you go into the game against a
stronger opponent with only a 40% chance of winning. So if you double,
the match is decided in one game, and your chance of winning the match
is....40%. If you don't double, you will either (a) end up taking your
superior opponents double at a time when his odds of winning are even
greater or (b) have to play at least two games, maybe three, for the
match. Thirty-six times out of 100 (.6 times .6), your opponent will
beat you 2-0. Only sixteen times out of 100, you will beat your opponent
2-0. In the remaining 48 times out of 100, you will play a third game
for the match, and you will win only 19 or 20 of those games. You can
see that by playing multiple games, rather than a single game, your
chances of winning the match have gone down from 40% to maybe 35%, if
your opponent does not double in the first game, and even worse if he does.
Fredrik Dahl
> OC1 OC2 <---- opponent's choices
> ------------
> Choice 1 || 4 4 ||
>YOU: Choice 2 || 2 3 || <--payoffs to you.
> Choice 3 || 6 4 ||
> ------------
>
>It's the payoff matrix for a simple one-(simultaneously, hidden)-choice-each
>zero-sum game.
>
>Your choice 1 is optimal, and you can play it with a clear conscience.
>You will win 4.
>
>Your choice 2 is just plain wrong and bad, you will win only 3, (maybe only 2).
>
>But your choice 3 is "the best", making choice 1 just a little bit wrongish.
>Choice 3 will still only win you 4; unless the opponent goes mad and plays OC1.
>
>A sensible opponent will always play OC2, so it doesn't matter if you pick 1
>rather than 3. But every so often there is a stupid oponent who plays OC1,
>and you don't know exactly who they are, (though you can bet Kit & Patti
>are excluded!) So; you may as well play the "best" choice 3, and win more.
>
>Please keep your silly remarks about props to yourself. Of course they're
>correct legalisticly, but you will make less than the rest of us against
>the bunnies.
>
>True, there are no hidden moves in BG; but it is still very similar.
>
>----
>
>But in spite of all my arrogant remarks I still play choice 2 myself,
>occasionally, by oversight, and even OC1....
>
>-------------------------------------------------------------------------------
> Bill Taylor w...@math.canterbury.ac.nz
>-------------------------------------------------------------------------------
I agree completely (except for my prop being silly, I think it's an elegant
proof that that doubling right away is ok...). This is one of the best
article I've seen in here on this subject.
Btw, one can proove that the 'best' of the optimal strategies is to wait till
the first time you have a marketloser.
Also one can proove that if both players use one optimal strategy or another,
the game will be played to the end with the cube on 2, so gammons should be
disregarded from the start.
Optimal play against a weak opponent is indeed very nontrivial,
and I must admit that I do speculate quite a bit myself.
But one thing is clear: for the bunnies cubing right away must be
just as correct as it is for the heffalumps not to.
Fredrik Dahl.
Geraldine Peabody
hello FIBSters,
there will be a mini fibs gathering on sunday august 18th in the early
evening near the university of maryland campus.....
a few of us are going to meet in a local bar/restaurant for a few hours
of eating, drinking and general fun !
IF you are in the area and would like more information please contact
me via e mail OR message me at FIBS, username peabod :)
hoping to see a few of you there !
peabod
Peter Fankhauser
71242...@compuserve.com (John Graas) wrote:
>
> I have a question about this. What is everybody's opinion about which
> table is most practical to use over-the-board??
>
> I curious whether it is your experience that it is easier to use Kit's
> table and do the calculations on-the-fly, or is it easier to memorize
> one of the published expansions of the base table for use during a
> match??
I guess this really depends on you. I know the equities up to
5-away, 5-away, and with some hard work could produce it up to 7-away
7-away. Others use Neils Numbers, or the Janowski Formula, or
Stephen Turner's Formula. But then, unless it is one roll-situations,
I find it very hard to estimate the equities beyond a general
"hmmmm, I'm ahead - gammons really hurt me..., or ha! I'm 2-away
in a pure race I can take almost "anything".
Maybe the new Jacobs&Trice book contains some better advice?
