[JSSMP1]

I'm not sure what to do odds-wise with a guess that occurs quite frequently. Let's say the bidding goes: LHO opens 1♥, my partner bids 1♠, RHO passes, I bid 2♠, all Pass. When dummy comes down, it becomes clear our side has 22 HCP, 6♥ and our ♠suit (trump) is AJ98 opposite KT765 (missing 4 and the ♠Q). I can finesse either opponent for the Q or play for the drop.

What is the correct action?
- 8 ever 9 never says to play for the drop.
However, the odds of dropping or finessing (after first cashing a single A or K) are extremely close...
- Since LHO has more hearts (likely 5 vs 2), RHO has more room in his hand for the ♠Q. This seems to give the edge to finessing RHO.
- Since LHO has more HCP, he is likely to hold missing HCP. This seems to give the edge to finessing LHO
All actions are probably close, but I'm wondering which is mathematically optimal. What are your takes on this?

[bluenikki]

 JSSMP1, on 2023-September-18, 03:18, said:

I'm not sure what to do odds-wise with a guess that occurs quite frequently. Let's say the bidding goes: LHO opens 1♥, my partner bids 1♠, RHO passes, I bid 2♠, all Pass. When dummy comes down, it becomes clear our side has 22 HCP, 6♥ and our ♠suit (trump) is AJ98 opposite KT765 (missing 4 and the ♠Q). I can finesse either opponent for the Q or play for the drop.

What is the correct action?
- 8 ever 9 never says to play for the drop.
However, the odds of dropping or finessing (after first cashing a single A or K) are extremely close...
- Since LHO has more hearts (likely 5 vs 2), RHO has more room in his hand for the ♠Q. This seems to give the edge to finessing RHO.
- Since LHO has more HCP, he is likely to hold missing HCP. This seems to give the edge to finessing LHO
All actions are probably close, but I'm wondering which is mathematically optimal. What are your takes on this?

I don't believe the HCP rationale is valid: In Goren, at least, singleton and Qxx are the same two points.

[P_Marlowe]

The distribution is a stronger argument, you are looking for a 2HCP card, when 18HCP are missing,
they may split 12:6 or 10:8.

The possible option is to find out more about HCPs in the weaker hand, ..., if the time allowes it,
we are talking about the trump suit.

With kind regards
Marlowe

[smerriman]

Ha. Almost 7 years ago I posted basically exactly the same question, and (after most of the posts dealing with the specific hand rather than the general question), Marlowe posted an almost identical response to the above

I remember doing some simulations back then and came to the same conclusion myself; the distribution virtually always outweighs the HCP imbalance.

[Stephen Tu]

Though if opener has singleton spade, with his stronger hands he is likely to act again, double or showing a second suit, so lack of action probably tilts it back somewhat towards drop? Responder with singleton spade also more likely to come in with more shape.

[JSSMP1]

Thanks for all the responses. As far as I can see, the conclusion should be along the lines of 'it depends'. Bidding, vulnarability etc should all play a role in the decision. It is useful to know that length is generally a better indicator than HCP. Maybe I'll research that a bit myself in the future.

[smerriman]

 smerriman, on 2023-September-18, 05:03, said:

I remember doing some simulations back then and came to the same conclusion myself; the distribution virtually always outweighs the HCP imbalance.

.. at least I thought I did, but rerunning the numbers now, I get different results to what I recall. If you take these sample hands:

---

and assume the very simplistic (and not very accurate) rule that West has any 11+ HCP hand with 5+ hearts, no other constraints.

By my calculations:

- king from North, then finesse if needed: 60%
- king from North, then drop if needed: 64%
- ace from South, then finesse if needed: 55%
- ace from South, then drop if needed: 55%

That isn't what I would have expected.. perhaps someone else can confirm my numbers Feels somewhat contradictory how you want to initially play East for length, but then switch to playing West for length if the 0-4 break doesn't materialize..

Again, probably not too relevant practically since spade voids are likely to impact the bidding, but still intriguing.

[thepossum]

Since it is unlikely to be repeated very often in an individual bridge life I don't think it matters much to most of us. Try to get a bit more information if you can

I may try to replicate smerriman's numbers privately for a bit of fun

Sorry what was the lead?

Without having run a sim with details after a King of clubs lead you win with the Ace in dummy and lead back to South's Ace - according to one piece of software
West has 5+ hearts and more than 10 HCPs and East has fewer than 7 HCPs and the King of clubs was led. Difference in number of tricks was approximately 9.25 versus 9.20 on average after East plays low. Before you play you were looking at approximately 9.68 tricks. If East plays the Queen you can smile a bit
As I said it doesn't matter much to me anyway
DISCLAIMER. Just one layout of the cards as per smerriman and approximately the same simplistic points assumption and making the assumption of the lead of the King of Clubs. Not a full analysis which would require a lot of time

[fuzzyquack]

No action by opps lowers chances for 3-1 break. Simulations provide little help in considering the relation of the distribution to the opps action/inaction.