[mgoetze]

Welp, I just got 54.81% on a Robot Rebate 55%, mainly thanks to blowing this hand:

---

I'm sure all the experts can figure out the correct line, so do give my fellow I/As a crack at it please.

[monikrazy]

Spoiler

Plan for a dummy reversal

win the A
win a top trump
ruff a spade (high)
win a 2nd round of trumps
ruff another spade (high)
draw trumps
if trumps break 4-0 we are going to give up on the heart finesse and hope clubs break favorably
if trumps break 3-1 or 2-2 and clubs break poorly we may also have to fall back on the heart finesse, when jt drops in the first 3 tricks we can ruff a heart in north

[Cyberyeti]

monikrazy, on 2014-October-05, 11:49, said:

Spoiler

Plan for a dummy reversal

win the A
win a top trump
ruff a spade (high)
win a 2nd round of trumps
ruff another spade (high)
draw trumps
if trumps break 4-0 we are going to give up on the heart finesse and hope clubs break favorably
if trumps break 3-1 or 2-2 and clubs break poorly we may also have to fall back on the heart finesse, when jt drops in the first 3 tricks we can ruff a heart in north

If you click the next button a few times, you get to find out certain things about what breaks how

[monikrazy]

Cyberyeti, on 2014-October-05, 13:15, said:

If you click the next button a few times, you get to find out certain things about what breaks how

Spoiler

i looked after my initial post
we should still run clubs 66.3% of the time accounting for vacant spaces, i don't think we can do better trying to make

if we are worried about undertricks cashing one club honor before drawing trumps to cater for the stiff j or t with w might be a tiny improvement - not really sure on the math here

[Lovera]

It is intesting what's happen when we lead Queen of heart.

[Lovera]

Why in this topic dasn't continue the discussion ? This one seems not hardly to risolve and a nice problem. A consideration: after we know 4-0 in diamonds is higly probably that East has clubs (unbidding) 5th ..

[mgoetze]

The correct line was indeed the dummy reversal, as spotted by monikrazy. For some reason, at the table, when I saw the 4-0 trump split I panicked and played the heart finesse, which lost.

[johnu]

Lovera, on 2014-October-05, 16:17, said:

It is intesting what's happen when we lead Queen of heart.

When are you planning to play hearts?

[Trinidad]

I don't think it is that simple. The fact that West has shown up with all the trumps changes the odds a little bit. (This might make the problem more than I/A.)

Disclaimer: I am notoriously bad at these calculations. Take the word of an expert over mine.

West was forced to show 5 cards: the spade at trick 1 and his 4 trumps. East was forced to show 1 card: his spade at trick 1. The heart discard was a free choice.

That means that at that point West has only 8 vacant spaces, whereas East has 12. This means that the probability for a successful finesse against the ♥K has increased from 50% to 60%. At the same time, the probabilities for the club split are affected. Originally, the probability for a 3-2 split was 67.83%, making playing for the club split superior. But when the vacant spaces split 8-12, this decreases.

When you ruff 2 spades (assuming no one shows out) the probabilities change even more. Now West has 6 vacant spaces and East 10. The finesse is now 62.5%. And, the probability for a 3-2 split will be even lower.

I would guess that playing for the 3-2 split is technically still superior, but not by much. This means that against robots I would play for the dummy reversal, but against people I might take the finesse based on my table feel (which, unfortunately, is also notoriously bad ).

Rik

[Lovera]

We can fullfil the contract only with the condition of club honors divided. This play become probably when we think 3-2 diamonds and clubs. In this cases when we have to find two tricks to think dummy reversal is natural (it gains one trick) re-entries allowing for ruffing (remainig a trick to find) otherwise we can think (if is it possible) to a repeat triple squeeze to obtain the two tricks that we want. Here are possible both this plains, on the assumption King of heart in East and having (on opening leads) the indication that Queen of spade also, we don't warry of clubs.

