[kenrexford]

Work Point Count, Goren, Losing Trick Count, etc.: I look at my hand, and perhaps partner's.

LTT, I Fought the LTT: I look at the deal, plus our fits or outr shortness or our working values, or whatever.

A while back, I was curious about whether any mathematical tools might assist people in evaluating position. I found a lot of teammates missing games because of HCP-itis. I had recognized that certain layouts produced more tricks than expected, because of position, and I tried to explain this. But, it was useless.

Nonetheless, I had a rudimentary concept I called the "Fifth Ace." When the high cards are laid out N(14)-E(14)-S(4)-W(8), roughly, E-W make game more often than "should be." I called this "phenonomon" the missing "fifth Ace." The reliability of this thesis was increased when East held greater numbers of "finessable positions," meaning honor holdings that could be promoted by position (KJx, AQx, KQx, AJx, and the like). A sexier mathematical analysis could be done if East added a point for each "finessable position." (+1 for AQx, +2 for AQ10, etc.)

The same principle worked for 14-4-8-14, for the opening side.

A similar principle seemed to enable unexpected tricks when the layout was 16-10-4-10, with no fit after a two-suited overcall of a strong 1NT, played in 2NT by the overcallers.

I then dropped the issue for other matters.

I am curious as to whether anyone has ever worked this sort of thing up into a workable theory.

On a similar note, the inverse of this principle facilitates penalty doubles. This is especially the case when "finessable positions" are present in the opposition trump suit, well-placed. Or, for penalty redoubles.

[inquiry]

This is something you can investigate with BRidgeBRowser (not the mathematical desciption, but rather or not your theory is right).

With bridge browser, you can do a shape seach (which can include HCP and/or ignore shape). Then you can use the plot and/or report feature to see how many tricks are won, etc.

I am not sure you will be exactly proven correct. There was a theory of Kaplan sometime ago that 12 hcp opposite 12 hcp (both balanced) made game more often than 16 opposite 10, or at least as often. That is easy enough to test with massive databases. It is also easy to test the theory you expose, although some though needs to go into fit or balanced criteria.

Anyone with BRidgeBRowser wanting to know how to do this, I will provide the sequence to set up the search and generate the reports

[EricK]

Isn't this just the phenomenon that when most of the strength is concentrated in one hand (especially if you know that it is there) you can make extra tricks because that hand often comes under pressure - either thrown in to lead away from his other honours or squeezed out of some his high cards.

[awm]

There are a couple principles at work here:

(1) There is an advantage to having most of your side's strength "behind" most of the opponents strength. The normal valuation of honors and holdings is based on it being equally likely for missing cards to appear on either side of you. So for example, KJx averages one trick -- it produces two if the AQ are in front of you and 0 if they're both behind you, and 1 the rest of the time. This makes it worth "roughly the same" as an ace in a notrump contract (4 hcp each). But if you know that almost all the missing high cards are in front of the KJx, you will get one trick virtually always and two tricks fairly often, for a substantial upgrade. On the other hand if you know almost all missing cards are behind the KJx, you will get zero tricks fairly often and two tricks virtually never, for a substantial downgrade.

(2) There is an advantage to having entries back and forth. For example, say I hold AJT9x in a suit and partner has three small. I can play this suit for four tricks almost 75% of the time by finessing twice (needs one of two honors onside and not the 5-0 break). But if there are no entries to partner's hand, I am forced to play AJT9x from my hand alone and will almost always lose two tricks (I can pick up only stiff honor or doubleton with two honors, 4/32 positions instead of 23/32).
This suggests that 12 hcp opposite 12 (lots of entries) will do better than 20 opposite 4 for example.

My feeling is that by the time you're thinking about these sorts of things at the table, you probably have enough experience to judge hands "by feel" without having to resort to complicated numerical calculations. I suppose we could help computers to play bridge by factoring these things in, but for humans an extremely complicated numerical formula is probably not that worthwhile.

[kenrexford]

See, this is the core of the "problem." Of course, the "feel" works for the experienced player. But, I still wonder if a "grand theory" could be developed, with little rules.

