[kgr]

Hi,
I'm developing a single dummy analysis program (Testing the capabilities of developing a program with AI). I was testing the program on some Bridge Master deals.
I saw that Level 5 A-4 it is advised to play a small diamond in trick 3.
Without entering constraints for the E-W hands my program gives (I think that I played HA first for these):
D2: 48% to make the contract; 9.40 tricks
S2: 50% to make the contract; 9.48 tricks
So, without constraints (based on 20000 deals) the play of S2 is slightly better.
...I added an extra functionality to my program to compare two cards and give the distributions where one is better than the other.
Using 2000 deals:
S3 makes and D2 fails: 2.6%; e.g.: East void D (then you can end-play W); E CA6 and HT9 (East wil get a ruff); West T97=Q8=KJT9=JT97 (an end-play is possible)
D2 makes and S3 fails: 0.7%; e.g.: East KJT7
=> So, I thought that play of D2 was not best. Now I realize that the end-plays are probably not findable at the table, but still the play of small Diamonds at trick 3 is maybe not so obvious?
With additional constraint for W hand to have 3cC my program gives:
D2: 38% to make the contract; 9.18 tricks
S2: 38% to make the contract; 9.23 tricks
=> If there is interest then I will later post a link where you can download a test version of my program.

[kgr]

I also have added analysis SD5. Then it compares cards and uses after the card the next 5 decisions Single Dummy (and after that it continues DD). Using that for 1000 analyzed deals it gets:
S3: makes 41%
D2: makes 42%
And SD adaptive for 1000 analyzed deals:
S3: makes 40%
D2: makes 42%
AI added SD Adaptive to my program and explains it:
Adaptive Single Dummy looks ahead through up to twelve later declarer/dummy decisions. A decision counts only when the double-dummy best card differs among the possible deals; forced choices or choices with the same best card in every deal do not count. After at most five such material decisions, double dummy completes the play.
It is a practical heuristic, not a model of human declarer play.
(I'm not sure with it really does )

[kerkido]

I don't understand your post. What do you mean by 'the play of S2'? What line are you comparing with the line of ducking a diamond?

I can see it easily being true that on a double dummy basis, playing a low spade will leave the contract makeable more often than playing a low diamond. But that has zero relevance to what the best play is single dummy. That's only because as soon as you play the spade, it knows where every card is, and can choose what line to take based on that knowledge. If you're writing a single dummy analysis program, you have to specifically prevent that type of logic.

[kgr]

kerkido, on 2026-July-28, 19:25, said:

I don't understand your post. What do you mean by 'the play of S2'? What line are you comparing with the line of ducking a diamond?

I can see it easily being true that on a double dummy basis, playing a low spade will leave the contract makeable more often than playing a low diamond. But that has zero relevance to what the best play is single dummy. That's only because as soon as you play the spade, it knows where every card is, and can choose what line to take based on that knowledge. If you're writing a single dummy analysis program, you have to specifically prevent that type of logic.

You’re right. By “S3” I meant playing a low spade at trick 3, or after drawing one high trump, as the immediate alternative to ducking a diamond with D2.
With SD5, the program makes the first five relevant decisions from the hand being analysed on a single-dummy basis; after that, it uses double-dummy continuation:
S3 makes: 41%
D2 makes: 42%
With Full single-dummy, the hand being analysed continues on a single-dummy basis until the end of the deal (while the defenders are still played double-dummy). Using 1,000 analysed deals:
S3 makes: 39%
D2 makes: 41%
So neither play is universally best: playing a spade and ducking a diamond each have their advantages in particular distributions. That is why I also added a “compare two cards” feature, to show the distributions in which one card makes the contract while the other does not.

[kerkido]

kgr, on 2026-July-29, 01:14, said:

You’re right. By “S3” I meant playing a low spade at trick 3, or after drawing one high trump, as the immediate alternative to ducking a diamond with D2.

I know you planned to lead a low spade, but that is meaningless. I'm asking what your *line* is. Do you mean your line is to play a low spade from both hands? It looks to me like that will guarantee you go down.

If you're intending to win that spade trick, you will learn nothing by both defenders following, so must already have a plan of what to do next (unlike double dummy, which will lead a spade intending to differ its next trick after it learns what the hands are). What is your single-dummy line that you believe has some upside?

(My guess is that your "SD5" program is playing a spade to dummy, then ducking a diamond. So you're not comparing a diamond duck with "a low spade", just the same line but with one extra trick cashed in between. This is a zero-gain play, just failing in the rare case when that extra cashed spade costs a ruff - a typical mistake by robots - which lines up with your numbers.)

[kgr]

Yes, you are correct. When playing to SA it will still duck a D the next trick.
I now added "Compleet Single Dummy" analysis tot my program. This makes the analysis slower, and therefore I have a parameter to enter the analysis count. This is the number of deals that are considered for every card in a single dummy analysis.
"Compleet Single Dummy" analysis for 300 analyzed deals gives:
- It is slightly better to play one high Heart first
- After that it selects S3 or D3 as the best card; it depends on the selected deals.
When it gives S3 the probability of making is same as D3 (but expected nr of tricks is higher).
When it gives D3 the probability of making is same as S3, or 1% better.
Therefore, we can say that D3 is a little better.
Without a "Compleet Single Dummy" analysis it will include some throw in possibilities for S3 that are not findable Single Dummy.