[Zelandakh]

I assume this response means you are not prepared to run the alternative forumla through your tests for comparison purposes.

[jogs]

Zelandakh, on 2013-July-05, 02:54, said:

I assume this response means you are not prepared to run the alternative forumla through your tests for comparison purposes.

Waste of time. You are free to run your own test.

[Zelandakh]

T o be honest I agree. The whole exercise is a waste of time. At least testing the idea against an alternative might have given some sort of legitimacy to the process but I see now this is as necessary for you as statistical data is for AI.

[helene_t]

Zelandakh, on 2013-July-02, 01:08, said:

and MH = modified hcp (A = 6, K = 4, Q = 2, J = 1)

See if that improves your estimate for >= 10 tricks.

it certainly does, at least as far as the ratio between the coefficients of the honours is concerned. You can see in the post I linked to that it comes reasonably close to the optimal coefficients.

[Scarabin]

Interesting thread but is the suggested method more accurate than the old Bissell system or the Roman club losing trick count?

[jogs]

POWER

Power is one of two multi-dimensional independent random variables
used for estimating tricks. High card point count is the main component
of this estimator. Most systems treat high card points as if it were the
estimator, power. The location of the HCP and how honors interact are
also components of the power estimator. Honors in long suits are worth
more than honors in short suits. Honors working together are worth
more than honors standing alone.

Point count: ace=4, king=3, queen=2, and jack=1
♠ AKQJ ♥ 432 ♦ 432 ♣ 432
♠ A432 ♥ K32 ♦ Q32 ♣ J32
♠ AK32 ♥ QJ2 ♦ 432 ♣ 432
Each is an example of a 10 point hand. They are obviously not
of exactly equal value. It is difficult to measure the exact effects
of the honors in each hand. 10 is the approximately correct value
for each hand. In statistics there is the error component in every
model to account for the deviations.
Power is the independent random variable. High card points is
the dependent variable of power which is proportional to tricks.
Therefore it is easier to use HCP to estimate tricks than the
actual independent random variable, power.

[Scarabin]

jogs, on 2013-July-09, 13:03, said:

POWER

Power is one of two multi-dimensional independent random variables
used for estimating tricks. High card point count is the main component
of this estimator. Most systems treat high card points as if it were the
estimator, power. The location of the HCP and how honors interact are
also components of the power estimator. Honors in long suits are worth
more than honors in short suits. Honors working together are worth
more than honors standing alone.

Point count: ace=4, king=3, queen=2, and jack=1
♠ AKQJ ♥ 432 ♦ 432 ♣ 432
♠ A432 ♥ K32 ♦ Q32 ♣ J32
♠ AK32 ♥ QJ2 ♦ 432 ♣ 432
Each is an example of a 10 point hand. They are obviously not
of exactly equal value. It is difficult to measure the exact effects
of the honors in each hand. 10 is the approximately correct value
for each hand. In statistics there is the error component in every
model to account for the deviations.
Power is the independent random variable. High card points is
the dependent variable of power which is proportional to tricks.
Therefore it is easier to use HCP to estimate tricks than the
actual independent random variable, power.

Of the 3 example hands 1&3 clearly have less losing tricks than 2, because the high cards are concentrated. Culbertson honour tricks, Bissell point count, and surely all losing trick counts reflect this.

Milton Work HCP are only good for:
ease of calculation
balanced hands
locating missing honours.

I feel I must be missing some deep point, otherwise what is the problem?

[FM75]

jogs, on 2013-June-24, 16:02, said:

Estimating Our Tricks
<snip>
The estimate of our tricks for the general case.