Take an example. Work's HCP's were designed to help the masses have an easy analysis. But, it is too simplistic once you get more to the game.

The Law of Total Tricks also helped the masses. It gave rules, like eight never, nine never, that serve a great purpose for many. Sure, it has flaws, but the flaws are less than the general ignorance without knowledge of this concept.

If certain high-yeild, common layouts can be identified as positionally advantageous (like, concentrated strength in one opposition hand, or open-soundovercall-pass-constructive), and if certain rules can be applied (like +1 HCP for every finesse you could take), then you would have a nice, easy lesson.

If the mathematics justify it, I can see an easy, quick tool arising. An example. You hold AQxxx-Kxx-AJx-xx. You overcall 1♥ with 1♠, hear a pass from LHO, and partner raises to 2♠, showing 6-9 HCP's. You have 14 HCP's. With three finesses possible (spade Q, heart K, and diamond J), you add +1 for each, yielding 17 HCP's. The doubleton club adds +1, for 18 points. Thus, if partner has 8-9, a maximum, you should make game.

That is not too difficult, and it probably works. Give partner Kxx-xx-KQx-xxxxx, and I like my chances. A 3♣ game try hits gold.

[mikeh]

This is more of the same... akin to the discussion of zar points, etc. There comes a point in the progression of a good player where metrics begin to assume less and less of a role... no matter what the rule is.

The more complex the rule is, the more one needs to know about the game in order to apply it and the less one needs it. In fact, in my opinion, at a certain stage, if you are dwelling upon this kind of analysis, you are in danger of missing the point... of becoming so 'rules focussed' that you will miss out on the true beauty of the game..

I suspect we have all known players who spend countless hours devising complex methods that don't really work and whose bidding is flawed because they have focussed on these methods rather than learning how to PLAY the game. Your suggestion smacks of that approach... it has some intriguing facets and might make for an interesting academic analysis, but it won't help you really play the game.

Of course, that's my own opinion, and I may be entirely wrong... as I may be with respect to Zar... all new ideas encounter resistance

[inquiry]

Well, all evaulation schemes (Zar, LOTT, FTL, LTC, Goren, BLINKY, etc) are flawed because there is more than just counting points. The location of the specific points (especially in a competitive auction) is important. In this current example if RHO opens 1S with 14 hcp and you sit behind with 14 hcp and six of your partners ponits are the S-AQ, how much is that worth? What if four of his points was spade KJx? Just counting points "evaluation points" is not enough. Surely one has to use some judgement (4333 hands is bad, HCP in short suits, and weak long suits is bad, etc).

But ok, I did two quick BRidgeBRowser searchers to stretch this example.

The requirement of both was that dealer held 14 hcp, his partner held 4 hcp. In the first case, second seat held 14 hcp, in the second case, fourth seat held 14 hcp. In both examples, I forced dealer to open 1C to 1NT, and I only examined hands where the non-dealing (and non-opening side) decleared the hand. I then looked to see how many tricks, upon average, the non-dealing side won in NT, hearts, and spades. Of course, on any give deal, maybe the non-opening side had a 12 card spade fit, as I left no controls in for distribution, what I am hoping for is that over thousands of deals, these average out.

With 14 hcp behind opener.

In Notrump, the non-opening side averaged 7.94 tricks +/- 0.06 at imps, and 8.12 +/- 0.06 tricks at MP.

In Spades, the non-opening side averaged 9.07 +/- 0,04 tricks at imps, and 9.69 +/- 0.05 at MP (the imp hands had an average of 8.48 spades, while the MP hand had an average of 8.95 spades. An increase of half a spade in the average seems to account for the increase of half a trick.

In Hearts, the non-opening side averaged 9.21 +- 0.05 tricks at imps (8.13 trumps), and 9.46 +- tricks at MP (8.51 trumps). Again, the high number of trumps correlated with the higher trick total.

