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[Event "The Deletion Principle"]
[Site ""]
[Date ""]
[Board "1"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "N"]
[Vulnerable "None"]
[Deal "N:AT.AK.AK73.Q9632 KQJ72.762.986.54 98.QT543.542.AJT 6543.J98.QJT.K87"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ East leads \S King. 

 Initial Analysis:

 We have 7 top tricks and we require an additional 2 tricks.

 There is the obvious Club finesse, which, if successful, would give us those 2
additional tricks.

 There is also the Heart suit, which, if the suit was to divide 3-3 or the
\HJack is a doubleton, this\n
 would also give us 2 extra tricks.

 Calculations:

 At the start of the hand, the chance of the Heart suit dividing evenly at 3-3
is a 36% chance and\n
 the chance of the Heart suit dividing unevenly at 4-2 is a 48% chance,
however, when both\n
 defenders follow to two rounds of Hearts, both of these percentages rise as we
have eliminated\n
 the possibilities of the Heart suit dividing 5-1 and 6-0.

 A certain number of 4-2 divisions have also been eliminated, the ten 4-2
divisions that contain a\n
 doubleton \HJack.\n
 So, using the 'Deletion Principle' the even break in Hearts has now risen to
52.4%

 Meanwhile, the Club finesse has remained static at 50%.  \n
  \n
 Conclusion:

 We win the second round of Spades with our \SAce and we can cash our \HAce and
\HKing.\n
 We now play a Club to dummy's \CAce.\n
 We now cash our \HQueen, when the \HJack appears, we cash 2 more Hearts. \n
 }
[BCFlags "1f"]
[Auction "N"]
2NT Pass 3D Pass
3H Pass 3NT AP

[Event "More Than One Plan"]
[Site ""]
[Date ""]
[Board "2"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "E"]
[Vulnerable "NS"]
[Deal "E:AK4.AT972.AK3.K6 QJT98.KJ64.J97.9 75.3.8654.AQ5432 632.Q85.QT2.JT87"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ South leads \S Queen.

 Initial Analysis:

 We have 8 top tricks, so we just require one additional trick.

 We can get that one additional trick from the Club suit.

 As a 'Backup Plan', if the Club suit divides badly, there is a possibility
that the Diamond suit\n
 divides 3-3, which would provide us with our 9th trick.    

 Calculations:

 If the Club suit divides 3-2, which is a 68% chance, then we have more than
enough tricks.\n
 Failing that, we can hope that the Diamond suit divides 3-3, which is a 36%
chance.

 However, although it is called, our 'Backup Plan', we must action our 'Backup
Plan' first.

 If we play on the Club suit first and it fails, even when the Diamond suit
divides 3-3, we will not\n
 be able to get to our winning Diamond in dummy.\n
  \n
 Conclusion:

 We win the opening lead with the \SAce and play 3 rounds of Diamonds.

 When the Diamonds divide 3-3, we have our 9th trick waiting for us in dummy.}
[BCFlags "1f"]
[Auction "E"]
2NT Pass 3NT AP

[Event "One of Two Finesses "]
[Site ""]
[Date ""]
[Board "3"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "S"]
[Vulnerable "EW"]
[Deal "S:95.AKJ632.A53.AQ J863.754.KQJT.K6 AQ.QT9.764.87543 KT742.8.982.JT92"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ West leads \D King.

 Initial Analysis:

 We have 9 top tricks, so just one more trick is required.

 We have two black suit finesses available plus we have a long Club suit in
dummy.

 Calculations:

 To draw trumps and take the Club finesse followed by the Spade finesse is a
'One of Two\n
 Finesses' strategy, however, because we are finessing against two different
defenders, this\n
 equates to a 74% chance that we will get our extra trick.

 Trying to establish our 5th Club in dummy requires either a 3-3 or 4-2
division in the Club suit.\n
 The 3-3 break is a 36% chance and the 4-2 break is a 48% chance, so the total
chance of\n
 success is 84%.

 We should reject the 'One of Two Finesses' strategy (74% Chance), and instead
use the 84%\n
 strategy, which is to establish dummy's 5th Club. 

 Conclusion:

 We win the opening lead with the \DAce.\n
 Play a Heart to the 9 of Hearts.\n
 Play a Club to the \CAce and then play the \CQueen.\n
 When the defenders play a Spade, go up with the \SAce.\n
 Now ruff the 3rd round of Clubs with the \HAce and play a Heart to the 10 of
Hearts.\n
 Ruff the 4th round of Clubs with the \HKing and play a Heart to the \HQueen.\n
 We can now cash our 8 of Clubs, which gives us 6 Heart tricks, 2 Club tricks,
1 Spade trick and 1\n
 Diamond trick.}
[BCFlags "1f"]
[Auction "S"]
1H Pass 2H Pass
4H AP

[Event "Restricted Choice"]
[Site ""]
[Date ""]
[Board "4"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "W"]
[Vulnerable "All"]
[Deal "W:K6432.432.A.AKQ6 J97.AKQ.765.8754 AT85.765.KQT8.JT Q.JT98.J9432.932"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ South leads \H Ace.

