[gnasher]

I was quite surprised by Bluecalm's simulation results, so I did my own simulation of 30 hands and decided how each lead would work single-dummy. The results agree approximately with Bluecalm's:

Heart lead beats it: 3
Heart lead may beat it: 1
Spade lead beats it: 1
Spade lead probably beats it: 1
Club, diamond or spade may beat it: 1
Making on any lead: 21
Inconsistent with the bidding: 2

I'm still surprised.

I noticed that when the contract was making a heart lead usually cost an overtrick. However, this isn't enough to justify not leading a heart: Even if we beat 3NT only 3/28 times and concede an overtrick 25/28 times, the expectation from a heart lead is still
3/28 x 12 - 25/28 x 1 = +0.4

The hands and my code are below.

The hands:

          S: A86
          H: 52
          D: AQJ84
          C: 843
 S: T32            S: J97
 H: K6             H: T8743
 D: 9753           D: KT
 C: Q652           C: KT9
          S: KQ54
          H: AQJ9
          D: 62
          C: AJ7
Probably making on any lead.  C, D or S gives some chance.
--------------------------
          S: Q7
          H: J84
          D: K4
          C: AK9743
 S: T32            S: K8654
 H: K6             H: 9753
 D: 9753           D: QT8
 C: Q652           C: J
          S: AJ9
          H: AQT2
          D: AJ62
          C: T8
Making on any lead.
--------------------------
          S: J9
          H: Q4
          D: K862
          C: AKT87
 S: T32            S: 8764
 H: K6             H: JT853
 D: 9753           D: AQ
 C: Q652           C: 94
          S: AKQ5
          H: A972
          D: JT4
          C: J3
Making on any lead.
--------------------------
          S: AK8
          H: 83
          D: AQ82
          C: T987
 S: T32            S: J9754
 H: K6             H: JT95
 D: 9753           D: K4
 C: Q652           C: J4
          S: Q6
          H: AQ742
          D: JT6
          C: AK3
Making on any lead.
--------------------------
          S: KQ9
          H: JT3
          D: JT6
          C: K843
 S: T32            S: 74
 H: K6             H: Q9842
 D: 9753           D: AQ84
 C: Q652           C: JT
          S: AJ865
          H: A75
          D: K2
          C: A97
Making on any lead.
--------------------------
          S: 754
          H: AJ9
          D: J62
          C: AT97
 S: T32            S: Q96
 H: K6             H: T873
 D: 9753           D: QT8
 C: Q652           C: KJ3
          S: AKJ8
          H: Q542
          D: AK4
          C: 84
Making on any lead.
--------------------------
          S: 864
          H: QJ42
          D: K62
          C: A94
 S: T32            S: AKJ5
 H: K6             H: T85
 D: 9753           D: JT84
 C: Q652           C: T7
          S: Q97
          H: A973
          D: AQ
          C: KJ83
Making on any lead.
--------------------------
          S: A84
          H: Q8
          D: KJ864
          C: KT4
 S: T32            S: J96
 H: K6             H: JT9432
 D: 9753           D: A2
 C: Q652           C: 83
          S: KQ75
          H: A75
          D: QT
          C: AJ97
Making on any lead.
--------------------------
          S: AQ9
          H: 53
          D: Q64
          C: KT974
 S: T32            S: 7654
 H: K6             H: AQJ987
 D: 9753           D: J
 C: Q652           C: J3
          S: KJ8
          H: T42
          D: AKT82
          C: A8
H beats it.
--------------------------
          S: KQ87
          H: QJ7
          D: KJ4
          C: J98
 S: T32            S: J64
 H: K6             H: A98542
 D: 9753           D: Q
 C: Q652           C: T74
          S: A95
          H: T3
          D: AT862
          C: AK3
Making on any lead.
--------------------------
          S: J54
          H: A42
          D: QJT8
          C: K73
 S: T32            S: 87
 H: K6             H: QT753
 D: 9753           D: AK2
 C: Q652           C: JT9
          S: AKQ96
          H: J98
          D: 64
          C: A84
H beats it (declarer will duck opening lead).
--------------------------
          S: 85
          H: QT
          D: AT64
          C: AJT74
 S: T32            S: QJ974
 H: K6             H: AJ72
 D: 9753           D: J2
 C: Q652           C: 83
          S: AK6
          H: 98543
          D: KQ8
          C: K9
Making on any lead.
--------------------------
          S: 654
          H: AJ7
          D: QJT82
          C: A8
 S: T32            S: K9
 H: K6             H: T5432
 D: 9753           D: A6
 C: Q652           C: JT97
          S: AQJ87
          H: Q98
          D: K4
          C: K43
Making on any lead.
--------------------------
          S: J95
          H: 92
          D: AKQJ6
          C: K73
 S: T32            S: AQ87
 H: K6             H: T873
 D: 9753           D: 8
 C: Q652           C: J984
          S: K64
          H: AQJ54
          D: T42
          C: AT