Move the 14 point hand to the fourth seat and you get,

In NT, 7.61 +/- 0.5 at imps, and 7.79 +/- 0.08 at mp (a decrease of 0.3 of a trick)

In spades, 9.29 +/- 0.06 at imps (average 8.43 spades), 8.47 +/- 0.07 at MP (only averaging 7.68 spades). This is a reduction of tricks, but you will h ave to factor into it the dramatic reduction of the number of trumps. For example, in Spades, the HP + Distribution average was 25.79 at imps and only 24.26 at MP.

In hearts, 8.63 +/- 0.04 at imps (7.89 trumps), and 9.88 +/- 0.07 tricks in MP (9.12 trumps).

As you can see, this is a little bit all over the place. The NT contract is probably the best guestimate due to the influence the number of trumps have on the trick taking potential. But I think we can agree that what ever the positional value is worth, it doesn’t seem to worth a full trick (such a fifth ace). The reason for this is clear, what ever partners 8 points are, some of them will be “wasted” in that the HCP are behind them. I think position value based upon the Bidding, rather than just total HCP is a better metric.

But having said that, I took the same data set, and included all contracts played by the non-opening side (includes minors).

With 14 hcp behind opener, the statistic are
8.79 +/- 0.02 Imp tricks (8.22 trumps*) , 9.10 +/- 0.02 MP tricks (8.51 trumps*)

With 14 hcp in front of opener,
8.69 +/- 0.03 Imps (8.19 trumps*), 8.79 +/- 0.04 MP (8.34 trumps*)

* trumps only when not played in Notrump of course. So I next removed the notrump contracts (only trump contracts).

With 14 hcp behind opener (only suit contract)
9.06 +/- 0.02 imp tricks (8.22 trumps), 9.33 +/- 0.02 MP tricks (8.51 trumps)

With 14 hcp in front of opener,
8.97 +/- 0.03 Imps (8.19 trumps), 8.99 +/- 0.04 MP (8.34 trumps)

If we average the notrump contracts at imps and mp, we find 14 hcp behind opener averaged 0.33 more tricks per hand (8.03 versus 7.70). If we average the suit contracts, is is a little tricker. The 14 hcp behind the opener averaged 0.215 more tricks, but also averaged 0.10 more trumps per hand. The extra trump should be corrected for by reducing this difference by about 0.1 trick.

So the 14 hcp behind rather than in front, is worth, on average, somewhere between 0.33 trick (at NT) and 0.115 trick (at a suit contract). There was roughly 6200 hands that meet the requirements for each test condition. Clearly, it seems counting this as a fifth ace is way, way over-evaluating.

[SoTired]

inquiry, on Aug 4 2006, 11:12 AM, said:

So the 14 hcp behind rather than in front, is worth, on average, somewhere between 0.33 trick (at NT) and 0.115 trick (at a suit contract). There was roughly 6200 hands that meet the requirements for each test condition. Clearly, it seems counting this as a fifth ace is way, way over-evaluating.

Thanks, Ben. Very useful information. When people talk about "scientific bidding" this is what I think of: Bidding rules that are based on hand studies. Another example is the argument about opening bid preempts. Many have all these "rules" they apply, but noone has any true studies to back up which rules work and which rules don't.

[SoTired]

So .33 trick = about 1 hcp. And .115 trick = about 1/2 HCP.
So if the opening bidder is in front of your partner's 15-18 1N overcall, add a point to your hand when raising partner's NT
If the opening bidder is in front of your suit overcalling partner, add a ten to your hand....

[inquiry]

SoTired, on Aug 4 2006, 11:28 AM, said:

So .33 trick = about 1 hcp. And .115 trick = about 1/2 HCP.
So if the opening bidder is in front of your partner's 15-18 1N overcall, add a point to your hand when raising partner's NT
If the opening bidder is in front of your suit overcalling partner, add a ten to your hand....

I don't think this is what this shows. This was a very specific situation. Your opponents held EXACTLY 18 hcp. One of them 14 hcp, the other 4. And your side held exactly 22 hcp, one 14, one 8. The only thing was which one held the 14 and which held the 8. I would not generalize to other situations. For example, if all 18 where in one hand, that player would be endplayed more often, perhaps. Etc.

