[helene_t]

I have made a statistical analysis of the gib DD database aimed at finding a hand evaluation method for suit contracts.

I found the following coefficients:

Honours in 4+ card side suit: J=0.5299 Q= 1.0090 K=2.0736 A=3.4166
Honours in 3 card side suit: J=0.5077 Q= 1.0522 K=2.1437 A= 3.4068
Honours in 2 card side suit: J=0.2450 Q= 0.6769 K= 1.9807 A= 3.2087
Sec side suit honours: J= 0.2160 Q= 0.3607 K= 1.0344 A=2.9640
Trump honours: J=0.8713 Q= 1.5316 K=2.5131 A=3.6570
Shortnesses: Void=2.9892 Stiff=1.8826 Doubleton= 0.7095

I was interested in finding out how accurate modified LTC is. That is
Ace=1.5 (but 1 if stiff)
King=1 (but zero if stiff)
Q=0.5 (zero if stiff or if in doubleton)
Void=3
Singleton=2
Doubleton=1

It appears that mLTC is not far off w.r.t relative values of honours and honours in short suits, but it undervalues trump honours and sec aces and kings, and overvalues shortness drastically.

This analysis is based on the probability of making ten tricks double dummy. If right-siding is an issue I have discarded the record. Only 4-4 trump fits considered. Note that honour combinations are not considered, nor is synergy between the two hands. 198382 deals included in the analysis (actually a little less since if a pair has two 4-4 fits the hand is counted twice).

[hotShot]

I think your results indicate that 7421 is a better description than the usual 4321.
This is no big surprise as many use "4321 + controls" resulting in an effective 6421 evaluation.

[gnasher]

Some things I found interesting:
- Honours in a three-card suit are worth nearly as much as in a four-card suit. I'd consider Kxx xxxx significantly worse than xxx Kxxx, but apparently there isn't much in it.
- I usually regard a singleton ace as being worth about 3HCP, but your figures suggest that this evaluation is unduly pessimistic.

And a couple of comments:
- The trick-taking value of an honour is only relevant on the hands where we'd actually consider taking offensive action. Did you look at all hands, or only at hands where the partnership has a reasonable proportion of the combined strength?
- It would be interesting to know how much an honour goes up in value if it's in the same suit as another honour. For example, I'd assume that xxx HHxx is worth rather more than Hxx Hxxx, but your results so far suggest that I might be wrong.

Sorry - I know it's a bit unfair to reward your public-spirited publication of these results by demanding more.

[helene_t]

gnasher, on May 20 2009, 03:20 PM, said:

- Honours in a three-card suit are worth nearly as much as in a four-card suit.  I'd consider Kxx xxxx significantly worse than xxx Kxxx, but apparently there isn't much in it.

My estimate says queens and kings are worth more in 3-card suits, while aces and jacks are worth more in 4-card suits. Doesn't make much sense. I should include some confidence bounds on the estimates as I suspect these small differences are not significant

Quote

The trick-taking value of an honour is only relevant on the hands where we'd actually consider taking offensive action.  Did you look at all hands, or only at hands where the partnership has a reasonable proportion of the combined strength?

I include all hands but the response variable is binary (10+tricks or 9- tricks, I use logistic regression). So the fact that with ten combined HCPs and two flat hands we won't make games does not influence the estimates as any parameter values would be consistent with this observation.

Quote

It would be interesting to know how much an honour goes up in value if it's in the same suit as another honour.  For example, I'd assume that xxx HHxx is worth rather more than Hxx Hxxx, but your results so far suggest that I might be wrong.

My results do not say anything about this. This is among the next things I will explore, along with wasted values opposite shortness, and the 9th trump.

What would also be interesting would be to compare to real data. Something to discuss with Stephen. DD data differ from real data in some ways, the most obvious one for the simple honour-scale construction for notrump games was devaluation of queens, presumably because DD declarer always makes the two-way finesses right.

I am happy to share the code if anyone wants to try similar analyzes.

[NickRW]

gnasher, on May 20 2009, 02:20 PM, said:

- I usually regard a singleton ace as being worth about 3HCP, but your figures suggest that this evaluation is unduly pessimistic.