Making on any lead.
--------------------------
          S: K64
          H: 72
          D: AKJ642
          C: 43
 S: T32            S: A85
 H: K6             H: J9843
 D: 9753           D: Q
 C: Q652           C: T987
          S: QJ97
          H: AQT5
          D: T8
          C: AKJ
Making on any lead.
--------------------------
          S: KJ7
          H: A98
          D: KQJ4
          C: T43
 S: T32            S: AQ65
 H: K6             H: T74
 D: 9753           D: T62
 C: Q652           C: J87
          S: 984
          H: QJ532
          D: A8
          C: AK9
Making on any lead.
--------------------------
          S: K64
          H: J42
          D: JT2
          C: AK93
 S: T32            S: 87
 H: K6             H: AT9853
 D: 9753           D: A86
 C: Q652           C: T8
          S: AQJ95
          H: Q7
          D: KQ4
          C: J74
H may beat it (defence ducks second heart, so declarer had no reason to get clubs right).
--------------------------
          S: Q87
          H: QJ73
          D: KJ6
          C: J43
 S: T32            S: KJ95
 H: K6             H: 9854
 D: 9753           D: QT82
 C: Q652           C: A
          S: A64
          H: AT2
          D: A4
          C: KT987
S probably beats it (S10 prevents declarer's ducking; S2 probably causes declarer to play for K onside).
--------------------------
          S: A7
          H: Q52
          D: K8642
          C: AT7
 S: T32            S: J9865
 H: K6             H: T94
 D: 9753           D: AJ
 C: Q652           C: J98
          S: KQ4
          H: AJ873
          D: QT
          C: K43
Making on any lead.
--------------------------
          S: 964
          H: T5
          D: AKQ84
          C: T83
 S: T32            S: 87
 H: K6             H: AQJ942
 D: 9753           D: JT
 C: Q652           C: KJ7
          S: AKQJ5
          H: 873
          D: 62
          C: A94
H beats it.
--------------------------
          S: 95
          H: QT7
          D: AKJT2
          C: K94
 S: T32            S: KQJ87
 H: K6             H: 8532
 D: 9753           D: 4
 C: Q652           C: T83
          S: A64
          H: AJ94
          D: Q86
          C: AJ7
Making on any lead.
--------------------------
          S: J4
          H: T3
          D: QT8
          C: AJT873
 S: T32            S: AQ9876
 H: K6             H: 97542
 D: 9753           D: A4
 C: Q652           C: ---
          S: K5
          H: AQJ8
          D: KJ62
          C: K94
S beats it.
--------------------------
          S: 874
          H: A3
          D: Q6
          C: AKT973
 S: T32            S: Q65
 H: K6             H: T8542
 D: 9753           D: AJ84
 C: Q652           C: 4
          S: AKJ9
          H: QJ97
          D: KT2
          C: J8
North would make slam try.
--------------------------
          S: J874
          H: JT4
          D: AKJ
          C: 983
 S: T32            S: 5
 H: K6             H: Q9753
 D: 9753           D: Q62
 C: Q652           C: AJT4
          S: AKQ96
          H: A82
          D: T84
          C: K7
Making on any lead.
--------------------------
          S: A97
          H: T3
          D: AT864
          C: KJ4
 S: T32            S: QJ86
 H: K6             H: Q9874
 D: 9753           D: Q2
 C: Q652           C: T9
          S: K54
          H: AJ52
          D: KJ
          C: A873
Making on any lead.
--------------------------
          S: Q97
          H: 754
          D: A82
          C: A974
 S: T32            S: 864
 H: K6             H: QJ98
 D: 9753           D: KT64
 C: Q652           C: K8
          S: AKJ5
          H: AT32
          D: QJ
          C: JT3
Making on any lead.
--------------------------
          S: 94
          H: A9
          D: KQT
          C: KJT743
 S: T32            S: A8765
 H: K6             H: Q742
 D: 9753           D: 8642
 C: Q652           C: ---
          S: KQJ
          H: JT853
          D: AJ
          C: A98
N would make slam try.
--------------------------
          S: KJ9
          H: 83
          D: KQJ842
          C: K9
 S: T32            S: 76
 H: K6             H: QJT754
 D: 9753           D: 6
 C: Q652           C: A873
          S: AQ854
          H: A92
          D: AT
          C: JT4
Making on any lead.
--------------------------
          S: KJ5
          H: 83
          D: QJ84
          C: AJ73
 S: T32            S: 976
 H: K6             H: JT972
 D: 9753           D: A6
 C: Q652           C: K94
          S: AQ84
          H: AQ54
          D: KT2
          C: T8
Making on any lead.
--------------------------
          S: K84
          H: 9832
          D: AQ6
          C: AT8
 S: T32            S: A976
 H: K6             H: QT74
 D: 9753           D: J8
 C: Q652           C: 973
          S: QJ5
          H: AJ5
          D: KT42
          C: KJ4
Making on any lead.
--------------------------

