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   Small heart slam (bridge puzzle)
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   Author  Topic: Small heart slam (bridge puzzle)  (Read 4689 times)
Aryabhatta
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Small heart slam (bridge puzzle)  
« on: Jul 14th, 2007, 5:46pm »
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A bridge deal.
 
(If you are a bridge player already you can skip the longish explanation and go straight to the puzzle at the end: It is Rubber bridge and you need to make 6H as South)
 
4 players: North, South. East, West (N,S,E,W). N and S are partners and their opponents are East and West. East and West are also partners.  
 
Rules:  
This is a trick taking puzzle. Using standard deck of 4 suits.  
 
Each trick consists of each person playing exactly one card (i.e a trick consists of 4 played cards). The cards are played in a clockwise order. i.e if South plays the first card, West plays next, then North and finally East.  
 
Each player must follow suit to the first card led. If the player cannot follow suit, he/she may play any card of his/her choice.  
 
So if say West plays the first card to a trick and it is a spade, each player must play a spade if he has one. So if West leads a spade, even if North plays a heart, East must play a spade if he has it.  
 
The winner of the trick is decided by who played the highest card of the suit led (or in case there is a trump suit decided, the highest trump played {if at least one trump played})
 
The order of cards:
 Ace > King > Queen > Jack  > Ten > 9 > 8 > 7 > 6 > 5 > 4 > 3 > 2  
 
The winner of a trick gets to lead the first card to the next trick.  
 
Explanation of trump suit:
 
In some cases, the players before hand decide on a special suit called the "trump" suit.  As referred earlier, this suit has special trick taking abilities.  
 
For instance, say the players have decided that the Heart suit is the trump suit. Consider a trick in which South plays spade A, West plays heart 2 (he is out of spades), North plays spade 2 and East plays spade 3.
 
Since Hearts were trump, and West played a trump and no one else did, West wins the trick!
 
Note, the trump can only be played if you are out of the suit led, or the suit led is trumps.
 
In the above trick, if North had played the heart 3, then North would have won the trick as 3 would be the highest trump played. (In effect, N has "over trumped" West)
 
Now for the puzzle:
 
The 4 players (you are South) have distributed 13 cards to each player and have decided before hand that hearts is trump. They have also decided the West would lead the first card of the first trick.
(In bridge, this happens during the bidding)
 
After West leads the first card to the first trick, North shows his cards to everyone by placing them face up on the table and asks South to play for him. (In bridge terms, North is the "dummy"). Note, South cannot see the cards which East and West hold.
 
 
The aim of South and North is to make 12 tricks. (If they make 13 that is fine, but the aim is 12).  
 
Here are the cards which you (South) can see after North displays his cards:
 
 
Code:

North
 
Spades: A K 5 4
Hearts: 5 3 2
Diamonds: J T
Clubs: A K J T
 
South
 
Spades: 3 2
Hearts: A K Q J T 4
Diamonds:  
Clubs: 9 8 7 6 5
 

 
(A = Ace, K = King, Q = Queen, J = Jack, T = Ten)
 
The first two tricks proceed as follows:
 
Diamond 4, Diamond J, Diamond King, Heart T : You win the trick!
(remember Heart is trump)
 
Now South (you) play the trump Ace.
W plays trump 6, N plays trump 2 and E plays the diamond 5 (E has no trumps!): You win this trick too.
 
How will you (i.e South) play so as to maximize the chances of N and S together making atleast 12 tricks (given the fact that you cannot see E/W cards and you tell North which card to play)?
« Last Edit: Jul 14th, 2007, 10:31pm by Aryabhatta » IP Logged
denis
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Re: Small heart slam (bridge puzzle)  
« Reply #1 on: Jul 14th, 2007, 10:17pm »
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Looking at North and South’s hands, you can make a guaranteed 6 heart trick from South, 2 Spade tricks from North (assuming all trumps are out), and at least 3 Club tricks from North (assuming all trumps are out). That gives us a guaranteed 11 but we want 12 to make a small slam.  
 
The card that will be problematic to us is the Club Q. If we can take the Club Q with a higher Club from North, then we are assured the small slam since we can make 4 Club tricks from North instead of 3 (assuming all trumps are out).  
 
Now we don’t know if the Club Q is in West or East. There are 4 Clubs distributed between East and West.  If Club Q is in West’s hand and West has three or less Club cards, then we can get the Club Q using the “finesse” (South leading low Club and if West throws low, then respond with lowest North Club).  
 