[mgoetze]

Trinidad, on 2014-October-07, 11:56, said:

When you ruff 2 spades (assuming no one shows out) the probabilities change even more. Now West has 6 vacant spaces and East 10. The finesse is now 62.5%. And, the probability for a 3-2 split will be even lower.

Playing fast and loose with vacant spaces unfortunately does not give the correct answer in this case.

Given that diamonds split 4-0, the a priori chances of various spade splits are:

3-6 28.98%
4-5 32.60%
5-4 18.11%
6-3 4.83%

If we know that it is one of these splits, we can normalise these to 100% and get

3-6 34.29%
4-5 38.57%
5-4 21.43%
6-3 5.71%

Multiplying these chances by the respective portion of heart cards East holds in these scenarios gives only a 61.43% chance for the finesse to work.

On the other hand, here are some W-E open spaces and the chance of a 3-2 or 2-3 club split in each case:

6-7 73.43%
5-8 65.27%
4-9 50.35%
3-10 31.47%

Multiplying with the previous table, there is a 62.94% chance that clubs break.

So you are correct that it is actually very close.

Edit: I was originally off by one on the number of hearts held by East giving worse odds for the finesse.

This post has been edited by mgoetze: 2014-October-07, 15:10

[antonylee]

It's actually awfully close (assuming nobody shows out on spades), 10K sims give 63% of 3-2 splits making it barely superior (I haven't bothered computing an error bar).

[johnu]

That's a lot of work to calculate heart and club odds to 4 decimal places. I prefer simpler math. 4 trumps in dummy, spade ace, 2 spade ruffs in hand, and 3 top clubs is 10 tricks. If you finesse in hearts, that's 12 tricks. To get 13 tricks, you would still need a club-heart squeeze. If West has 3 or more hearts, East can break up a squeeze by covering a heart honor.

[mgoetze]

johnu, on 2014-October-07, 17:23, said:

That's a lot of work to calculate heart and club odds to 4 decimal places. I prefer simpler math. 4 trumps in dummy, spade ace, 2 spade ruffs in hand, and 3 top clubs is 10 tricks. If you finesse in hearts, that's 12 tricks. To get 13 tricks, you would still need a club-heart squeeze. If West has 3 or more hearts, East can break up a squeeze by covering a heart honor.

So basically what you're saying is, you're not even going to bother trying to make the contract?

[nige1]

mgoetze, on 2014-October-05, 10:23, said:

Welp, I just got 54.81% on a Robot Rebate 55%, mainly thanks to blowing this hand: I'm sure all the experts can figure out the correct line, so do give my fellow I/As a crack at it please

---

Dummy-reversal-reversal

Spoiler

♠A, ♦Q (finding West has 4♦s), ♠ ruff, ♣AK. Now...

• If West has 5♣s, then ♣Q, ruff a ♣ high ♥Q finessing, ♥A, ruff a ♣ high, ♦J9. (West must be 2245 or 1345)
• If West has 4♣s, then ♣Q ruff a ♣ high and take the ♥ finesse, draw trumps, and cash your good ♣.
• If both defenders follow to ♣AK), then claim: ♦K, ♠ ruff, ♦AT, discarding a ♥, ♣Qxx, ♥A

If West played ♣J or ♣T on ♣A and you guess it's a singleton then you might cash ♥A next so that you can later cash ♥QJ if ♥K was singleton -- rather unlikely so not worth bothering about!

Anyway, If West played a ♣ honour on ♣A then you might decide not to cash a second ♣ while in dummy but instead continue with the dummy reversal, and consider the finesse of ♣9. Not simple restricted choice because West may have played an honour from ♣JTx(x). So probably line 1/2/3 is better against a good defender.

[johnu]

mgoetze, on 2014-October-07, 17:55, said:

So basically what you're saying is, you're not even going to bother trying to make the contract?

I'm saying that all those detailed heart/club calculations are basically a waste of time because if clubs come in you have the 2 additional tricks you need without the parlay of heart finesse and squeeze where you probably East to make a mistake.