-1hcp for a singleton ace is certainly, in itself, rather pessimistic. However, for realtively average hands, this adjustment may still be not that far from the mark when you consider that your longer suits will be 4hcp worse than they might have been.

For very strong hands with a singleton ace -1hcp is certainly pessimistic full stop - the honours have to be somewhere after all and the other suits may not be particularly weakened by the fact that 4hcp has disappeared into the shortest suit.

Just my .02

Nick

[hotShot]

helene_t, on May 20 2009, 03:29 PM, said:

My estimate says queens and kings are worth more in 3-card suits, while aces and jacks are worth more in 4-card suits. Doesn't make much sense.

I would guess that if you look at the distribution of the suit at the other 3 players, you will find, that it's a little more likely that the 2nd or 3rd trick are not ruffed by the opponents if you hold 3 cards compared to 4 cards. This would result in K or Q being a little more valuable in a 3 card suit.

After you have drawn trump there is a good chance to get the 4th round trick with the 4rth J. This should make the J a little more valuable in a 4 card suit.

I have no idea why the ace would gain with a 4 card suit. A wild guess would be that this is a side effect from the devaluation of K and Q.

[NickRW]

helene_t, on May 20 2009, 12:23 AM, said:

It appears that mLTC is not far off w.r.t relative values of honours and honours in short suits, but it undervalues trump honours and sec aces and kings, and overvalues shortness drastically.

Is this an entirely safe conclusion? You say that you were only looking at 4/4 fits, but hands with a void will quite often have a nine card fit in another suit - where you will often be playing, rather than the 4/4 fit.

I have a tendency to be at least a little pessimistic about shortness with only 8 trumps - but get rather more excited about it when we have more trumps - especially if mine is the shorter trump hand - I think this is a more rounded view to take...

Nick

[NickRW]

helene_t, on May 20 2009, 02:29 PM, said:

What would also be interesting would be to compare to real data. Something to discuss with Stephen. DD data differ from real data in some ways, the most obvious one for the simple honour-scale construction for notrump games was devaluation of queens, presumably because DD declarer always makes the two-way finesses right.

I think this point about DD analysis always taking a two way finesse the right way (and therefore queens tend to get undervalued) is overstated.

I think I am correct in saying that for contracts of 5m and above, DD analysis tends to overstate the trick taking potential of hands compared to sinlge dummy - this is because with the necessary aces and voids etc to make a 5 level contract you almost always have the controls necessary to enjoy several possible lines - and DD analysis, is, of course, always going to pick the right one - whereas - at the table, single dummy, even a bot is going to go wrong sometimes.

I think I am also right that, at the 4M level, although DD analysis will still tend to take two way finesses right etc, the analysis still gives (over a large number of hands) approx correct trick taking expectation (In real life, defenders give away tricks and so on).

For lower level contracts, however, DD analysis starts to favour the defenders and the tricks taking expectation tends to be on the low side compared to real life. (Now the DD analysis always selects the right lead and the defenders tend to have enough cards that this will count for something).

Nick

[helene_t]

NickRW, on May 20 2009, 07:43 PM, said:

helene_t, on May 20 2009, 12:23 AM, said:

It appears that mLTC is not far off w.r.t relative values of honours and honours in short suits, but it undervalues trump honours and sec aces and kings, and overvalues shortness drastically.

Is this an entirely safe conclusion? You say that you were only looking at 4/4 fits, but hands with a void will quite often have a nine card fit in another suit - where you will often be playing, rather than the 4/4 fit.

I have a tendency to be at least a little pessimistic about shortness with only 8 trumps - but get rather more excited about it when we have more trumps - especially if mine is the shorter trump hand - I think this is a more rounded view to take...

Nick

Good point. For the 5-4 fits, the values of the shortnesses are 4.0203 , 2.3589 and 0.7777.

The value of the 9th trump is 1.099 btw. But now the model is getting too complex for my 512MB stoneage laptop.

[kenrexford]

I'm curious about the methodology.

First, does the data reflect the interplay of multiple honors working together? I would imagine that a Queen has less value on average when isolated and more when joined, with 10's and 9's also adding to the calculations.

Second, does the data reflect the value an honor has on a lesser card or just the value of the card itself? For example, the honors in a 4+ suit make the possibility of the 4th and subsequent card taking a trick in real life higher. Furthermore, honors in short suits bolster lesser cards in longer suits by provision of control, which allows us to cash the long-suit winners rather than pitch them while the opponents are cashing their long suit.