 Initial Analysis:

 After the defence cash their 3 top Hearts, our only other potential loser is
going to be in Spades.

 How do we play the trump suit?


 Calculations:

 If Spades are 2-2, we have zero Spade losers (40% Chance).

 If Spades are 3-1, we will lose a Spade, unless South has a singleton Spade
honour.\n
 \n
 Conclusion:

 We play our \SK and observe South playing their \SQueen.\n
 According to the 'Restricted Choice' rule, South is twice as likely to have
started with the\n
 singleton \SQueen than the alternative holding of the Queen, Jack doubleton
Spade holding.\n
 Consequently, we now play a winning Spade finesse, by playing a Spade to
dummy's 10.}
[BCFlags "1f"]
[Auction "W"]
1S Pass 3S Pass
4S AP

[Event "Plan Ahead"]
[Site ""]
[Date ""]
[Board "5"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "N"]
[Vulnerable "NS"]
[Deal "N:AJ6.AQ5.A953.AKJ T84.JT98.KT86.T9 Q3.K73.QJ742.Q76 K9752.642..85432"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ East leads \H Jack.

 Initial Analysis:

 We have a potential Spade loser and at least 1 potential Diamond loser.\n
 A successful Spade finesse will remove our potential Spade loser.\n
 A successful Diamond finesse, will remove our potential Diamond loser, but
only if West holds\n
 precisely the doubleton \DKing.

 The worrying factor is that there are scenarios, if we were to lead the
\DQueen, hoping not to lose\n
 any Diamond tricks, we could end up losing 2 Diamond tricks. \n
  \n
 Calculations:

 The only way we can avoid our Spade loser is with a successful finesse.

 The big question is: How should we be playing the Diamond suit?

 The answer to that question is: "It Depends".

 If it turns out that we have a Spade loser, then our only hope is to find West
with the doubleton   \n
 \DKing and we must therefore run the Queen of Diamonds.

 However, if it turns out that we have zero Spade losers, we can afford the
luxury of a 'Safety\n
 Play' in the Diamond suit, which guarantees that we can never lose more than 1
Diamond trick.

 The only way to find out how to play the Diamond suit is to first find out how
many Spade losers\n
 that we have. \n
  \n
 Conclusion:

 We win the opening lead with dummy's \HKing and take an immediate Spade
finesse.

 When the \SJack wins trick 2, we play our 'Safety Play' in the Diamond suit,
which is to play a\n
 Diamond towards dummy's \DJack. If East shows out, we can subsequently play a
Diamond to our\n
 9 and if West shows out, we can subsequently play a Diamond towards our
\DQueen.
}
[BCFlags "1f"]
[Auction "N"]
2C Pass 2D Pass
2NT Pass 6NT AP

[Event "The Deletion Principle"]
[Site ""]
[Date ""]
[Board "6"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "E"]
[Vulnerable "EW"]
[Deal "E:98.Q5432.542.AJT 7654.JT98.QJT.87 AT.AK.AK73.Q9632 KQJ32.76.986.K54"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ North leads \S King.

 Initial Analysis:

 We have 7 top tricks and we require an additional 2 tricks.

 There is the obvious Club finesse, which, if successful, would give us those 2
additional tricks.

 There is also the Heart suit, which, if the suit was to divide 3-3, would also
give us 2 extra tricks.

 Calculations:

 At the start of the hand, the chance of the Heart suit dividing evenly at 3-3
is a 36% chance and\n
 the chance of the Heart suit dividing unevenly at 4-2 is a 48% chance,
however, when both\n
 defenders follow to two rounds of Hearts, both of these percentages rise as we
have eliminated\n
 the possibilities of the Heart suit dividing 5-1 and 6-0.

 According to the 'Deletion Principle' they both rise proportionally to their
original values.\n
 So, although the even split (1-1), has risen, the uneven split (2-0), is still
the favourite, which\n
 means that the even split of 1-1 will be less than 50% (42.3% Chance).

 Meanwhile, the Club finesse has remained static at 50%.  \n
  \n
 Conclusion:

 We win the second round of Spades with our \SAce, and "Just for Fun", we can
cash our \HAce\n
 and \HKing, however we are next going to take the Club finesse, by playing our
Club towards\n
 dummy's \CJack and when that wins, return to our hand and repeat the Club
finesse.}
[BCFlags "1f"]
[Auction "E"]
Pass Pass 2NT Pass
3D Pass 3H Pass
3NT AP

[Event "Combining Our Chances"]
[Site ""]
[Date ""]
[Board "7"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "S"]
[Vulnerable "All"]
[Deal "S:QJ82.Q6432.7.653 A43.75.K32.AQJ72 T65.JT98.AJ98.K4 K97.AK.QT654.T98"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ North leads \H Jack.

 Initial Analysis:

 We have just 5 top tricks and we require an additional 4 tricks.\n
 There is the obvious Club finesse, which if successful, would give us those 4
additional tricks.\n
 With some 'Guessing', the Diamond suit could also give us those 4 additional
tricks.