And my code:

west is {T32 K6 9753 Q652}

main {
  if {[1nt south] && [1nt_3nt north]} { accept }
  reject
}

#######################################################################################################################################################
proc 1nt {hand} {
  set hcp [hcp $hand]
  set ptn [$hand pattern]
  set shp [$hand shape]
  
  # 4333 or 4432, 15-17
  if {$ptn == "4 3 3 3" || $ptn == "4 4 3 2"} {
    if {$hcp > 14 && $hcp < 18} { accept }
    reject
    }
    
  # 5332 or 22(54), 14-16
  if {$ptn == "5 3 3 2" || $shp == "2 2 4 5" || $shp == "2 2 5 4"} {
    if {$hcp > 13 && $hcp < 17} { accept }
    reject
    }

  # 6m332, 13-16
  if { $ptn == "6 3 2 2" && ([diamonds $hand] == 6 || [clubs $hand] == 6) } {
    if {$hcp > 12 && $hcp < 17} { accept }
    reject
    }
    
  reject
  }

#######################################################################################################################################################
proc 1nt_3nt {hand} {
  set hcp [hcp $hand]
  set ptn [$hand pattern]
  set spades [spades $hand]
  set hearts [hearts $hand]
  
  # major-suit hands that wouldn't raise directly
  if {$spades > 4 || $hearts > 4} { reject }
  if {($spades == 4 || $hearts == 4) && $ptn != "4 3 3 3"} { reject }

  # 4333 or 4432, 10-15
  if {$ptn == "4 3 3 3" || $ptn == "4 4 3 2"} {
    if {$hcp > 9 && $hcp < 16} { accept }
    reject
    }
    
  # 5332 or 22(54), 9-14
  if {$ptn == "5 3 3 2" || $ptn == "5 4 2 2"} {
    if {$hcp > 8 && $hcp < 15} { accept }
    reject
    }

  # 6332, 8-13
  if {$ptn == "6 3 2 2"} {
    if {$hcp > 7 && $hcp < 14} { accept }
    reject
    }
    
  reject
  }

[bluecalm]

It would be great if it was possible to generate the hands using some kind of simulation software and give them to strong computer program to play. That should be much more reliable than double dummy analysis.
Your analysis is great but it would take some time to reach significant number of hands :-)

[bluecalm]

Quote

Could you please add ♦K to our hand and see the difference it makes?

