Calculating the take point considering gammons
bmorgul
gammons
If I am wrong please correct.
Method 1:
First calculating the take point using match equity table then
adjusting the take point with gammon price
Method 2:
Calculating take point using weighted average equity which is
calculated with non-gammon equity and equity with gammon.using match
equity table.
I calculate different take points for each method for same match
conditions.
Which is right. I do not know.
Please can you explain this?
BM
paulde...@att.net
It seems normal to me that different methods will lead to different
take points (so long as they're not wildly different.)
Here's why.
Suppose you have the following info:
Match score, cube value, probabilities for each player of winning
singles, gammons, and backgammons.
Then this is not enough info to calculate cube actions with total
accuracy. For example, you need to consider volatility etc.
Thus "take points" only give a very approximate guide to cube actions
because they leave out important info.
And, whenever you deal with approximations, you should expect that
different approximations give you different answers.
Paul Epstein
Adam Tansley
Firstly, Paul says "Suppose you have the following info: Match score,
cube value, probabilities for each player of winning singles, gammons,
and backgammons. Then this is not enough info to calculate cube
actions with total accuracy. For example, you need to consider
volatility etc."
This is wrong. Volatility has nothing whatsoever to do with take-
points. It should enter your calculations when deciding whether to
double or not, but for take-points the probabilities you mention are
all that are required. It makes no difference whether you win 25% of
games from a volatile position or a non-volatile position - you still
win 25% of games.
Ok, BM. I have wondered about this question in the past as well. If
you follow Kit Woolsey's advice you use the average weighted equites.
On the other hand I have seen top players such as John O'Hagan and
Neil Kazaross advocate the first method you outline, using gammon
values. And you're right, these two methods give conflicting answers.
The answer is that using weighted equites gives the correct take-
point. This can be checked by calculating the various match equities
for wins, gammons etc, assuming you win exactly the same percentage as
your calculated take-point. You will arrive at the match equity for
passing. What's more, this method gives a take-point that exactly
agrees with that given by gnubg in the market window.
I'm not sure why some use the gammon value for calculating take-
points. It doesn't seem any simpler, given that you have to use as
many different match equities to calculate the gammon value as you do
for calculating the weighted average. Possibly, some players do not
calculate the gammon value (perhaps memorising g.v.s for various
scores) in which case there would seem to be slightly less work to do,
albeit for an approximation to the correct answer. Given that there
has been some discussion on GOL recently re. an algorithm to calculate
match equities of the g11 table to an accuracy of less than 1% over
the board, I doubt that an approximation is the desired outcome.
So stick with Woolsey's weighted average method, and your take-points
should be accurate - given that you correctly estimate the gammon
rate. Now you just need to be sure that you are then capable of
estimating your win chances as accurately!
tansley
bob
> On 5 Aug, 11:32, bmorgul <bmor...@yahoo.com.tr> wrote:
>
>
>
>
>
> > I saw 2 methods in the posts.for calculating take point considering
> > gammons
> > If I am wrong please correct.
> > Method 1:
> > First calculating the take point using match equity table then
> > adjusting the take point with gammon price
> > Method 2:
> > Calculating take point using weighted average equity which is
> > calculated with non-gammon equity and equity with gammon.using match
> > equity table.
>
> > I calculate different take points for each method for same match
> > conditions.
>
> > Which is right. I do not know.
> > Please can you explain this?
>
> > BM
>
> Firstly, Paul says "Suppose you have the following info: Match score,
> cube value, probabilities for each player of winning singles, gammons,
> and backgammons. Then this is not enough info to calculate cube
> actions with total accuracy. For example, you need to consider
> volatility etc."
>
> This is wrong. Volatility has nothing whatsoever to do with take-
> points.
Perhaps Paul meant "cubeless probabilities of winning singles,
gammons, and backgammons". Estimating cubeless first is usually more
straightforward
then estimating cubeful directly. Once you have your cubeless
estimates you factor in the cube value in which future volatility is
relevant to arrive at
your cubeful estimate.
>Ok, BM. I have wondered about this question in the past as well. If
>you follow Kit Woolsey's advice you use the average weighted equites.
>On the other hand I have seen top players such as John O'Hagan and
>Neil Kazaross advocate the first method you outline, using gammon
>values. And you're right, these two methods give conflicting answers.
I also use the first method. Let's use 2 away 4 away, with 4 away
player doubling as an example.