Boy, if it just wasn't so complicated to send money from Europe
to the US. When will there be a distributor for bg-literature,
who is willing to sell me stuff, and accepts credit card?
funk
Sheldon Richter
FIBS D.C. gathering this Sunday <aug 18th> @ 5pm @ Pizzeria Uno at
Connecticut Ave and Ordway
: Geraldine Peabody (pea...@magik.albany.net) wrote:
: hello FIBSters,
: peabod
: http://www.albany.net/~peabod
--
magic_one
Erik Gravgaard
The Backgammon Shop in Denmark offers a full ane of products.
Books, dice, boards, position cards, computer programs - you name it.
- and we accept credit cards.
Erik Gravgaard,
President of
The EMG Group
Gersonsvej 25
DK-2900 Hellerup
DENMARK
bob koca
er...@pip.dknet.dk (Erik Gravgaard) wrote:
>Peter Fankhauser <fank...@darmstadt.gmd.de> wrote:
>>71242...@compuserve.com (John Graas) wrote:
>>>
>>> I have a question about this. What is everybody's opinion about which
>>> table is most practical to use over-the-board??
>>>
>>> I curious whether it is your experience that it is easier to use Kit's
>>> table and do the calculations on-the-fly, or is it easier to memorize
>>> one of the published expansions of the base table for use during a
>>> match??
>>
>>I guess this really depends on you. I know the equities up to
>>5-away, 5-away, and with some hard work could produce it up to 7-away
>>7-away. Others use Neils Numbers, or the Janowski Formula, or
>>Stephen Turner's Formula. But then, unless it is one roll-situations,
>>I find it very hard to estimate the equities beyond a general
>>"hmmmm, I'm ahead - gammons really hurt me..., or ha! I'm 2-away
>>in a pure race I can take almost "anything".
>>
Rather than memorize the match equity table and then use this to
find doubling windows during a match , I think it is worth it to just
memorize the last roll doubling windows and gammon prices for all
the cube levels for small matches. I suggest up to 5 away 5 away.
It will be a small effort to do this but think about how often you
would be doing the exact same calculations during your backgammon
playing life. Wouldn't you rather spend the over the board time
analyzing the position instead of doing match equity math in your
head. (Of course must do mental math for checker plays often.)
,Bob Koca
bobk on FIBS
Peter Fankhauser
ko...@bobrae.bd.psu.edu (bob koca) wrote:
>
> Rather than memorize the match equity table and then use this to
> find doubling windows during a match , I think it is worth it to just
> memorize the last roll doubling windows and gammon prices for all
> the cube levels for small matches. I suggest up to 5 away 5 away.
>
I've heard this term now quite often, but neither Kit Woolsey's
monography on Tournament Backgammon, nor Tom Keith's pages on
cube strategy in matches (nor his glossary btw) use this term.
Although the market-window-tables (takepts for both players)
for different gammon rates in TK's pages might be a different
perspective on this.
If anyone knowledgeable cares to post doubling window table
(that's the easy part) + a definition of gammon prices + a
few hints how to use this stuff (that is how to adjust the
doubling window according to the gammon price) I'd be very greatful
(and I assume lots of others too:)
funk
Chuck Bower
In article <4vnjog$6...@news.erie.net>, bob koca <ko...@bobrae.bd.psu.edu> wrote:
(snip)
> Rather than memorize the match equity table and then use this to
>find doubling windows during a match , I think it is worth it to just
>memorize the last roll doubling windows and gammon prices for all
>the cube levels for small matches. I suggest up to 5 away 5 away.
>
> It will be a small effort to do this but think about how often you
>would be doing the exact same calculations during your backgammon
>playing life. Wouldn't you rather spend the over the board time
>analyzing the position instead of doing match equity math in your
>head. (Of course must do mental math for checker plays often.)
(snip)
Bob, although I often agree with your informative postings, on this
one I cannot. The reason is that the doubling window depends (often
STRONGLY) on gammons. If you memorize a table of doubling windows,
you are assuming some fixed gammon fraction, which is often (most
of the time?) not applicable. If you memorize a table (like the
Woolsey-Heinrich table), then you can fold in the gammon fractions
to get a doubling window which is "customized" to the position you
are considering.
Here is an example:
What is the drop point for a player who is leading 2-away, 4-away?