If Club Q is in East hand’s and East has two Clubs or less, then we can win it as well  but this would require the south leading the high Clubs and thus a different strategy altogether. However, if East has Club Q and at least 3 Clubs, or if either East or West has all four Clubs, then you lose this trick any way you play it.  
 
I would go with the assumption that the Clubs are distributed 3-1, or 2-2 or 1-3 with the West holding the Queen (I’m not sure of the exact odds of this but I think its 7/16) and go with the finesse. The odds that the Queen is in East hand or that West holds all four Clubs is 9/16. But out of these 9 combinations you lose at 5 of these any way you play it (4 Clubs in East, 4 Clubs in West, or Club Q in East with East holding three cards) and can only win 4 of these combinations (i.e. if East has Club Q and has at most 2 cards) using the high Club lead from North with probability 4/16 .
 
In summary, the finesse would win the Club Q with prob 7/16, the North high Club lead would win the Club Q with prob 4/16=1/4 and you would lose the Club Q with prob 5/16 with any strategy used.
 
So lets go with the finesse.
 
I would first lead three large trumps from South to remove all remaining trump from West. Then lead a low Club from South and see how West responds. If West responds with the Club Q, then take it with North’s Club A (we will get the small slam).  
 
If West responds with a low Club, North’s response is the Club T. Here East will either take the trick with Club Q (in which case we lose the trick) or respond with a lower Club in which case the finesse worked and we get the trick with North’s Club T (in this case bring the lead back to South and repeat the Club lead until you flush out the Club Q).  
 
If East throws a non Club on the first Club lead, then all four remaining Clubs are in the West hands and you will eventually lose the trick.  
 
« Last Edit: Jul 14th, 2007, 10:47pm by denis » IP Logged
Aryabhatta
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Re: Small heart slam (bridge puzzle)  
« Reply #2 on: Jul 14th, 2007, 10:41pm »
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Good try denis, but we can do better.
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Re: Small heart slam (bridge puzzle)  
« Reply #3 on: Jul 14th, 2007, 10:49pm »
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Yeah, I'm not surprised as I haven't played bridge in over 25 years  Undecided
« Last Edit: Jul 14th, 2007, 10:53pm by denis » IP Logged
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Re: Small heart slam (bridge puzzle)  
« Reply #4 on: Jul 15th, 2007, 8:15am »
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Well, personally I would have taken the first trick with a small ruff - OK, cuts communication in the suit, but there's plenty of ways to get into North's hand, and saves the problem of worrying about being over-ruffed later.
 
That aside, the key to this is playing the clubs. Not knowing how the auction went (so assuming there's no relevant information given by oppo), playing for the queen to drop in the first 2 tricks will do better that playing for the finesse, plus you can still adjust if West has all 4 clubs (very unlikely, since he already has the 4 missing hearts).
 
The real problem is that, although we don't want West to trump the club lead, since then we lose to the queen of clubs in East, at the same time if we draw trumps, we then cut off any way back to the long clubs, since we're left with only a trump entry to hand, an over-club in North, and almost certainly facing a diamond lead, and so we lose the two spade tricks on top of the club trick. Hence, if it is a 4-0 club split in favour of East, we're screwed whatever we do.
 
I think we do best drawing two rounds of clubs if the queen doesn't drop on the first round, before drawing trumps, then clearing out clubs, AK of spades, and using the last trump to get back to hand for the last club - if we're not facing East 4-0 or West Qxx (face the same communication problems), then we have one loser if East has Qxx (duck the ruff from West, win the next trick, draw trumps and continue), and no losers with any other hand.
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Re: Small heart slam (bridge puzzle)  
« Reply #5 on: Jul 15th, 2007, 10:53am »
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on Jul 15th, 2007, 8:15am, Three Hands wrote:
Well, personally I would have taken the first trick with a small ruff - OK, cuts communication in the suit, but there's plenty of ways to get into North's hand, and saves the problem of worrying about being over-ruffed later.

 
Does not matter as AKQJ should be enough to draw the outstanding trump even if they split 4-0.
 
On general principles ruffing with the T might be better though (at least Jeff Rubens thinks so, I found this puzzle in a book by him).
 
Quote:

<snip>
 
I think we do best drawing two rounds of clubs if the queen doesn't drop on the first round, before drawing trumps, then clearing out clubs, AK of spades, and using the last trump to get back to hand for the last club - if we're not facing East 4-0 or West Qxx (face the same communication problems), then we have one loser if East has Qxx (duck the ruff from West, win the next trick, draw trumps and continue), and no losers with any other hand.