E(tricks) = trumps + (HCP-20)/3 + e

Trumps is the total combined trumps of the partnership.
(HCP-20)/3 means for every HCP over 20 assign another 1/3 trick to the estimate.
The curve generated by this equation is approximated by the normal curve(bell curve).
'e' is the error of the observations. E(e)=0.
For large samples the average error will approach zero.
<snip>

Strain = NT, HCP = 29,
E(tricks) = 3

Huh? Does that mean we get 9 tricks, 3 tricks, or the formula is garbage for NT? (The assumption is that e = 0, because this is a large sample case). Or does it mean we expect 6.5 +3 = 9.5?

Strain NT, HCP = 40, 6.23 trick, 12.73 tricks?
Strain some suit, HCP=40, trumps = 13, 19.23 tricks or 25.73 tricks?

Strain some suit, hcp =11, trumps = 13, 16 tricks, 22.5 tricks? I suspect that the "average" is closer to making 7 tricks (1 suit) than 16 tricks.

If the formula does not predict the simple cases, toss it in the garbage bin.

(Ok, I studied physics, and expected the friction free limit of a formula including friction to reduce to the friction-free formula.)

[jogs]

FM75, on 2013-July-09, 22:23, said:

Huh? Does that mean we get 9 tricks, 3 tricks, or the formula is garbage for NT? (The assumption is that e = 0, because this is a large sample case). Or does it mean we expect 6.5 +3 = 9.5?

This model is for suit strains and the general case.
E(e) = 0, The expected error is zero.
The standard deviation of the error is approximately
1.25 tricks/boards.

Turns out E(e) <0 for combined trumps >= 10 or expected tricks >= 10.
This model works best when the expected tricks is between 3 to 10.
Our expected tricks fluctuated wildly depending on whether we
declare in our suit or defend in their suit.

When trumps >= 10 or expected tricks >= 10 it requires a much more
complex polynomial model. For a specific board in high level auctions
we should attempt to count the tricks.

[jogs]

test: trying to post west/east hands

---

[jogs]

retest: trying to post west/east hands

---

[jogs]

Scarabin, on 2013-July-09, 21:41, said:

Of the 3 example hands 1&3 clearly have less losing tricks than 2, because the high cards are concentrated. Culbertson honour tricks, Bissell point count, and surely all losing trick counts reflect this.

Milton Work HCP are only good for:
ease of calculation
balanced hands
locating missing honours.

I feel I must be missing some deep point, otherwise what is the problem?

The point is the estimator isn't linear. It isn't a straight line. It is more like
multi-dimensional blob. It isn't only our honor count that matters. The
location of those honors and whether they are working together also
matter. During the initial evaluation of the hand there is no need to be
precise.
Bissell points and workcount are just loose guidelines for valuation.
I use Milton Work HCP because of ease of calculation.
Other methods are much harder to calculate. Have never seen evidence
any of those methods are more than a small marginal incremental
improvement. The variance of the calculations from those methods are
just as large as the variance of workcount.
Assuming we are dealer, what do we need to know? First, whether or
not to open. If we decide to open, what to open. Why do we need
a more precise valuation of our hand?
During the auction when we learn more about how partner's hand fits
with our hand the valuation can change dramatically. This negates the
efforts of a complex initial valuation. This model is in terms of our tricks
rather than my points.

Quote

Point count: ace=4, king=3, queen=2, and jack=1
♠ AKQJ ♥ 432 ♦ 432 ♣ 432
♠ A432 ♥ K32 ♦ Q32 ♣ J32
♠ AK32 ♥ QJ2 ♦ 432 ♣ 432

These hands are 10 +/- e points and this error is large. As we learn
more about partner's hand the error will be reduced. During the
initial evaluation, it is sufficient to know to pass these hands as dealer.

E(tricks) = trumps + (HCP-20)/3 + e
Std dev is about 1.25 tricks/board.
E(tricks) = trumps + (HCP-20)/3 + SF + e
For flat hands the std dev can be as low as 1 trick/board.
This SF term is skewness/flatness as suggested by Lawrence/Wirgren.
Flat boards reduce the trick estimates. Skewed boards increase the
trick estimates.