[SoTired]

True - but "adding an ace" is clearly over-compensating.

We have seen in many books, articles, discussions, etc, experts talk about competitive bidding and re-evaluating your hand based on where the opps points are. The comments always seemed subjective to me. Here we have some objective information. +1 HCP in NT auctions and +.5 in suit auctions is a reasonable extrapolation of your research until further evidence is presented.

[hrothgar]

SoTired, on Aug 4 2006, 08:39 PM, said:

True - but "adding an ace" is clearly over-compensating.

We have seen in many books, articles, discussions, etc, experts talk about competitive bidding and re-evaluating your hand based on where the opps points are. The comments always seemed subjective to me. Here we have some objective information. +1 HCP in NT auctions and +.5 in suit auctions is a reasonable extrapolation of your research until further evidence is presented.

From my perspective, this is a very complicated problem...

On an intuitive basis, I'm perfectly comfortable with the basic theory being discussed... Its better to have our strength sitting over the opponents than vice-versa. However, I question whether its really possible to quantity with any great precision. Consider the following: No one seems able to agree what the best metric is to measure hand strength... Now we're talking about using some kind of imprecise metric to measure second - if not third - order effects. The imprecision is going to snow ball.

Here is how I'd approach the problem

Step 1: To start with, you need to select a hand evaluation metric. (Note that the choice of metrics might depend on a number of factors including whether you're looking at NT contracts, suit contracts, yada, yada, yada). There is a lot of good information in the the various Zar point threads about how to study the accuracy of a given metric.

Step 2: Study whether the accuracy of the metric depends on the distribution of HCPs. For example, suppose that you - hypothetically - determine that 26 combined HCPs between the N/S hands predicts 10 tricks in a suit contract. (There will be some kind of Probability Density Function describing the expected number of tricks with a mean of 10). Next, you want to try to determine whether the distribution of the strength between the N/S hands has a statistically significant effect of the expected trick taking capability. You might find that 13 opposite 13 suggests that you'll take 10.7 tricks, but 20 opposite 6 is only worth 9.7 tricks. (please note: Its probably worth while to revist your hand evaluation metric in light of this new information. The accuracy of your metric should increase, however, you might find that some other metric has actually become a better predictor)

Step 3: Once you're comfortable with the basic stuff, you can start worrying about how the distribtution of the opponent's strength impacts your metric. You might find it easiest conceptualize this whole proceedure as adding "dimensions" to this space.

Initially, you have a number line that displays whatever metric you're using to measure the combined strength of the hands. The height (measured on the Y axis) shows the expected number of tricks.

Next, expand the number line into an two dimensional array that shows North strength on one axis and South strength on the other. Once again, the height of a surface will measure playing strength.

Finally, move to a four dimensional array that describes the strength of all four hands...

[mikeh]

Ben, as always we are indebted to you for you time and ability to pull these kinds of numbers. While you properly admit that it is dangerous to over-generalize, it seems to me that your results suggest a reasonable assessment of relative upgrades based on the bidding and apparent location of hcp.

However, and this is not a knock on your approach, I think we'd all agree that such studies should not guide us too tightly.

Thus, you cannot (or cannot without ridiculous amounts of time) hope to analyze this kind of data in the detail needed to generate specific rules applicable to speciific holdings.

Give me 14 points sitting over a 1♠ opener:

If those points include the ♠AQ, that is certainly worth valuing as approximately 7 hcp, whereas if I am in front of the ♠ bidder, the issue is more complex.... entailing the possibility that opener will at some point lead away from the King, either because we are in notrump or because of an endplay etc... and possession of these cards will assist me in maintenance of tempo on some hands...so I would not devalue the AQ down to, say, 5 hcp

But give me QJ tight, and these hcp may be worthless on offence and have some value on defence behind opener and less if in front and so on.