 
We can do better.
« Last Edit: Jul 15th, 2007, 10:54am by Aryabhatta » IP Logged
Margit
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Re: Small heart slam (bridge puzzle)  
« Reply #6 on: Jul 15th, 2007, 12:11pm »
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If clubs are 2-2 or 3-1, we can always make
it.
Draw trumps and on the last round discard
the ten of clubs from dummy.
Cash high spades.  
Then A K and J clubs.
South hand is then high.
 
Can't figure out what to do with
a 4-0 club split.
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Re: Small heart slam (bridge puzzle)  
« Reply #7 on: Jul 15th, 2007, 1:04pm »
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on Jul 15th, 2007, 12:11pm, Margit wrote:
Can't figure out what to do with a 4-0 club split.

Lead a round of clubs before taking out more trumps and you can cope with E being void - win A on the first trick, and use trump leads to get back to hand twice to finesse the Q - though I'm not sure what to do if W turns up void in C...
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Aryabhatta
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Re: Small heart slam (bridge puzzle)  
« Reply #8 on: Jul 15th, 2007, 6:11pm »
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Margit, rmsgrey you guys are close.
 
We can cater to East holding all four clubs. i.e we can guarantee 12 tricks no matter how the cards lie.
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Re: Small heart slam (bridge puzzle)  
« Reply #9 on: Jul 16th, 2007, 7:18am »
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OK, if we take the worst-case scenario of East having all 4 clubs, the only way to win the 12 tricks is to draw trumps straight off, discarding the 10 or J of clubs on the 4th round. Then draw clubs from the top, losing to the Q on the 3rd round, ruff the diamond return (going to be the best option for them), run your long clubs while throwing the small spades, and cash the AK of spades for 12.
 
If West has at least 3 clubs to the Q, this approach should also work - West wins the 3rd round of clubs, you win the rest. So I guess the line Margit had opted for is pretty much the optimal, or equivalent to the one I've just suggested. However, if West has 4 clubs, I think the sub-optimal line of taking a round of clubs first potentially earns all 13 tricks by allowing the finesse shown by rmsgrey, but that's the only benefit that line has (and is a pretty unlikely setup...)
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Re: Small heart slam (bridge puzzle)  
« Reply #10 on: Jul 16th, 2007, 8:22am »
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on Jul 16th, 2007, 7:18am, Three Hands wrote:
OK, if we take the worst-case scenario of East having all 4 clubs, the only way to win the 12 tricks is to draw trumps straight off, discarding the 10 or J of clubs on the 4th round. Then draw clubs from the top, losing to the Q on the 3rd round, ruff the diamond return (going to be the best option for them), run your long clubs while throwing the small spades, and cash the AK of spades for 12.

What if E fails to co-operate and holds up the QC until the 4th trick?
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Re: Small heart slam (bridge puzzle)  
« Reply #11 on: Jul 16th, 2007, 8:35am »
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on Jul 15th, 2007, 10:53am, Aryabhatta wrote:
On general principles ruffing with the T might be better though (at least Jeff Rubens thinks so, I found this puzzle in a book by him).

As a matter of interest, where does that general principle come from? And are there layouts for this hand where ruffing with the T is better than the 4?
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Aryabhatta
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Re: Small heart slam (bridge puzzle)  
« Reply #12 on: Jul 16th, 2007, 10:06am »
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on Jul 16th, 2007, 8:35am, rmsgrey wrote:

As a matter of interest, where does that general principle come from? And are there layouts for this hand where ruffing with the T is better than the 4?

 
We are maintaining communication with the dummy.
 
Basically by playing the 4 we have blocked the trump suit. By playing the T (which costs nothing) we can use the 5 as an entry to dummy (using the 4 from hand) in case we need it.
 
I do not know exactly where this principle came from... but I think it is sound enough.
 
For this hand it does not matter if you ruff with the T or the 4.
« Last Edit: Jul 16th, 2007, 10:08am by Aryabhatta » IP Logged
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Re: Small heart slam (bridge puzzle)  
« Reply #13 on: Jul 16th, 2007, 11:41am »
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Does this make when west has
a 0 4 9 0 distribution ?
 
ie. 4 (known) hearts and the rest diamonds.
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Re: Small heart slam (bridge puzzle)  
« Reply #14 on: Jul 16th, 2007, 11:44am »
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on Jul 16th, 2007, 11:41am, Margit wrote:
Does this make when west has
a 0 4 9 0 distribution ?
 
ie. 4 (known) hearts and the rest diamonds.