These two models are for fitting partner's hand with our hand.
With luck we will know the value of the terms by the second
or third call of the auction.

These models are best for assisting the contested auctions 3 over 2
and 3 over 3. In general the flat hand should not bid 3 over 3.
5332 should rarely compete 3 over 3.
.................
In another post I will introduce the other independent random
variable, pattern.

[jogs]

PATTERN

Pattern is the ordered configuration of the four suits in one hand.
Joint pattern is the joint pattern of the two partnership hands.
Trumps is usually the suit with the longest combined length. Larry
Cohen has chosen trumps as his parameter from estimating tricks.
SST(short suit totals) is the sum of the two shortest suit holdings of
the partnership. Lawrence/Wirgren uses the shorter suit holding of
each partner. Cohen and Lawrence/Wirgren are just using a
different end of the same variable(pattern) to estimate tricks.
Trumps is the coarse estimate. SST is the fine tuning. Using
both gives us better estimates than either on a stand alone basis.

Now for a naive test of joint pattern. Each side will be given
20 points with all points in two suits.

---

This example has 18 trumps and only 16 tricks.

---

Do not assume that when we hold flat patterns, opponents will also
hold flat patterns. In this example EW is 2434//2533, while NS is
4342//5134. EW makes 8 tricks in hearts. NS makes 10 tricks
in spades. 18 trumps producing to 18 tricks. This is compensating
errors. LoTT is credited for being 'right' when it is 'right' for the
'wrong' reasons.

---

In this example the points between the diamonds and clubs have
been exchanged. EW is 2434//2533, while NS remains
4342//5134. EW makes 8 tricks in hearts. NS makes 9 tricks
in spades. 18 trumps producing to 17 tricks.

---

On all three examples EW held 9 hearts and made only 8 tricks.
So maybe the expected tricks are usually only dependent on our power
and pattern. Their pattern and trump length has little effect on our tricks.
There are exceptions where their pattern reduces out tricks. Usually a
singleton to an ace, followed by a ruff. It is rare. We should just
ignore their hands and use only ours to estimate tricks.

E(tricks) = trumps + (HCP-20)/3 + SF + e

-----------------
Aside: this model applies mostly to when we expect to win 7 to 10
tricks. Very useful for making contested part score auctions. At higher
levels controls play a larger role.

Examined hand records from BBO minis, most part score boards had
a std dev between 0.5 to 1 when played in the same strain. Admittedly
the range of playing abilities on these minis was huge. Even in flight A
events it was rare to see the std dev fall under 0.5.
Could not find any evidence knowing their trump length assisted us in
better competitive decisions. Knowing their joint distribution would
have been useful.

[jogs]

The objective of hand valuation should be to find the best contract
for the partnership. It is not to find the most precise valuation of
my hand in a vacuum. The initial point count is just a transitory
value which will be readjusted with every successive bid in the
auction.
Power is the independent random variable used to estimate tricks.
Point count is a dependent component of power.

Example 1. I have an ace, two kings and a jack. My pattern is
1=5=4=3. In work count I have 11 points regardless of the
location of the honors.

a) ♠2 ♥AK752 ♦KJ82 ♣642
b) ♠K ♥J8752 ♦K852 ♣A42

Many would open hand 'a' 1♥. Few would open hand 'b'. Yet
both are 11 point hands. The location of the honors and whether
they are working together does affect the ability of a hand to generate
tricks. Hand valuation is about how honors interact with one another.
Hand valuation is more complex than assigning a fixed value to each
honor.

Example 2.

---

West has 11 points. East has 9 points. 4♥ should make nearly
every time. The joint pattern 1543//3442 fits well. No wasted
honors in the short suits.

Example 3.