The gammon price is 1 and in the absence of gammons the cashpoint is
19.9%. On a 2 cube the gammon price
is +1. So if I am getting doubled as 2 away player what I would do is
to estimate the percent of games that
opponent wins (of any sort) and then add a +1 bonus (the gammon price
for me) for any gammon/bg wins.
If that puts my opponent at 80.1% or more its a pass. For example If
I estimate that opponent wins 70.1% of the games (at any level)
and that will win 10% of the games a t abonus level it is a breakeven
decision.
I don't see anyhting wrong with that at all so could you demonstrate
how Woolsey's method would do it? Are you sure there is not an
inconsistency with definitions? In the method above think of gammons
as a percentage of all games. In the other method though I think the
gammon rate
is considered as a percentage of all wins.
In the first method you just need the gammon price once for the
entire game. Then once you have your estimates it involves adding
and multiplying gammon estimate by gammon price. The weighted average
seems to involve more calculations. Also isn't it easier
to think of gammon% in terms of total games instead of games won?
Results of rollouts are given that way for example.
Bob Koca
robadams
I'm also not surprised that you get different answers, but it might be
useful in order to more fully try to answer the question if bmorgul
would share how the two different answers were calculated.
Say a 7 point match with your opponent doubling while trailing 1-2 or
while you are at -5,-6 and have to decide whether to take the initial
double, like here:
GNU Backgammon Position ID: 4PPgAVDMTvABMA
Match ID : MJn6ABAAEAAA
+12-11-10--9--8--7-------6--5--4--3--2--1-+ O: o
| X O | | O O O X | 1 point
| X | | O O O |
| X | | O |
| X | | |
| | | |
^| |BAR| |
| O | | X |
| O X | | X |
| O X | | X |
| O X | | X O | Cube offered at 2
| O X | X | X O | 2 points
+13-14-15-16-17-18------19-20-21-22-23-24-+ X: x
How would you try to use these two methods to get a take point...
perhaps guess that O wins 30% gammons and loses 10%?
In general I think that finding take points is very difficult and well
worth some study. Here's a little article about one match score
without gammons involved:
robadams
wins. Ok, so as X guess perhaps 45% of your losses are gammon losses
and 20% of your wins are gammon wins. What then is your take point on
the initial double at -5,-6?
paulde...@att.net
>
> - Show quoted text -
Adam,
Even given Bob's correction, that I should have said "cubeful
gammons, ... etc",
you are clearly wrong that only cubeful probs of gammons, singles etc.
need to be considered.
For example, for money (and there are match scores that play almost
exactly like money), there is a position which is an exactly marginal
take/pass where there are no gammons at all, and where the taker/
dropper has 18.75% cubeful wins (assuming the initial offerer is
prepared to take recubes unless taking actually loses equity).
However, in most no-gammon positions, in a score that plays like
money, 18.75% wins is a clear drop.
So the probabilities I mentioned were certainly not "all that is
required" -- you need to consider future cube values.
In fact, you need to consider so many extra variables that exact
calculation of take points is impossible unless either the position or
the match score is very simple.
Hence you need approximation, which was part of the point of my
initial reply.
Paul Epstein
Adam Tansley
>
> - Show quoted text -
You're quite right Bob, it seems that different use of the term gammon
rate explains the difference.
In your example, with your opponent winning gammons in 10% of all
games, and winning 70.1% of all games at any level, this gives a
gammon rate of 14.265% (gammons as a % of wins). Then both methods
give the same answer:
Pass; 2away/3away; 59.964% MWC (using g11).
Take & win; 100% MWC.
Take & lose single; 2a/2a; 50% MWC.
take & lose gammon; 0 MWC.
A gammon rate of 14.265% gives an average MWC of 42.868% on the loss.
So I'm getting 40.036 to 17.097, which gives a take-point of 29.925%,
which exactly agrees with your figure. (By the way Paul, do you still
think these are approximations? They are both precise and accurate.)
As to the amount of calculations, do you calculate the gammon value
for each game using something like (G-W)/(W-L)? Let's take a less
trivial example, you're leading 6 away/ 13 away. So for the gammon
value, you need to derive MWCs for 6a/11a, 6a/9a and 4a/13a, then do a
calculation. Then for your take-point, you do a further calculation
involving 6a/12a, 6a/11a and 4a/13a. That's two different
calculations instead of one with Woolsey's method.