 
 
Yes, we can.
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Re: Small heart slam (bridge puzzle)  
« Reply #15 on: Jul 17th, 2007, 5:30am »
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OK. Let's try this -
Draw trumps and on the last round discard
the last diamond from dummy.
Now the A K J of clubs.
If clubs are 2-2 or 3-1 we can claim.
If the person holding 4 clubs holds up on
the J clubs, lead the 10 C and likewise claim.
 
If however, the J is taken with the Q, what can  
be returned ?
If a spade, we win, cash 10 C and we still
have a trump to get back to hand for the good
clubs.
If a club, same as above.
If a diamond, throw the 10 C from dummy,
trump in hand and we are once again high.
 
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Re: Small heart slam (bridge puzzle)  
« Reply #16 on: Jul 17th, 2007, 6:46am »
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Looks good to me.
 
After seeing the possibility of the Q being held up until the 4th round, I'd been trying to come up with a way of discarding the Ten of Clubs if the Q comes out on the 3rd round. Looks like you've found it, Margit.
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Re: Small heart slam (bridge puzzle)  
« Reply #17 on: Jul 17th, 2007, 7:30am »
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Looks like I spent too long in the bath earlier!
 
I wasn't quite there yet, but close enough that the moment Margit mentioned ditching the Diamond on the 4th round of trumps, I got the whole thing...
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Re: Small heart slam (bridge puzzle)  
« Reply #18 on: Jul 17th, 2007, 9:30am »
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Well done Margit!
 
The key play is to discard a diamond on the fourth round of trumps.
 
If dummy had had a spade less and a diamond more, then rmsgrey's line, of playing a club to A before drawing trumps (to cater to 4 clubs with W) would probably be the best one.
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Re: Small heart slam (bridge puzzle)  
« Reply #19 on: Jul 17th, 2007, 9:46am »
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Small problem variation.
Same North/South hands, same contract.
This time however West leads a small club.
 
Dummy to play. What is your best chance.
 
(Note here there are distributions which will
 break the contract)
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Re: Small heart slam (bridge puzzle)  
« Reply #20 on: Jul 17th, 2007, 1:55pm »
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on Jul 17th, 2007, 9:46am, Margit wrote:
Small problem variation.
Same North/South hands, same contract.
This time however West leads a small club.
 
Dummy to play. What is your best chance.
 
(Note here there are distributions which will
 break the contract)

 
(Note, not a detailed analysis, but seems right)
 
I would probably just rise with the club A. If it gets ruffed and a diamond comes back, I might still survive with 3-1 trumps. If a non-diamond comes back, i can survive a 4-0 trump break.
 
If A holds and east follows it is easy.
If A holds and east discards, a trump to A will reveal the situation in trumps and I think we can make it.
 
Alternative to this line is to play the J from dummy. I think we go down in same scenarios as above line and in addition if the lead was a singleton (J loses to Q and W ruffs the club return).
 
This seems to be inferior to rising with the A.
« Last Edit: Jul 17th, 2007, 1:56pm by Aryabhatta » IP Logged
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Re: Small heart slam (bridge puzzle)  
« Reply #21 on: Jul 19th, 2007, 4:59am »
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Yes, a top club must be played
to prevent a return ruff by west.
So -
East follows -  
We can claim.
 
East discards -
We trump a diamond high and we are
exactly in the original position,
 
East trumps and returns ?
(This is the point that a distribution
 can screw this eg. 7/0 spade or  
 theorectically 11 d with East and divided
 trumps. ie. West can trump a return)
 
We can still make it :-)
 
 
 
 
 
 
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Re: Small heart slam (bridge puzzle)  
« Reply #22 on: Sep 10th, 2007, 9:23am »
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A nice warm-up exercise, Aryabhatta.   Wink
 
Now then, you are playing South and hold
SPADES: 4,3,2
DIAMONDS: 4,3,2
CLUBS:  5,4,3,2
HEARTS: 4,3,2
 
Find the other hands and a line of play such that you make 6 tricks in a 4-Clubs contract.
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Re: Small heart slam (bridge puzzle)  
« Reply #23 on: Sep 10th, 2007, 1:16pm »
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It was in hard for a reason  Wink
 
In your puzzle, do you want the defense to cooperate? or are you looking for best play (double dummy) from both sides?
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Re: Small heart slam (bridge puzzle)  
« Reply #24 on: Sep 10th, 2007, 1:36pm »
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on Sep 10th, 2007, 1:16pm, Aryabhatta wrote:
In your puzzle, do you want the defense to cooperate?

Yes.
 
 
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