---

West has the same 11. East still has 9 points. 1543//4234 This pair of
hands do not fit nicely. If everything goes wrong west may make only 3
or 4 tricks in hearts. It is about power, points, location of those points,
and how those points fit together. It is also about joint pattern.
Too many systems go to great pains to evaluate individual hands to too
many decimal places. It isn't about points. Taking tricks depends on
how well those points are working together and how well the patterns
of the partnership hands fit.
.............
The main theme is this thread is

Quote

The objective of hand evaluation should be to find the best contract
for the partnership.

The best method to achieve this objective is to estimate partnership
tricks. Finding a more precise initial point count will do little to help
us achieve this objective. We need better methods to determine
the fit of the partnership, and thus would be better able to estimate
the partnership tricks. We must realize that expected tricks may vary
radically with every successive bid.

E(tricks) = trumps + (HCP-20)/3 + e
Std dev is about 1.25 tricks/board.
E(tricks) = trumps + (HCP-20)/3 + SF + e
For flat hands the std dev can be as low as 1 trick/board.

There are four models for expected tricks, one for each suit. Expected
tricks fluctuate wildly depending on strain of the final contract. We want
to be in the strain which maximizes our expected tricks.

[Scarabin]

OK so far. We can easily agree on the general principles but I expect problems only arise when we get to the details of your proposed complete evaluation system.

[jogs]

Scarabin, on 2013-July-21, 04:20, said:

OK so far. We can easily agree on the general principles but I expect problems only arise when we get to the details of your proposed complete evaluation system.

There will be no proposed detailed complete evaluation system presented
here. The theme of this thread is think in terms of tricks for our partnership
rather than points in our hand.. These statistical models are for the general
case. Often completed by the third bid of the auction. Our expected tricks
is X +/- e. All estimates come with errors and this e >=1.

There are three phases to the evaluation process. The first phase is the
initial point count. The two our tricks models are the second phase.
By using the model which consist of HCP, trumps, and skewness/flatness
one can improve his starting point for the third phase. The first two
phases are for the general case. This third phase is counting the tricks
for the actual board. This will require uncovering the effects of addtional
parameters. This thread will make no suggestions on how to accomplish
this task of counting. Future posts will suggest how to utilize the models
for better bidding decisions, often at the part score level.

[jogs]

Power and Pattern

Review of the material.
Power and pattern are two multi-dimensional independent random
variables used to estimate tricks.
Power is high card points, the location of those HCP, and how they
interact with each other. This would require a complex polynomial
too difficult to solve at the table. HCP is the component of power
which is roughly proportional to tricks. HCP will be used as a
proxy for power in the our tricks model.
Pattern is the ordered configuration of the four suits in one hand.
Joint pattern is the joint pattern of the two partnership hands.
All four suits have effects on tricks. Combined trumps is the
component of pattern which is roughly proportional to tricks.
Trumps is the proxy for pattern.

E(tricks) = trumps + (HCP-20)/3 + e

Skewness/flatness. Singletons and voids increases the expected
tricks. The absence of singletons and voids(or flatness) reduces
the expected tricks. Singletons and voids are components of
pattern, not power.

E(tricks) = trumps + (HCP-20)/3 + SF + e

Interaction. There are effects due directly to each individual
parameter. There are also effects due to the interaction of those
parameters.
Most systems assign a fixed value to a singleton. Singletons are
components of pattern, not power. The true value of a singleton
is dependent on how it reacts with other parameters. Therefore a
singleton should have a variable value expressed in expected tricks.

5431 // 3343
The singleton is valuable when we play in spades. Singletons in the
hand with the long trumps limits opponents to one trick in that suit.
The ruffing in spades is probably tricks we already had.

5431 // 3523
Singletons in the hand with the short trumps are additional trump
tricks, provided there are sufficient trumps. Played in the 5-4
heart fit we are able to ruff clubs with the short hearts. That is
potentially seven trump tricks with hearts as trumps.

These examples show that singletons do have a variable value
depending on how it interacts with other parameters and in the
general case that value should be measured in expected tricks.
On any particular board attempt to count the actual tricks
during the auction.