 Another idea is to try and 'Sneak' through one Diamond trick and having
secured our 1 Diamond\n
 trick, we can now play the Club suit, knowing that we can afford to lose a
Club trick.

 It must be correct to play the Diamond suit first, because even if we 'Guess'
wrong and we lead\n
 the wrong Diamond and the defence wins with their \DAce, there is still a
chance that we can drop\n
 a doubleton \DJack and still make 4 Diamond tricks. As a last resort, we can
still fallback on the\n
 Club finesse.

 The big question is, do we play a Diamond to our King or a Diamond to the
Queen?\n
 \n
 Calculations:

 The Club finesse is going to be our 'Last Resort', so we will leave that until
last.\n
 If there is a doubleton \DJack, then we cannot go wrong.\n
 If the Diamonds divide 3-2, it is a complete 'Guess' how we play the Diamond
suit.\n
 If the Diamonds are 4-1 and a defender is holding AJxx of Diamonds and that
defender is South,\n
 there is nothing we can do with the Diamonds, because if we lead a Diamond
from the East hand,\n
 South will know that it is ok to rise with the \DAce and clear the Heart suit,
because South is in\n
 control of the Diamond suit.\n
 If North is the defender holding AJxx in the Diamond suit, they cannot rise
with their Ace,\n
 because the finesse of their Jack will show up on the next round of Diamonds,
so for that reason,\n
 the percentage play is to lead a Diamond through North.\n
  \n
 Conclusion:

 We win the opening lead with the \HKing and lead a Spade to our \SAce.\n
 We now lead a small Diamond towards dummy's \DQueen. When the \DQueen wins, we
play on\n
 the Club suit. If North rises with their \DAce in front of our \DQueen, we
will make 4 Diamond\n
 tricks. }
[BCFlags "1f"]
[Auction "S"]
Pass 1NT Pass 3NT
AP

[Event "Which Line To Take?"]
[Site ""]
[Date ""]
[Board "8"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "W"]
[Vulnerable "None"]
[Deal "W:8.632.9865.K6532 AKT32.AJT98.Q.A4 Q76.K74.JT.JT987 J954.Q5.AK7432.Q"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ East leads \C Jack.

 Initial Analysis:

 Potentially we have a Spade loser and potentially we have a Heart loser.\n
 If we play the Ace and King of Spades, the Queen may drop and we make our
contract.

 If it turns out that we have a Spade loser, then there is a chance that the
Diamond suit will\n
 generate us enough discards to eliminate all of our Heart losers.\n
 If Diamonds divide 3-3, we have five discards to more than eliminate our
losing Hearts.\n
 Even if Diamonds divide 4-2, we have four discards, which we can use to
eliminate our losing\n
 Hearts.

 Calculations:

 The chances of Diamonds dividing 3-3 or 4-2 is extremely high (84%).\n
 The problem is that when Diamonds divide 4-2 (A 48% Chance), we require 2
entries into\n
 dummy and we only have one, which is when we ruff our Club.\n
 Can we find a second entry into dummy to establish our Diamonds?\n
 \n
 If we reject the idea of trying to drop a doubleton \SQueen (Only a 40%
Chance), we have a\n
 second Spade entry, if we play towards dummy's Spade suit twice.

 Conclusion:

 We win the opening lead with \CAce and we lay down the \SAce and \DQueen.\n
 We play a Spade to dummy's \SJack and at some stage, we will play a Spade to
dummy's 9 and\n
 set up dummy's Diamonds and we still have a Club ruff to enter to our
established Diamond suit.\n
 We discard our 4 losing Hearts on our 4 established winning Diamonds.}
[BCFlags "1f"]
[Auction "W"]
Pass 1S Pass 2D
Pass 3H Pass 3S
Pass 4NT Pass 5C
Pass 5D Pass 5S
Pass 6S AP

[Event "One of Two Finesses"]
[Site ""]
[Date ""]
[Board "9"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "N"]
[Vulnerable "EW"]
[Deal "N:A72.A75.AQT82.AQ K.QJT98.K54.J982 J9.K3.973.K76543 QT86543.642.J6.T"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ East leads \H Queen.

 Initial Analysis:

 We have 7 top tricks.

 Prospects look good as all we require is for the Club suit to divide 3-2.

 Another source of extra tricks on this hand is the Diamond suit, as we have a
'One of Two\n
 Finesses' strategy available.\n
 \n
 Calculations:

 Clubs to divide 3-2 is a 68% chance and this will give us an extra 3 tricks.\n
 Leading Diamonds twice from the South hand gives us a 76% chance of an extra 3
tricks.

 Maybe we can use both strategies?

 Conclusion:

 We win the opening lead with the \HAce.\n
 Play the \CAce and then play the \CQueen and overtake the \CQueen with the
\CKing.\n
 If both defenders follow to the 2nd round of Clubs, we know that the Club suit
divides 3-2, so we\n
 can play a third round of Clubs, knowing that we still have the \HKing as an
entry to our Clubs, so\n
 we would end up making 5 Club tricks, 1 Spade trick, 2 Heart tricks and 1
Diamond trick.