New simul. 1000 hands. Our hand :
T32 K6 K975 Q652.
Opponent opens 15-17NT (5card major possible) and responder jumps to 3NT (9-14 balaced without 4+card major or any 4-3-3-3 10-15).

The winning (setting) lead:

T♠ - 103
3♠ - 104
K♥ - 88
9♦- 66
5[♦ - 70
2♣ - 76

All makes sense in my opinion. Now we are not desperate so leading spades is good. I wonder how meaningful is that opener can have 5card major but it can only be bad fo rmajor suit leads. I am pretty sure that including any 4-3-3-3 is also bad for major suit leads which suggest that against opponents who always stayaman leading spade in this example and Kh in the previous one is clear (and big) winner.

I am going to find out how good the minor suit need to be to lead it. Is it possible that 4 card minor like QT8x is good enough ? What about KQTx ? Do you lead any 5 card minor ? If how strong it needs to be ? Results soon

[Fluffy]

what suprises me now is that we have much less chances of beating this by leading ♥K than previously. I expected the number of heart beats to drop a bit, but droping from 140 to 88 by having more strenght sounds a bit too much.

[bluecalm]

Quote

but droping from 140 to 88 by having more strenght sounds a bit too much.

We didn't drop from 140. The first simul didn't include 4-3-3-3 hands with 4 card major in 3nt (they would stayman). The second one did. In the second one the score was 1030 (for 10k hands) so it's a drop from 103 to 88 not from 140 to 88. Seems like you have very good intuition noticing that it's too big a difference

By they way from my experience those simuls are statistically significant after 1k hands. I am yet to see the case with big difference for different sets of 1000 hands. At least if the hands are "not wild".

[rduran1216]

If this is MP, I would never lead the K of hearts.

If it is imps, K of hearts is definitely my lead.

With 5 pts my partner certainly has the balance of the strength, and so he could have 2 entries or even one entry with honors in hearts, add that he's almost sure to have some kind of heart length and if I dont care about allowing overtricks, K♥ looks best.

[bluecalm]

I did some more simuls and it seems that they confirm common wisdom more or less (lead major against 1nt - 3nt auctions unless you have good suit etc).
Some examples :

1)♠T32 ♥K6 ♦K975 ♣QT83
Best leads :

3♠ 173
K♥ 109
5♦ 123
3♣ 121

2)♠T32 ♥K6 ♦K95 ♣QT853

3♠ - 124
K♥ - 100
5♦ - 86
5/3♣ = 139

3)Same as above but opponents always stayman with 4 card major :
3♠ - 175
K♥ - 122
5♦ - 117
3/5♣ - 154

One thing which those simuls clearly shows is that it's very important if opponents always use stayman or not. I wonder how many honest answers would you get if you ask this before your lead.
I guess matchpoints is different animal. I am not feeling like doing those simuls for mp's (they take a lot of time) but maybe I will leave my comp for the night to calculate one or two cases.
Hands like those tell me that those simuls despite being simple/imperfect/not always on spot with the bidding and double dummy can tell us a lot about correct leads in different situations.

[gnasher]

bluecalm, on Jan 4 2010, 12:16 AM, said:

One thing which those simuls clearly shows is that it's very important if opponents always use stayman or not. I wonder how many honest answers would you get if you ask this before your lead.

I'd expect an honest answer to such a question from about 99% of players. That doesn't mean I'd necessarily get a good answer - I suspect that many people would find it hard to estimate how often their partner eschews Stayman.