[RunemPard]

Do not have the exact cards, but they were not very relevant.

You are 2nd to bid after a pass from your righty...You are NV, opps are V...2/1

Opps leads are 3rd/5th

If I recall correctly, the lead was the C9 or C8..

---

2N=GF raise
3♠=extras+diamond single
4♥=control

[nige1]

RunemPard, on 2014-November-26, 16:51, said:

2N=GF raise
3♠=extras+diamond single
4♥=control

Do not have the exact cards, but they were not very relevant.
You are 2nd to bid after a pass from your righty...You are NV, opps are V...2/1
Opps leads are 3rd/5th
If I recall correctly, the lead was the C9 or C8..

---

Spoiler

For a 50% chance run the ♠T.
Slightly better is to cash ♠A and, if ♠K doesn't drop, then discard ♣s on dummy's ♦. This works when

• Singleton ♠K is in either opponent's hand.
• Doubleton ♠Kx is with 3+ ♦s or
• Trebleton ♠Kxx is with 4 + ♦s or
• Trebleton ♠Kxx is in RHO's hand with 3 ♦s (he will ruff the 4th ♦ low but you over-ruff and re-enter dummy with ♥A to lead another ♦.

[PhantomSac]

MATH alert, no idea what the right answer is but SA feels right to me. Recently I was totally wrong on one of these though so look forward to the numbers.

[mikeh]

I don't know the percentages either.

I tried to do my estimating as I would at the table.

The Ace wins with stiff K offside, and breaks even with stiff K onside, compared to the finesse.

When LHO has Kx, we need him to hold 3+ diamonds. When he has Kxx we need him to hold 4+ diamonds. Doing the best I can without looking up suit split percentages, I'd estimate about 12.5% for the stiff K offside, about 15% for Kx and 3+ diamonds (Kx being 25% and 3+ diamonds being somewhat over 50%) and about 2-3% for Kxx and 4+ diamonds. Total of about 30%.

The hook wins 37.5%, since it is a straight 50% proposition but breaks even, rather than wins, 12.5% of the time.

Looks like the hook to me. Having said that, my instinct is exactly the same as Justin's....the A seems best on a gut level. However, at the table I think I would do the finesse. I'll wait to see if the probability whizzes here can show me that my gut is smarter than my head

edit: My error was that I forgot to realize that the A breaks even on many other hands...Kx of spades onside and the diamonds lying right for us. That's what my gut was telling me:)

[WesleyC]

Spade hook:

= 50% 52% (tks PhantomSac)

Spade Ace:
26% (Kingleton) +
52% (chance of Kxs)* 63.5% (chance of 3 or more diamonds with the Ks) +
22% (chance of Kxxs) * 20% (chance of 4 or more diamonds with the Kxx spades)

= 63%

mikeh's gut was right!

[PhantomSac]

Spade hook is better than 50 % since it also makes on Kxx off with 4+ diamonds but still seems like SA is better based on your math. More MATH plz

[WesleyC]

Good point - SPADE HOOK: Now with a bonus 2.2%

[cherdano]

Here is the math I'd actually do at the table.

• Spade hook is 50% (ignoring the extra chance pointed out by Justin).
  
• Spade A is
  
  • 100% with stiff king
    
  • Much better than 50% with Kx (we need Kx with at least half the outstanding diamonds)
    
  • Quite a bit better than 0% with Kxx
  
  Since 1. and 3. are approximately equally likely, it's easy to see that ♠A is significantly better than 50%.

Really that seems enough to make the decision. I'd maybe note in addition that stiff king is more likely than Kxx, widening the gap even further.

(Btw, the "quite a bit better than 0% with Kxx" part actually covers twice the likelihood of the extra chance for the hook.)

[awm]

Here's another line: cash diamonds from the top! We have:

1. 3-3 break. After two pitches, revert to spade ace, making if spades are 2-1 (same as starting with spade ace).
2. 4-2/5-1 break with all three trumps in the long hand. Make.
3. 4-2/5-1 break with shortness on right. When RHO ruffs, overruff and return to dummy in hearts. Continue diamonds. If RHO ruffs a second time before the 5th diamond, overruff and pick up spades. If not, pitch all clubs as LHO ruffs in, and pick up spades.

Compared to just playing spade ace, this wins when diamond shortage is on the right along with Kx(x) trumps and loses when diamond shortage is on the left along with x or K stiff or xx trumps. Slightly more losing trump layouts but surely the short trumps are less likely to be with short diamonds than vice versa...

[WesleyC]

1. 3-3 break. After two pitches, revert to spade ace, making if spades are 2-1 (same as starting with spade ace).

(3/3 hearts) * (spades 2/1)
=35.5% * 79%
=28%

2. 4-2/5-1 break with all three trumps OFFSIDE in the long hand. Make.

(4/2 or 5/1 hearts) * (spades 3/0 offside)
=11%*20%
=2.2%

3. 4-2/5-1 break with shortness on right. When RHO ruffs, overruff and return to dummy in hearts. Continue diamonds. If RHO ruffs a second time before the 5th diamond, overruff and pick up spades. If not, pitch all clubs as LHO ruffs in, and pick up spades.

I think you can actually pickup ALL spade layouts when the short hearts are onside. However you do risk going down on some layouts where the opponents can discard a couple of times and engineer a ruff in a side suit (or a trump promotion). Not very likely and i'm just going to guess a number rather than working one out.

(Short hearts onside) - (chance of an overruff/trump promo in a different suit)
=31% - (chance of an overruff)


Overall
= 61% - (the chance of an overruff/promotion)
~=59%.

So definitely better than taking the finesse and only slightly worse than starting with the As.

Interesting to know because I would never have considered that line at the table...

[awm]

There might be another factor in that LHO *might* have bid with only 2-3 pointed cards. Obviously the colors reduce the odds but some x KQxxx x KJxxxx might have found a call. Dunno if this makes up the difference between the lines (although if opponents were NV more likely it would).

[kgr]

PhantomSac, on 2014-November-26, 22:20, said:

MATH alert, no idea what the right answer is but SA feels right to me. Recently I was totally wrong on one of these though so look forward to the numbers.

I wonder if this is a psychology thing: If an expert doesn't know the odds, he will prefer the line on which he is not immediately down?