 However, when the Club suit does not divide kindly, we are in the perfect
position to use our\n
 backup plan of taking 2 finesses in the Diamond suit, to make 2 Club tricks, 4
Diamond tricks, 2\n
 Heart tricks and 1 Spade trick.
}
[BCFlags "1f"]
[Auction "N"]
2NT Pass 3NT AP

[Event "One of Two Finesses "]
[Site ""]
[Date ""]
[Board "10"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "E"]
[Vulnerable "All"]
[Deal "E:AKQ.KJ5.AQT8.Q76 532.AT862.3.5432 964.73.J942.AJT9 JT87.Q94.K765.K8"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ West leads \H 6.

 Initial Analysis:

 After the Heart lead, we have just 6 top tricks.

 The good news is that a successful Club OR Diamond finesse will give us our 3
extra tricks.

 Which finesse do we take first or can we take both finesses? \n
 \n
 Calculations:

 If we could take both finesses our chance of successfully making our extra 3
tricks is 74%.\n
 (Finessing against two different defenders).

 The problem is that if we take the Club finesse first and North wins, the
defence will quickly take\n
 their 5 tricks and defeat our contract.

 We must take the Diamond finesse first, because if this loses our vulnerable J
5 of Hearts holding\n
 is protected.

 Conclusion:

 We win the opening lead with the \HKing.\n
 Play a Club to the \CAce and run the 9 of Diamonds, carefully playing the 8 of
Diamonds from the\n
 East hand.\n
 Now run the Jack of Diamonds again carefully playing the 10 of Diamonds, so
that we stay in\n
 dummy, so that we can repeat the Diamond finesse for the third time.

 We end up making our 9 tricks via 3 Spades, 1 Heart, 4 Diamonds and 1 Club.

}
[BCFlags "1f"]
[Auction "E"]
2NT Pass 3C Pass
3NT AP

[Event "Once in a Lifetime"]
[Site ""]
[Date ""]
[Board "11"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "S"]
[Vulnerable "None"]
[Deal "S:AKQJ643.75.Q.A54 95.A432.K76.KQJT T87.QJ.A5432.962 2.KT986.JT98.873"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ West leads \C King.

 Initial Analysis:

 It appears that we have 2 Heart losers and 2 Club losers.\n
 \n
 The only suit that we could potentially set up, is dummy's Diamond suit, when
the Diamond suit\n
 divides 4-3 (62% Chance), but that is going to require 3 entries outside of
the Diamond suit.

 Our only hope is that dummy's Spades provide us with those 3 required entries.

 Calculations:

 For the 9 of Spades to be a singleton, the Spades are required to divide 2-1
(78% Chance).

 It is a 1 in 3 chance that the singleton will be the 9 of Spades (26% Chance).

 It is a 50% chance that West is holding the 9 of Spades.\n
 \n
 Conclusion:

 We win the opening lead with our \CAce and play our Diamond to dummy's \DAce
and ruff the\n
 2 of Diamonds with our \SAce.\n
 We now play a Spade to dummy's 7 of Spades.\n
 When that wins, we ruff what is the 3rd round of Diamonds with our \SKing.\n
 We now play our Spade to dummy's 10 of Spades and ruff the 4th round of
Diamonds with\n
 our \SQueen.\n
 We now play a Spade to dummy's 8 of Spade to reach our established 5 of
Diamonds.

 We now fill out our 'Lotto Ticket'.}
[BCFlags "1f"]
[Auction "S"]
1S Pass 2S Pass
4S AP

[Event "Which Line To Take? "]
[Site ""]
[Date ""]
[Board "12"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "W"]
[Vulnerable "NS"]
[Deal "W:KQJ.T98765.J.AT9 5432.2.Q432.KQJ5 T987.A43.AKT.876 A6.KQJ.98765.432"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ \n
 North leads \C King.

 Initial Analysis:

 1 Spade loser; 2 Club losers, but 1 Club loser can be discarded on dummy's
\DKing.

 We also have 1 or 2 Heart losers.\n
  \n
 If Hearts divide 2-2 (40% Chance), we only have 3 losers, in total. \n
 If Hearts divide 3-1 or 4-0 (60% Chance), we have 4 losers in total.

 Calculations:

 Hearts are more likely to divide 3-1 than 2-2, so we need to eliminate another
Club loser by\n
 taking the Diamond finesse at trick 2. (50% Chance).

 Conclusion:

 We win the opening lead with \CAce.\n
 Run the \DJack.\n
 Play a Heart to dummy's \HAce.\n
 Cash dummy's \DAce and \DKing, discarding our 2 losing Clubs.\n
 Continue drawing trumps.