Horses for courses, perhaps.
tansley
bob
> As to the amount of calculations, do you calculate the gammon value
> for each game using something like (G-W)/(W-L)? Let's take a less
> trivial example, you're leading 6 away/ 13 away. So for the gammon
> value, you need to derive MWCs for 6a/11a, 6a/9a and 4a/13a, then do a
> calculation. Then for your take-point, you do a further calculation
> involving 6a/12a, 6a/11a and 4a/13a. That's two different
> calculations instead of one with Woolsey's method.
>
> Horses for courses, perhaps.
>
Knowing the gammon prices though has additional value beyond knowing
when to take as
they can influence checker play. Also, once you have it you have it
for that entire game
whereas with Woolsey's method you need to constantly update the
calculation as the gammon rate changes.
At 6 away 13 away though I think it is an o.k. policy for initial
takes to just play it like
a money game and then just fudge slightly if gammonish. For the 6 away
player the much more important
consideration is not the gammon price on the 2 cube but that his
recube to 4 will be less powerful.
Never heard the phrase Horses for courses.
Bob Koca
Adam Tansley
With either method, you only need to do the calculations once. With
the gammon value method, if you're calculating it, you do it once,
early in the game I guess. With Woolsey's method, you're only ever
going to be cubed to two/four etc once in the game, and you do the
calculation then.
I guess knowing the gammon value helps a bit with checker play, but
it's kind of intuitive anyway. For example, how do you play an
opening 32? At what gammon value would two down be correct? I doubt
it helps that much.
Horses for courses must be a British thing. How about each to his
own?
tansley
paulde...@att.net
As to what I think, I would like to emphasise that I have the greatest
respect for
the expertise of you and Bob K. (not to imply that others on this
thread lack expertise).
Your comments are of great value.
Are the take-point results approximations? Well, they clearly are
because METs are approximations,
and that explains why METs differ. The only non-approximate result
about METs is the completely trivial one
that, at level scores, each player has 0 match equity.
Because of this approximation, it's misleading to quote answers like
59.964%. It's an established principle of
scientific reporting that you shouldn't quote results to a higher
degree of precision than is capable of being measured.
In other words, if the MET is accurate to within 0.1%, you should
quote the result as 60.0%.
Furthermore, suppose, as a thought experiment, that it was possible to
calculate METs exactly.
Would the take-point results be approximations? Well, that depends on
the match-score. At 4 away, 2 away with the trailer doubling,
the answer is no because there is no recube.
If recubes are possible, then probs of each side getting cubeful
single wins, cubeful gammons etc. don't give enough information,
because they leave out recube possibilities. If recubes and rerecubes
are possible, then any analysis which ignores this factor can only
give approximate results.
Furthermore, no one seems to be talking about backgammon prices, so
clearly a further approximation is being made. (I approve of this
approximation because of the rarity of backgammons -- I'm just giving
reasons to indicate why this analysis is approximate.)
(In the 4 away, 2 away, trailer doubles case, backgammons don't need
to be considered.)
Paul Epstein
bmorgul
On 7 A ustos, 02:15, bob <bob_k...@hotmail.com> wrote:
> I don't see anyhting wrong with that at all so could you demonstrate
> how Woolsey's method would do it? Are you sure there is not an
> inconsistency with definitions? In the method above think of gammons
> as a percentage of all games. In the other method though I think the
> gammon rate
> is considered as a percentage of all wins.
On 7 A ustos, 12:44, Adam Tansley <a...@tansley.wanadoo.co.uk> wrote:
>You're quite right Bob, it seems that different use of the term gammon
>rate explains the difference.
Thank you all of you for answers and explanations
I solved my problem from comments above.
Method 1: (using gammon price)
Gammon rate is considered as a percentage of all games
Method 2: (using average equity)
Gammon rate is considered as a percentage of all wins
BM
paulde...@att.net
...
>
> Horsesforcoursesmust be a British thing. How about each to his
> own?
>
Yes, it's British. But it doesn't mean the same thing as "each to his
own".
"Horses for courses" gives an analogy with the horse-racing situation
where the owner carefully selects the correct horse, matching the
horse's proclivities to the course. The expression advocates adapting
to the specific situation at hand.
In your context, therefore, the phrases "horses for courses" and "each
to his own" mean completely different things -- indeed, they have
virtually _opposite_ meanings.
"Horses for courses": The method to use depends on the match score --
you should pick the method according to the score, as different scores
imply differences in which method is the easier/ more accurate.
"Each to his own" -- It's a matter of personal choice. Do what you
find easiest.
Paul Epstein