I would expect that the higher the honor (Aces, then Kings), the higher the internal value (value in establishing long pips) as well as the higher the vicarious value (protection value for cashing long cards in a different suit).

As an example of "vicarious" value, consider Ax-Ax-Ax-Axxxxxx. On the lead of any short suit, Declarer expects a reasonable likelihood that he can win, cash the Ace in the long suit, play one more card in the long suit to establish it, lose on average three tricks in the opening-lead suit, win the next suit, and claim. So, this 16-count has a fair expectation of producing 9 tricks opposite a yarborough. Not quite, but you understand, I'm sure, my point. This 16-count, therefore, is worth something approaching 26 HCP, because of the value of the four Aces, the internal one for helping to establish clubs quickly, the external ones because they help take advantage of the established clubs, a "vicarious" value.

Consider, in contrast, AK-xx-xx-AKQJxxx, a 17-count. One more HCP. However, the average expectation opposite a yarb might be to lose 4 tricks in each red suit before claiming. Not only do you lose all pips, but you lose an honor also. The internal honors maintain their value, to a degree, albeit redundantly in the case of the Queen and Jack. Furthermore, you have lost two degrees of vicarious value because two suits lack Aces. This 17-count has an impure trick-taking expectancy that is 4 tricks lower than the prior hand, sort of. Hence, in some respects, the third and fourth side Ace have the most "vacarious" value. Or, both the suit-establishing value and the control value of cards interplay and add together.

Taking all of this into consideration would be a daunting task.

[helene_t]

Ken, I compute coefficients for each honour, depends only on the length of the suit and whether it's in the trump suit or not. Whether there are other honours in the suit or not is not considered. The hands I use are randomly dealt so the coefficients should be correct "on average", but of course for a particular hand you could always argue that one feature is overvalued and another undervalued, and some hands will at the bottom line be over- or undervalues.

It won't be a problem to incorporate supporting honours in the model and I will probably do so shortly.

One has to make some simplifications, however. If the value of an honour also depends on the length of other suits and which honours there are in other suits, it could easily be so complex that I would need billions of hand records and weeks of computer time.

For the purpose of making bridge bots, it doesn't really matter how complex the model is. For the purpose of making rule-of-thumps to be used by humans, it has to be simple, obviously.

[blackshoe]

There's only one rule of thump I know: "do what I tell you or I'll thump you!"

[Mbodell]

Maybe I'm just being dumb, but could you explain your coefficients a little. Like exactly what do they mean? Does it mean how many tricks I expect to take (like the presence of an A in a 4+ side suit gives me +3.4166 to the number of tricks I take)? I don't think that's it, but I can't figure out what it is.

[NickRW]

Looking at these coefficients reminds me of tysen2k's TSP (multiplying up they are very close to honours counted 6/4/2/1 with shortness 1/3/5)

Anyway, I think this was the old thread:
http://forums.bridge...wtopic=3278&hl=

Still worth a read for those with an interest in hand valuation.

Nick

[helene_t]

Mbodell, on May 21 2009, 02:30 AM, said:

Maybe I'm just being dumb, but could you explain your coefficients a little.  Like exactly what do they mean?  Does it mean how many tricks I expect to take (like the presence of an A in a 4+ side suit gives me +3.4166 to the number of tricks I take)?  I don't think that's it, but I can't figure out what it is.

I didn't explain it because I thought people would just skip it when I went into those details but thanks for asking

The model is that the probability that 10 or more tricks make is
1/(1+exp(-a0 - a1*x1 - a2*x2 - ..... a24*x24))
where x1, x2 etc are the 24 predictors (for example x1=2 if you and p together have two jacks in long side suits, x21=0 if you and p have zero voids together).

a1, a2 etc. are the coefficients.

Since (1/(1+exp(0))) = 0.5 and (1/(1+exp(-1))) = 0.731, a coefficient of 1 means that if the probability of making game without the honour is 0.5, it would be 0.731 with the honour.

To (roughly) translate it into HCPs you can multiply the coefficients with 1.4 since that would lead to the sum of an ace, king, queen and jack in a long side suit being 10.