 We make our contract by losing just 2 Hearts and 1 Spade.}
[BCFlags "1f"]
[Auction "W"]
1H Pass 1S Pass
2H Pass 4H AP

[Event "Plan Ahead "]
[Site ""]
[Date ""]
[Board "13"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "N"]
[Vulnerable "All"]
[Deal "N:84.432.AT63.Q854 763.KJT9.K4.J976 AT2.AQ.QJ92.AK32 KQJ95.8765.875.T"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ West leads \S King. 

 Initial Analysis:

 We have 6 top tricks and therefore we require 3 additional tricks.

 A successful Diamond finesse will certainly produce those 3 additional tricks.

 If we hold back on taking our \SAce until the 3rd round, we can probably
afford to lose the\n
 Diamond finesse as there will be no entry into the West hand and we can
probably get our 9th\n
 trick from an expected favourable Club division and we even have a Heart
finesse as a last\n
 resort, but we must plan ahead.

 Calculations:

 Using the 'Rule of 7' (See previous notes on declarer play), we must hold up 2
rounds of Spades,\n
 cutting off West from all their tricks.\n
 \n
 When we take a losing Diamond finesse and East comes back the \HJack, do we
take the Heart\n
 finesse or do we rely on the Club suit dividing 3-2 for our 9th trick?

 The Heart finesse is a 50% chance and the Clubs dividing 3-2 is a 68% chance.

 If we had planned ahead, we would not be faced with this dilemma.

 Conclusion:

 We duck the first 2 rounds of Spades and win trick 3 with the \SAce.\n
 Planning ahead, we know that if the Diamond finesse was to lose and East
returns the inevitable\n
 Heart, we would have the dilemma of not knowing whether to take the Heart
finesse or trust that\n
 the Clubs suit will divide 3-2.\n
 Why don't we solve that future dilemma at trick 4, by immediately playing our
\CAce and our\n
 \CKing at tricks 4 and 5?\n
 When we observe that the Clubs divide 4-1, we know that our only hope of
making our 9 tricks,\n
 when East plays their \HJack, is to take a successful Heart finesse for our
9th trick. \n
 }
[BCFlags "1f"]
[Auction "N"]
Pass Pass 2NT Pass
3C Pass 3NT AP

[Event "Which Line To Take?"]
[Site ""]
[Date ""]
[Board "14"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "E"]
[Vulnerable "None"]
[Deal "E:AJT9832.4.KQ.A32 K6.982.T942.QJT9 Q7.AJT65.AJ.K654 54.KQ73.87653.87"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{

 South leads \C Queen.

 Initial Analysis:

 1 Club loser and potentially, 1 Spade loser.

 A successful Spade finesse would more or less eliminate our Spade loser.\n
 If we could establish our 5th Heart in dummy, we could use it to discard our
losing Club.

 Calculations:

 A successful Spade finesse is 50%, however, if North held Kxxx in Spades, we
would still lose a\n
 Spade trick.\n
 To establish our 5th Heart in dummy, we require Hearts to divide 4-3, which is
62%.

 To establish our 5th Heart in dummy, we require 3 entries outside of the Heart
suit.

 The \CKing is our first entry, the \DAce is our second entry. \n
 Where is our 3rd entry?  It is in Spades.

 We must reject the 50% Spade finesse and instead go for the 62% chance of the
Heart suit\n
 dividing 4-3.

 Conclusion:

 We win the opening lead with \CAce.\n
 Play a Heart to the \HAce and ruff the 5 of Hearts with the \SJack.\n
 Play a Spade to dummy's 7 of Spades, when this loses, get back to dummy, with
the \CKing.\n
 Ruff the 3rd round of Hearts with a high Spade.\n
 Return to dummy with the \SQueen.\n
 Ruff the 4th round of Hearts.\n
 We still have the \DAce in dummy to get to our established \HJack, which we
use to discard our\n
 losing Club.\n
 


}
[BCFlags "1f"]
[Auction "E"]
1S Pass 2H Pass
3S Pass 4NT Pass
5H Pass 6S AP

[Event "One of Two Finesses"]
[Site ""]
[Date ""]
[Board "15"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "S"]
[Vulnerable "NS"]
[Deal "S:T76.K82.T543.Q76 AKQ4.A73.K6.A832 J932.QJT9.J9.K54 85.654.AQ872.JT9"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ North leads \H Queen.

 Initial Analysis:

 We have 8 top tricks and surely with a combined 27 count, we can find 1 extra
trick?

 If Diamonds divide 3-3, we have our 9th trick.

 The Club pattern looks promising, if we could get to dummy twice.

 Calculations:

 Diamonds dividing 3-3 is only a 36% chance as it is not the mostly likely
division, when we are\n
 missing 6 cards. (The 4-2 break is more likely at 48%).

 If we could get to dummy to lead Clubs twice, there is a 76% chance that we
will make 3 tricks in\n
 Clubs, by using the 'One of Two Finesses' strategy, but how are we going to
get to dummy twice?

 Conclusion:

 We duck a couple of rounds of Hearts and take the third round with the
\HAce.\n
 Now play a Diamond to the \DQueen.\n
 Run the \CJack and when North wins this and cashes their Heart, discard our
small Spade and win \n
 their Spade continuation with the \SAce,\n
 Now lead the \DKing and overtake it with dummy's \DAce.\n
 Now run the 10 of Clubs and subsequently the 9 of Clubs.