Dropping leaves 2-away, 3-away = 60%
Taking and winning: WIN Match = 100%
Taking and losing non-gammon: tied at 2-away = 50%
Taking and losing gammon: LOSE Match = 0%
So, if the trailer (who is about to double?) has a gammon fraction
(defined as gammon win chances divided by total winning chances) of
"f", then the match leader (about to be looking at a cube?) is risking
0.6 - (1-f)*0.5 to gain 0.4 and the drop points are then
0.6 - (1-f)*0.5 0.1 + 0.5*f
--------------- = -----------
1.0 - (1-f)*0.5 0.5 + 0.5*f
Or in tabular form for some possible gammon fractions:
f leader's drop point
0 20%
0.2 33%
0.4 43%
0.6 50%
As you can see, the drop point depends strongly on gammon fraction.
In the heat of battle (over the table), you will have to estimate
gammon fraction before doing the calculation. Then when you find
your drop point (as calculated above), you will have to deicde your
winning chances for the position under consideration. Is this
feasible? I believe so. JF and Loner do it, and I sure don't want
to admit they're smarter than me (oops, I already did in a previous
posting... Oh, well).
Chuck Bower
bo...@bigbang.astro.indiana.edu
P.S. For those curious readers who want to see more of the above
type of discussion, see my article in the August Flint Newsletter
(which CJC will be mailing this, week, I think.)
Ron Karr
Peter Fankhauser wrote:
> Just, what exactly is the famed "gammon price"?
> I've heard this term now quite often, but neither Kit Woolsey's
> monography on Tournament Backgammon, nor Tom Keith's pages on
> cube strategy in matches (nor his glossary btw) use this term.
> Although the market-window-tables (takepts for both players)
> for different gammon rates in TK's pages might be a different
> perspective on this.
>
> If anyone knowledgeable cares to post doubling window table
> (that's the easy part) + a definition of gammon prices + a
> few hints how to use this stuff (that is how to adjust the
> doubling window according to the gammon price) I'd be very greatful
> (and I assume lots of others too:)
The gammon price represents the relative value of a gammon swing vs a
win-loss swing. In money games, the gammon price is always 50%. It's
computed as:
GP = (equity from winning a gammon - equity from winning a plain game)
divided by (equity from winning a plain game - equity from losing a plain
game)
or GP = (G-W)/(W-L)
For money (G-W) is one unit, (W-L) is 2 units, so GP is 50%.
This figure is used in a couple of ways:
1. To adjust the take point to account for gammons. If I expect to get
gammoned x%, I need to add x% times the gammon price to my basic take
point. So for money, if I expect to be gammoned 20% of the time, I need an
additional 10% wins over the basic 25%, or 35%, to take.
2. To calculate play decisions. If I'm considering taking extra risks to win a
gammon, I can take the risk as long as my extra losses are no more than 50%
of my extra gammons. Conversely, if I'm risking losing a gammon in order
to try for the win, I must make sure that my extra wins are more than 50% of
my extra gammon losses.
(As far as computing the minimum doubling point, I don't know how to use the
gammon price. People seem to estimate a % of gammons and factor that into the
normal calculations.)
In match strategy, the gammon price can vary from 0 to 100%. For example,
at Crawford-odd, the trailer's gammon price is approximately zero; at
Crawford-even, it's 100%. (The leader's gammon price is zero in both cases)
At a score of 2-away, 4-away, for example, you need to know the gammon
price for both players, with a 1-cube or a 2-cube.
Leader, 1-cube: GP = (100 - 83)/ (83 - 60) = 74%
Leader, 2-cube: GP = (100-100)/(100-50) = 0
Trailer, 1-cube: GP = (50-40)/(40-17) = 43%
Trailer, 2-cube: GP = (100-50)/(50-0) = 100%
(There are some extra variables too, like what happens if both players have
significant gammon chances? For money, you can use net gammons times
gammon price to compute the offset to the take point. But in matches, where
each side's gammons are worth different amounts, it gets complicated and
I'm not really sure what the formula is.)
Ron
bob koca
bo...@bigbang.astro.indiana.edu (Chuck Bower) wrote:
>In article <4vnjog$6...@news.erie.net>, bob koca <ko...@bobrae.bd.psu.edu> wrote:
> (snip)
>> Rather than memorize the match equity table and then use this to
>>find doubling windows during a match , I think it is worth it to just
>>memorize the last roll doubling windows and gammon prices for all
>>the cube levels for small matches. I suggest up to 5 away 5 away.