I strongly believe that the variance in valuation on a per-hand basis is so great that it dwarfs the modest 'on average' figures. Moreover, the impact of positional value is not independent of declarer/defender ability. A skilled declarer will be able to maximize the positional advantages.

I guess I am really repeating myself... these kinds of studies, and any evaluation technique arising from them, are of vanishingly small use... by the time that a player can put them to proper use, he or she ought to have advanced to the stage that they are using the specific hand and the specific auction (which will be far more accurate) for their adjustments.

[inquiry]

I have no intention of studying the positional evaluation of HCP in this format. The only reason I did it was to put a reality check into the "fifth ace" idea, which seemed way over evalauted to me. The reason being, what works is positional values that win tricks. Not position of HCP. I suspect there is a greater chance of your positional values working when 64 percent of your values are behind 78% of their values than when 78% of theirs sits behind 64% of yours. It is when their aces kill your kings and their kings kill your queens, etc where you HCP might not be carrying full weight. I would speculate one could make some kind of probability function but why bother. I think we are on the same side of the fence on this one. However, I might take an odd way run at richards 26 hcp challenge, but I will not worry about positional values for that. Instead, looking at hcp and distributinal values and degree of fit issues.

I did this more as an interesting excercise for more compeling use of BRidgeBRowser. If you really wanted to use it, you might choose to look up all the FANTUNES auctions on BBO and sort by auction to see how their bidding system really works and how they handle different situation. Now that is a very useful application ... including distribution and suit hcp for different bids at a click of a mouse.

[inquiry]

Ok.. here is an approximation of the 26 hcp question. I found all 4S contracts where the dealers side held exactly 26 hcp. I used a small database for this, and only dealer side to limit the number of hands found, still found 17,429 such hands. Note this is not that many unique deals, but rather hands played in 4S.


I looked at tricks from 7 to 13, and for this study, I added the matchpoint hands to the imp hands. Here is the results...

Quote

All hands in 4S, all declarers+dummy had 26 hcp

Tricks    Hands    Average # trumps
7       176             7.083
8       701             7.544
9       2656             7.982
10       5584             8.218
11       5678             8.497
12       2263             8.631
13       371             8.897

Note, I had thought to use HCP+Distribution, but, there was a problem. The problem is the program counts 3 pts for void, 2 for singleton, 1 for doublton, in either hand, good fit or not. It should be noted that the Dist+HCP was lowest at 9 tricks and went up on either side. Since the number of turmps increased steadly, the 12 AND 13 trikc hands had good distributional values (average 4 and 5 distributional points respectively), 9 tricks had only 3 points, 7 tricks had 3.5 as did 11 tricks.

[Flame]

I thought about you today.
I held
AXXX
KJ
QJXXX
KX
RHO opened 1C i overcalled 1D LHO passed and partner bid 1S RHO passed.
(1C) 1D (P) 1S
(p)

I have 14 kind of bad 14 and thinking of bidding 3S, but i remembered this post and decided to shut for 4S and hope for best.
Partner had
KQXX
XXX
10
A10XXX
and made the game (could have made an overtrick. he would bid 4S on 3S i think so this doesnt say anythink but still had to post.

[Winstonm]

Quote

I found a lot of teammates missing games because of HCP-itis. I had recognized that certain layouts produced more tricks than expected, because of position, and I tried to explain this. But, it was useless.

I can understand the "between the lines" frustration you express, and appreciate trying to solve this problem by creating terms understandable to those being addressed. From what I hear you saying, you are simply trying to come up with a positional point count adjustment for those players who just don't get it when it comes to evaluation - very Goren-like and commendable I say.

If the goal is to turn an intermediate player into a better player the concept is probably worthwhile to pursue - but if the idea is to turn a decent to good player into a very good player rules just won't work. They have to understand the concepts and learn on their own how to apply them, IMO.

In your situation, what might work best is to stress that bridge contracts are determined by number of tricks, not number of points. There is no game bonus for holding a combined 26 HCP - it takes tricks. If a hand produces 10 tricks in spades, then the HCP is irrelevant. After that, it would be up to them to work out their own adjustments I would say.