 We end up making 3 Spade tricks, 1 Heart trick, 2 Diamond tricks and 3 Club
tricks. 

}
[BCFlags "1f"]
[Auction "S"]
Pass 2NT Pass 3C
Pass 3NT AP

[Event "More Than One Plan"]
[Site ""]
[Date ""]
[Board "16"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "W"]
[Vulnerable "EW"]
[Deal "W:A92.Q854.J986.J8 8765.AK72.Q3.AQT KQJT.JT93.2.9432 43.6.AKT754.K765"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ West leads \S King. 

 Initial Analysis:

 We have 8 top tricks and therefore require just 1 more additional trick.

 We have 3 plans:

 Plan Tom: Hope for an additional trick in the Diamond suit, when the Diamonds
divide 3-2.

 Plan Dick: Hope for a 3-3 division in the Club suit.

 Plan Harry: Hope for a singleton or doubleton \CJack to be held by one of the
defenders.

 Calculations:

 Plan Tom is certainly our best hope as Diamonds will divide 3-2 68% of the
time.

 Plan Dick will succeed 36% of the time, when the Clubs divide 3-3.

 Plan Harry requires a singleton or doubleton \CJack, which will occur 18.4% of
the time.

 We can try all 3 of these plans, providing we try them in the correct order.

 Conclusion:

 We let the defenders cash their first 4 Spade tricks.\n
 It is very important that we do <i>not</i> discard any Clubs from dummy,
otherwise plan Dick and Plan\n
 Harry will have no chance of success; we must discard 2 Diamonds from dummy.

 We must now cash the \CAce and \CQueen and when we observe the \CJack from
West, we cash\n
 our 10 of Clubs.

 We now have 4 Club tricks, 2 Heart tricks and 3 Diamond tricks.}
[BCFlags "1f"]
[Auction "W"]
Pass 1NT Pass 3NT
AP

[Event "More Than One Plan"]
[Site ""]
[Date ""]
[Board "17"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "N"]
[Vulnerable "None"]
[Deal "N:9743.J84.84.KQ96 A5.AQ7.AQ65.AJ42 QJT82.KT3.972.T7 K6.9652.KJT3.853"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ South leads \S Queen. 

 Initial Analysis:

 We have 8 top tricks and therefore we require just 1 more additional trick.

 We have lost Plan Harry for the moment, but we still have 2 plans.

 Plan Tom: Hope for an additional trick in the Heart suit, when North holds the
\HKing.

 Plan Dick: Hope for an additional trick in the Club suit, when North holds
both \CKing and\n
                \CQueen.

 Calculations:

 Obviously, 'Plan Tom' has a much better chance of success than 'Plan Dick' as
a simple finesse\n
 (Plan Tom),  is a 50% chance whereas hoping for North to hold both Club
honours (Plan Dick), is\n
 only a 24% chance.

 However, if we execute both plans in the correct order, we can attempt both
plans.

 Conclusion:

 We win the opening lead with the \SKing.\n
 We play a Club to the \CJack, when this wins, we have our 9 tricks.\n
 If the Club finesse had lost, we would subsequently have tried the Heart
finesse.

 Playing the Heart finesse before the Club finesse is a losing play.\n
 }
[BCFlags "1f"]
[Auction "N"]
Pass 2NT Pass 3C
Pass 3NT AP

[Event "Combining Our Chances"]
[Site ""]
[Date ""]
[Board "18"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "E"]
[Vulnerable "NS"]
[Deal "E:AK5.A6.AJ72.AJ83 32.QJT97.Q4.QT97 Q764.53.K863.K52 JT98.K842.T95.64"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ South leads \H Queen.

 Initial Analysis:

 We have 8 top tricks, so just one more trick is required.

 If the Spade suit divides 3-3, we have our 9th trick.\n
 If the Club finesse is successful we have our 9th trick.\n
 If the Diamond finesse is successful, we have our 9th trick.\n
 If the Queen of Clubs is doubleton, we have our 9th trick.\n
 If the Queen of Diamonds is doubleton, we have our 9th trick.

 How can we combine all these chances, without losing a trick?

 Calculations:

 We can perform the following tests, without losing the lead. \n
 We can test the Spade suit for dividing 3-3 (36% chance).\n
 We can test the Club suit for the \CQueen being a doubleton (16% chance).\n
 We can test the Diamond suit for the \DQueen being a doubleton (27% chance).

 We can finesse for the Queen in either Minor suit (50% chance), but we risk
losing the lead.