[Lovera]

johnu, on 2014-October-07, 17:23, said:

That's a lot of work to calculate heart and club odds to 4 decimal places. I prefer simpler math. 4 trumps in dummy, spade ace, 2 spade ruffs in hand, and 3 top clubs is 10 tricks. If you finesse in hearts, that's 12 tricks. To get 13 tricks, you would still need a club-heart squeeze. If West has 3 or more hearts, East can break up a squeeze by covering a heart honor.

The situation in heart is particolar: whatever East do doesn't escape. Let's suppose that he had King and play it then we have a re-entry with Jack and we ruff 5 (second ruff the first in spade). Now we run diamonds on the last East is squeezed spade/club (dummy reversal+simple squeeze)To avoid this East if don't play King Queen run, 5 to Ace and now we have spade J against Q, heart J against K, xxx/AKQxx in club for an automatic triple squeeze to gain two tricks (let's note that we don't consider clubs covering all shapes in suit). If East had (but is not probable here) hearts 6th 5 can consider menace (rare).

[nige1]

Lovera, on 2014-October-08, 10:22, said:

The situation in heart is particolar: whatever East do doesn't escape. Let's suppose that he had King and play it then we have a re-entry with Jack and we ruff 5 (second ruff the first in spade). Now we run diamonds on the last East is squeezed spade/club (dummy reversal+simple squeeze)To avoid this East if don't play King Queen run, 5 to Ace and now we have spade J against Q, heart J against K, xxx/AKQxx in club for an automatic triple squeeze to gain two tricks (let's note that we don't consider clubs covering all shapes in suit). If East had (but is not probable here) hearts 6th 5 can consider menace (rare).

JohnU echos John Matheson: First count your tricks. The dummy reversal gives you
♠A, ♥A, 2 ♠ ruffs, 4 top ♦s, and 3 top ♣s = 11 tricks, so you need to find 2 more.
If ♣s are 3-2, then the long ♣s suffice.
Otherwise..
Lovera can't' execute a ♣/♠ squeeze because all North's ♠s have been ruffed. Hence, as JohnU points out, if you have to finesse ♥ before finding out if ♣s break, then the ♥ finesse is likely to be a so-called "practice" finesse -- useful for rehearsing your finessing technique but unlikely to help make the contract. The ♥ finesse helps only if you can develop a ♣ / ♥ squeeze i.e. East fails to cover or he has 6 ♥s.

What might slightly increase your chances is (after ♠A, ♦Q, finding that west has 4 ♦s, ♠ ruff), at trick 4, try to cash ♣AK (see earlier reply).

[nige1]

mgoetze, on 2014-October-07, 15:00, said:

Playing fast and loose with vacant spaces unfortunately does not give the correct answer in this case.
Given that diamonds split 4-0, the a priori chances of various spade splits are:
3-6 28.98%
4-5 32.60%
5-4 18.11%
6-3 4.83%

If we know that it is one of these splits, we can normalise these to 100% and get
3-6 34.29%
4-5 38.57%
5-4 21.43%
6-3 5.71%

Multiplying these chances by the respective portion of heart cards East holds in these scenarios gives only a 61.43% chance for the finesse to work.
On the other hand, here are some W-E open spaces and the chance of a 3-2 or 2-3 club split in each case:
6-7 73.43%
5-8 65.27%
4-9 50.35%
3-10 31.47%

Multiplying with the previous table, there is a 62.94% chance that clubs break.
So you are correct that it is actually very close.

East led the ♠K, so he is quite likely to have ♠Q and perhaps ♠T, This affects vacant spaces and probabilities.
If East covers the North's first ♥ honour, then you need him ot have started with 6 ♥s for the squeeze to work.
Finally, the squeeze-line works only if West has fewer than 4 ♣s.

[PhantomSac]

It's as if no one considered the bidding