>>
>> It will be a small effort to do this but think about how often you
>>would be doing the exact same calculations during your backgammon
>>playing life. Wouldn't you rather spend the over the board time
>>analyzing the position instead of doing match equity math in your
>>head. (Of course must do mental math for checker plays often.)
> (snip)
>Bob, although I often agree with your informative postings, on this
>one I cannot. The reason is that the doubling window depends (often
>STRONGLY) on gammons. If you memorize a table of doubling windows,
>you are assuming some fixed gammon fraction, which is often (most
>of the time?) not applicable. If you memorize a table (like the
>Woolsey-Heinrich table), then you can fold in the gammon fractions
>to get a doubling window which is "customized" to the position you
>are considering.
I memorized doubling windows for the case of no gammons.
Gammon prices can be used to adjust for the amount of gammons.
Let me first define what I mean by gammon price.
Gammon price tells you how much of a bonus you should consider a
gammon win giving you. It can be used to decide how much risk to
accept if playing on for the gammon instead of cashing and also
how much extra vig you get on cubes because of the gammon chances.
I find it easiest to calculate by considering the play on or cash
decision. Let's illustrate first for money play. I''ll show the
technique for match play on the problem you pose below.
If have a cash then can get 1 *cube for sure. By not cashing you
risk losing the game and get -1*cube point. Thus the risk is 2*cube
points of swing. If you gain the gammon you get 2*cube instead of
1*cube. Thus the swing is 1*cube.
Some of the time you win the single game anyways. Then your
decision to play on breaks even. Since the risk is twice as large
as the gain, the times you will win the gammon by playing on must be
twice as often as times you blow it and lose. Gammon price is the
ratio of gain to risk. 1/2 in this case.
The other way it can be used is calculating equity if one takes.
Suppose that you are being cubed and will win single 30%, lose
a single 50% and lose a gammon 20%. Since the gammon price is
1/2 , the 20% of the time you get gammoned is like you winning 10%
less of the games. Thus it is like you winning 20% single and losing
80% single. Thus is a pass.
>Here is an example:
>What is the drop point for a player who is leading 2-away, 4-away?
>Dropping leaves 2-away, 3-away = 60%
>Taking and winning: WIN Match = 100%
>Taking and losing non-gammon: tied at 2-away = 50%
>Taking and losing gammon: LOSE Match = 0%
>So, if the trailer (who is about to double?) has a gammon fraction
>(defined as gammon win chances divided by total winning chances) of
>"f",
For the way I do these it is much easier to think about proportion
of total games which will be gammons rather then the proportion of
total wins which will be gammons.
Let's first find the gammon price for trailer if cube is on 2.
(keep in mind that G.P. can change as cube value changes and sometimes
this is very important to keep in mind.)
The idea is same as the money play example but of course we must
measure gain and risk in terms of match winning chances rather than
just points won or lost.
I know this would be a bizarre situation but suppose that trailer
is holding a 2 cube and is considering playing on for a gammon.
( Just find it the easier way to calculate it).
If cash can get 50% match winning chances for sure.
If get the gammon have 100% chance and if blow the game
have 0% chance. Since risk and gain is the same the gammon price
equals 1. Another way of thinkiing about this is that winning the
gammon is just as important as winning the game.
The gammonless cash point for the trailer at 4 away 2 away is
80%. Thus if the leader gets doubled he can think like this:
How often will I lose the game? How often will I get gammoned.
Add the losing chances and 1* get gammoned chance.
As examples if doubler will win no gammons can take if win 20%
of the games. If doubler wins 30% gammons can take only if win
50%.
then the match leader (about to be looking at a cube?) is risking
>0.6 - (1-f)*0.5 to gain 0.4 and the drop points are then
> 0.6 - (1-f)*0.5 0.1 + 0.5*f
> --------------- = -----------
> 1.0 - (1-f)*0.5 0.5 + 0.5*f
>Or in tabular form for some possible gammon fractions:
> f leader's drop point
> 0 20%
> 0.2 33%
> 0.4 43%
> 0.6 50%
If you have the estimates of winning chances and f, my method
is just as easy.