 We must play the minor suit that offers us the best chance of dropping a
doubleton Queen and\n
 then we take the finesse in the other minor suit.  \n
 \n
 Conclusion:

 We win the 2nd trick with the \HAce.\n
 Play 3 rounds of Spades.\n
 Play the \DKing and \DAce.\n
 When the \DQueen drops, we make our contract.\n
 If the \DQueen had not dropped, then we would have taken the Club finesse. }
[BCFlags "1f"]
[Auction "E"]
2NT Pass 3C Pass
3NT AP

[Event "One of Two Finesses"]
[Site ""]
[Date ""]
[Board "19"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "S"]
[Vulnerable "EW"]
[Deal "S:JT9.AKJ8.AK.KQ86 A42.Q32.QJT93.T3 Q653.94.542.A752 K87.T765.876.J94"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ West leads \D Queen.

 Initial Analysis:

 We have 7 top tricks and there is every chance that the Club suit will give us
our 8th trick.\n
 We can certainly knock out the Ace and King of Spades, which will give us our
9 tricks, but do we\n
 have enough time to do this?\n
 The most likely Diamond division is 5-3, so by the time we have knocked out
the Ace and King of\n
 Spades, the defence would have taken their 5 tricks.\n
 \n
 We need a better plan.\n
 We can take the Heart finesse, which is a 50% chance.\n
 \n
 However, nicely disguised within the Heart suit is our 76% chance finesse
pattern.

 Calculations:

 If we are able to lead Hearts twice from the North hand, we will make our
extra trick, providing\n
 East has either the Queen or 10 of Hearts. This gives rise to a 76% chance of
success.

 Conclusion:

 We win the opening lead with \DAce.\n
 Play the \CKing and \CQueen.\n
 \n
 Lead the 8 of Clubs to dummy's \CAce and run the 9 of Hearts.\n
 When we regain the lead, if necessary, lead our 6 of Clubs to dummy's 7 of
Clubs and take\n
 another Heart finesse. }
[BCFlags "1f"]
[Auction "S"]
2NT Pass 3C Pass
3D Pass 3H Pass
3NT AP

[Event "More Than One Plan"]
[Site ""]
[Date ""]
[Board "20"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "W"]
[Vulnerable "All"]
[Deal "W:AK.A92.7652.AKQ4 QJT96.K76.3.JT93 543.Q8.AK84.7652 872.JT543.QJT9.8"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ North leads \S Queen. 

 Initial Analysis:

 We have 8 top tricks and therefore require just 1 more additional trick.

 We have 3 plans:

 Plan Tom: Hope for an additional trick in the Club suit, when the Clubs divide
3-2.

 Plan Dick: Hope for an additional trick in the Diamond suit, when the Diamonds
divide 3-2.

 Plan Harry: Play a Heart towards dummy's Queen and hope that North holds the
King of Hearts.

 Calculations:

 Plans Tom and Dick are a 68% chance and Plan Harry is a 50% chance, however,
the\n
 percentages are irrelevant as we can action all 3 plans, but only if we action
them in a precise\n
 order. 

 Conclusion:

 We win the opening lead with the \SAce.\n
 We must play the \DAce and \DKing first, when we have no luck with that suit,
we return to our\n
 \CAce and lead towards the \HQueen. This plan works.\n
 If it had not worked, we would have then tried the Club suit for our
additional trick.

 Cashing our Club tricks too early or ducking a Diamond, will lead to trouble,
later in the hand.}
[BCFlags "1f"]
[Auction "W"]
2NT Pass 3NT AP

[Event "Combining Our Chances"]
[Site ""]
[Date ""]
[Board "21"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "N"]
[Vulnerable "NS"]
[Deal "N:T98.QJT98.KQ.AQT KQJ5.2.765.J8762 A76.A7654.JT98.9 432.K3.A432.K543"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ East leads \S King.

 Initial Analysis:

 After the \SKing lead, we appear to have 2 Spades to lose and the \DAce to
lose.\n
 The only other potential loser that we have is the \HKing.

 We can eliminate our potential Heart loser by taking a successful Heart
finesse. \n
 We could take a Club finesse, which, if successful, would allow us to discard
one of our Spade\n
 losers.

 Calculations:

 We can take the Club finesse, which is a 50% chance and if the finesse wins,
then we can discard\n
 one of our Spade losers.\n
 We can cross over to the Ace of Clubs and take the Heart finesse, which is
also a 50% chance.

 We can lay down our Ace of Hearts and try to drop a singleton \HKing, which is
a 26% chance. 

 If we immediately take one of the finesses, we are 'Putting All Our Eggs in
One Basket', because\n
 if the finesse loses, the defence will quickly take their 4 tricks.

 We can increase our chances of success by combining our strategy of trying to
drop the singleton\n
 \HKing with the taking of the Club finesse. \n
  \n
 Conclusion:

 We win the opening lead with the \SAce.\n
 Lay down the \HAce and if this fails to drop the singleton \HKing, we take the
Club finesse.}
[BCFlags "1f"]
[Auction "N"]
1H Pass 4H AP

[Event "More Than One Plan"]
[Site ""]
[Date ""]
[Board "22"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "E"]
[Vulnerable "EW"]
[Deal "E:Q32.652.K98.JT32 A64.QT9.AJ52.A54 K75.A8743.Q763.9 JT98.KJ.T4.KQ876"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ West leads \H Four.

