Help
I'm honestly surprised that someone hasn't already come up with a tool that can answer these types of questions. Is there relevant research that I missed? Or tools that I failed to find?
Either way, if anyone knows has suggestions on tools or methods I should be using, I'd appreciate any advice, especially advice that can save me time or hassle.
So far, I've found DDS, which seems to be the best option for a double-dummy solver. But it seems like I'll have to write my own scripts to generate a database of hands or otherwise use the program to create the data I need for any given statistical analysis. My understanding is that there's no consensus on what makes for a quality single-dummy solver. So my current plan is to average over the double-dummy results of a number of hands that share the relevant cards but are otherwise randomized.
To put things mathematically, I want to understand how many "bits" of information it costs to get a certain amount of variance reduction, and how the relevant information and its value changes in different bidding or card play scenarios. My initial plan is to use general linear regression models, but if someone has an alternative approach that would work better, please let me know.
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Bidding examples:
A ton of people have done hand evaluation analysis, but they mostly focused on how many tricks you can take as declarer. Unfortunately, that's not really what people need to know.
If you could make a system that always gave you the right bid to maximize the score differential, it wouldn't matter that you couldn't tell if 4♠ was a good sacrifice or a solid game until you saw dummy's cards. Knowing which one you have is information but not relevant information. The difference between what you can take on offense and what you can take on defense usually matters more (per the Law of Total Tricks).
Even if you had a perfect hand evaluation formula, the information you both need is not the same as the information you need. Getting partner exactly what they need to make a decision is the basis of most conventions and almost all of modern competitive bidding. It's also the reason for the captaincy principle and the distinction between telling and asking.
And hand evaluation formulas only report averages over all possible hands. But once bidding has started, you should only average over the remaining possibilities. Different things matter different situations, and the cost of communicating them depends on what has already happened in the bidding. Some information is almost always needed. But if you are designing a convention or a bidding system, you want to know which hands require accounting for something that only matters once in 100 hands. (Because it might matter in 50% of the hands being handled by that convention at that point in the bidding.)
Moreover, your hand's points, however you count them, aren't the only thing that matters. Once you see your cards, you *also* have a prediction about the cards of the other three players. And you should take this into account as you bid and revalue your hand. Knowing that your opponents didn't preempt, overcall, or double reduces the number of possibilities too.
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Card play examples:
I'd like to create some more detailed probability tables than the ones available in places like the Bridge Encyclopedia.
How often do lines of play or outcomes swing drastically based on additional information that could be revealed in bidding or learned from counting and discards? (And similarly, using game theory, when is honesty optimal vs when does false-carding or keeping quiet during bidding outweigh the benefits of giving partner a correct signal or lead suggestion?)
How often do different card-play techniques and situations end up mattering? How often can you combine lines of play vs having to make a choice?
How does the variance on different lines of play change in light of other information you have? Even if it is still a 50% play, it can be more or less risky in different situations. So whether or not it is worth taking that risk depends on the score you have and the number of boards you have left.
We have rules for how risky you should be on the average board, but can we quantify how you should shade that given the tournament situation and how that situation changes the balance between luck vs skill? If I have X deals left, what should I expect the distribution of hands to look like and how much uncertainty is there?
(To answer these questions, you'll need to know things like, if we have game, how often does the other side have game? When the other side has game, how often do we have a profitable sacrifice? What is the distribution of optimal contracts by score? How often can everyone make 1NT vs someone being able to make 2 of a major or 3 of a minor?)
[Edits made to correct typos]
This post has been edited by MaxHayden: 2020-May-21, 09:16
