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The classic hand evaluation system in contract bridge assigns 4 points to each ace, 3 to each king, 2 to each queen, 1 to each jack, and in a suit contract, an additional 3 points for each void, 2 points for each singleton, and 1 for each doubleton.

Marty Bergen's writings describe a more complex system that makes a number of adjustments to this system:

  • Slightly different values, supposedly from computer simulations, for high card points (A:K:Q:J:T = 4.5:3.0:1.5:0.75:0.25)
  • Downgrades for dubious singletons and doubletons
  • Upgrades for long suits and quality suits
  • In a suit contract, upgrades for declarer only for extra trump length and 4+ card side suits
  • Short suit points are counted using different systems for declarer and dummy

I'm curious whether people have run computer simulations that compare Bergen's system as a whole with the simple classic system, and whether or not they find that Bergen's system is significantly more accurate at hand evaluation than the classic system. If so, where can I read about the methodology and results?

I'm also curious about various subsets of Bergen's system. For example, how much improvement we get over the classic system by incorporating downgrades for dubious holdings only (something that should be easy to explain to beginners).

  • How do you evaluate a hand in a way that makes it possible to determine which system is more accurate? – Henrik - stop hurting Monica Jun 29 at 23:38
  • @Henrik you generate a bunch of deals randomly and use a double dummy solver to see what the false positive and false negative rates are for the system's prediction of whether game is makeable based on the total point count between a pair of hands, or something like that. – Brian Jun 29 at 23:53
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    There is an attempt to close this question as "Primarily opinion based". I disagree: (1) It asks an objective question that can be answered either Yes or No: "Has Marty Bergen's hand evaluation system been validated experimentally?" (2) For a reference to the results if yes: "*If so, where can I read about the methodology and results?"; (3) and finally whether analysis has been done on subsets of Bergen's system and where it can be found is Yes. Three objective questions. No opinion requested, or needed to answer. – Forget I was ever here Jun 30 at 23:17
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Has Marty Bergen's hand evaluation system been validated experimentally?

Yes - but not (as far as I know) with a Monte Carlo simulation. Experts have long known (and I mean long known - since before I learned the game in 1972) that Aces were undervalued and Quacks (Queens and Jacks) over-valued in Work's Point Count. Numerous remedies have been suggested over the years to address this. When you hear an expert talk about "a good 15" or "a bad 11", for example, they have performed the analysis above and noted that the hand has more Aces than Quacks perhaps, or no Aces at all, or weak spot cards in support of the Honours.

However, past attempts to devise a more accurate system, such as the following, have all relied on overly complex adjustments or expertise not available to average players:

  • add a point for every Ace-Ten in the hand past the first; subtract a point if none.

  • Use a 5/4/3/2/1 point count for Ace through Ten; and multiply the result by 2/3 to restore the count back to a 40 Point deck. My recollection is that this system has been verified with a Monte Carlo simulation - but I read that over 10 years ago and cannot remember the source.

  • Establishing minimum Quick Tricks standard for certain bids, especially openings - which weights Aces and Kings preferentially relative to Quacks:

    Ely Culbertson had it right when Bridge was in its infancy. He said that an opening bid should have around 2 1/2 quick tricks. This standard, he said, could be a benchmark for judging defensive capabilities of openers & general trick taking potential for competing [to] games & slams. In my opinion, quick tricks should be more than just a requirement for an opening bid. You should evaluate your hand re quick tricks for penalty doubles, forcing pass theory, T/O doubles, overcalling & balancing also.

    Edmonton Bridge Centre, Alberta, Canada

  • Apply personal fudge factors ( requires thousands of hours of experience to do correctly)

So if you are wondering if Bergen's proposal is more accurate than a straight Work Count - absolutely.

As for the other evaluation suggestions mentioned by Bergen - All experts - and I mean all - have made these adjustments for at least 75 years. Culbertson, Lightner, and Jacoby were making them, and teaching them, in the 1930's, as was Goren in the 1940's and 50's. Anyone who doesn't make these adjustments suffers poor results - in short order.

If you are wondering if it is the most accurate possibility - most likely not. However Bergen has managed to come up with a modification that is an improvement, and is fairly simple to evaluate. That latter is a big plus.


Additionally, there are two problems with using Monte Carlo simulations in analyzing Bridge:

  • Resulting is the practice of judging a bid or call solely by its results on a particular hand. Beginners are prone to this, and need to unlearn it as one prerequisite to becoming intermediate. Bids and calls are properly judged by the expected result, in a statistical sense, based solely on the information available at the time from the auction.

  • Double Dummy analysis is interesting, but Bridge is played as a Single Dummy game. That a particular result is possible on a hand does not necessarily imply that it can be reasonably reached at the table. This is one of the ways in which cheaters are detected - though it takes time to compile sufficiently robust statistical arguments.

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