 Initial Analysis:

 After the initial Heart lead, we have 6 top tricks and most likely a 7th in
the Heart suit.

 We require 2 additional tricks.

 The Club suit can most certainly provide us with those 2 additional tricks.

 The Spade suit can also provide us with those 2 additional tricks.

 Is there a way that we can utilise both of these plans? 

 Calculations:

 If the Club suit divides 3-2, which is a 68% chance, then we have enough
tricks.\n
 \n
 If East has at least one Spade honour, then we should have enough tricks.

 However, for the Spade strategy to work, we require 2 entries in dummy to lead
the Spades\n
 twice through East and probably a third to reach our established last Spade in
dummy.

 We have 2 Club entries and we find ourselves winning the first trick in dummy
with the \HJack.

 We must use this early entry to dummy wisely.

 Conclusion:

 We win the opening lead with dummy's \HJack and run the \SJack.\n
 When West cashes Ace and another Heart, lead the \CAce and then a Club to
dummy's \CQueen.\n
 Now run the 10 of Spades, cash the \SAce and enter dummy via the \CKing and
cash dummy's\n
 last Spade.

 We make 3 Club tricks, 2 Heart tricks, 3 Spades tricks and the Ace of Diamonds
for 9 tricks. \n
 }
[BCFlags "1f"]
[Auction "E"]
Pass 1NT Pass 2C
Pass 2D Pass 3NT
AP

[Event "Which Line To Take"]
[Site ""]
[Date ""]
[Board "23"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "S"]
[Vulnerable "All"]
[Deal "S:K32.AK732.AK4.A3 975.Q854.QJT9.J4 A64.6.6532.K8752 QJT8.JT9.87.QT96"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ West leads \D Queen.

 Initial Analysis:

 We have 4 Aces and 4 Kings, so we have 8 top tricks.\n
 What is our best chance to make our 9th trick?

 If Clubs break 3-3, we will have our 9th trick.\n
 If Diamonds break 3-3, we will have our 9th trick.\n
 If Hearts break 4-3, we will have our 9th trick.\n
 Clubs dividing 4-2 will be of no use to us as there are not enough entries to
dummy.


 Calculations:

 When we are missing 6 cards in a suit, the 3-3 division is not the most
likely. (36%).\n
 When we are missing 7 cards in a suit, the 4-3 division is the most likely.
(62%).\n
 So we must play on the Heart suit to develop our 9th trick.

 Conclusion:

 We win the opening lead with \DAce.\n
 We now lead the 2 of Hearts.\n
 When we regain the lead, we continue playing the Heart suit, to establish the
7 of Hearts for our\n
 9th trick.

 We make our contract with 2 Spade tricks, 3 Heart tricks, 2 Diamond tricks and
2 Club tricks.}
[BCFlags "1f"]
[Auction "S"]
2NT Pass 3C Pass
3H Pass 3NT AP

[Event "The Deletion Principle"]
[Site ""]
[Date ""]
[Board "24"]
[West ""]
[North ""]
[East ""]
[South ""]
[Dealer "W"]
[Vulnerable "None"]
[Deal "W:A5.AK.AJ5432.J92 QJT9.32.T86.6543 K432.7654.K.KT87 876.QJT98.Q97.AQ"]
[Scoring ""]
[Declarer ""]
[Contract ""]
[Result ""]
{ South leads \H Queen.

 Initial Analysis:

 We have 6 top tricks and we therefore require an additional 3 tricks.

 We can finesse for the \CQueen, which if successful, would give us those 3
additional tricks.\n
 There is also the Diamond suit, which if it divides 3-3 or a defender holds
the \DQueen doubleton,\n
 would also provide us with enough tricks.

 Calculations:

 At the start of the hand, the chance of the Diamond suit dividing evenly at
3-3 is a 36% chance\n
 and the chance of the Diamond suit dividing unevenly at 4-2 is a 48% chance,
however, when\n
 both defenders follow to two rounds of Diamonds, both of these percentages
rise as we have\n
 eliminated the possibilities of the Diamond suit dividing 5-1 and 6-0.

 A certain number of 4-2 divisions have also been eliminated, the ten 4-2
divisions that contain a\n
 doubleton \DQueen.\n
 So, using the 'Deletion Principle' the even break in Diamonds (1-1), has now
risen to 52.4%

 Meanwhile, the finesse for the \CQueen has remained static at 50%.  \n
  \n
 Conclusion:

 We win the opening lead with our \HAce and we can cash our \DKing and get back
into dummy\n
 with our \SAce.\n
 We now cash our\DAce.\n
 Note that at this stage it is still not too late to run dummy's \CJack and
finesse for the \CQueen,\n
 however, even though the \DQueen has not appeared the probability of the
Diamond suit now\n
 breaking 1-1 is higher then the finesse for the \CQueen, so we play another
Diamond and we use\n
 our \HKing as an entry to all of our Diamond winners.}
[BCFlags "1f"]
[Auction "W"]
1D Pass 1H Pass
3D Pass 3NT AP