>As you can see, the drop point depends strongly on gammon fraction.
>In the heat of battle (over the table), you will have to estimate
>gammon fraction before doing the calculation. Then when you find
>your drop point (as calculated above),
If memorize the gammonless doubling window and gammon prices
can bypass this step. That is why I never bothered learning doubling
windows based on certain gammon rates ( I think Tom Keith's tables are
like this). They are not as easily adjusted when gammon rates are
away from the assumed values.
you will have to deicde your
>winning chances for the position under consideration. Is this
>feasible? I believe so. JF and Loner do it, and I sure don't want
>to admit they're smarter than me (oops, I already did in a previous
>posting... Oh, well).
> Chuck Bower
> bo...@bigbang.astro.indiana.edu
>P.S. For those curious readers who want to see more of the above
>type of discussion, see my article in the August Flint Newsletter
>(which CJC will be mailing this, week, I think.)
Here is a slightly more involved question dealing with match play.
First some background information:
At 3 away 4 away, let's suppose that you believe in a match equity
table ( I use Kit's in Tournment Backgammon for this except changes
2 away 4 away to 67.5% instad of 68% BTW anyone know latest
developments here?) which gives
The gammonless doubling window for the leader
on a 1 cube is [39,64] ( I estimate that in a race need to get to
74% to cash becasue of much increased cube vig for 4 away player.)
on a 2 cube is [70,87]
GP(1 cube) = 8/9
GP(2 cube) = 2/5
For the trailer doubling window is
on a 1 cube [61,76.5]
on a 2 cube [30,60]
GP(1 cube)= 4/7
GP(2 cube)= 9/10
Now for the situation. Player X is 4 away player and gets doubled.
X believes that he will virtually never get gammoned and can win
12% single games and 10% gammons. The 22% of time that X wins
is close to the 26% X thinks he needs. Adding in the gammon vig as
counting 9/10 * 10* = 9% extra gives 31%. so X thinks easy take.
What error did X make?
Do the computers make this same error?
Chuck Bower
In article <4vtr0q$n...@news.erie.net>, bob koca <ko...@bobrae.bd.psu.edu> wrote:
(SNIP a whole bunch of explanation of his method of determining the
doubling window WITH gammons included).
OK, Bob, now I think I understand your preference. It appears that your
method and the one I described are equivalent (that is they come up with the
same answer). The differences are operational: your's requires more
memorization, mine more calculation. Flip that coin!
One other thing I do (which is also touched upon in the upcoming Flint
Newsletter) is to include the take equity IN A RIGOROUS WAY. That is,
I actually calculate it, I don't just "guess". I assume you either do
this, or can adjust your algorithm to do the same.
Now, I was looking forward to working your problem, but got
confused (were there typo's??). It follows (with my questions):
>
> Here is a slightly more involved question dealing with match play.
>
> First some background information:
>
> At 3 away 4 away, let's suppose that you believe in a match equity
>table ( I use Kit's in Tournment Backgammon for this except changes
>2 away 4 away to 67.5% instad of 68% BTW anyone know latest
Hold it. -3,-4 is 59%, I recall. Did you mean "2 away, 4 away"?
>developments here?) which gives
>
> The gammonless doubling window for the leader
>on a 1 cube is [39,64] ( I estimate that in a race need to get to
>74% to cash becasue of much increased cube vig for 4 away player.)
>on a 2 cube is [70,87]
>GP(1 cube) = 8/9
>GP(2 cube) = 2/5
>
> For the trailer doubling window is
>on a 1 cube [61,76.5]
>on a 2 cube [30,60]
>GP(1 cube)= 4/7
>GP(2 cube)= 9/10
>
>
> Now for the situation. Player X is 4 away player and gets doubled.
Halt, again. Are we talking about 3 away, 4 away? The previous
inconsistency has me confused. Please verify what score we're concerned
with.
>X believes that he will virtually never get gammoned and can win
>12% single games and 10% gammons. The 22% of time that X wins
> is close to the 26% X thinks he needs. Adding in the gammon vig as
>counting 9/10 * 10* = 9% extra gives 31%. so X thinks easy take.
>
> What error did X make?
> Do the computers make this same error?
>
>
>
>,Bob Koca
>bobk on FIBS
>
Anxiously awaiting your reply....