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        riddles >> hard >> Small heart slam (bridge puzzle)
        
(Message started by: Aryabhatta on Jul 14^th, 2007, 5:46pm)

Title: Small heart slam (bridge puzzle)
Post by Aryabhatta on Jul 14^th, 2007, 5:46pm

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)?

Title: Re: Small heart slam (bridge puzzle)
Post by denis on Jul 14^th, 2007, 10:17pm

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.

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Jul 14^th, 2007, 10:41pm

Good try denis, but we can do better.

Title: Re: Small heart slam (bridge puzzle)
Post by denis on Jul 14^th, 2007, 10:49pm

Yeah, I'm not surprised as I haven't played bridge in over 25 years :-/

Title: Re: Small heart slam (bridge puzzle)
Post by Three Hands on Jul 15^th, 2007, 8:15am

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.

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Jul 15^th, 2007, 10:53am

on 07/15/07 at 08:15:02, Three Hands wrote:

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.

Title: Re: Small heart slam (bridge puzzle)
Post by Margit on Jul 15^th, 2007, 12:11pm

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.

Title: Re: Small heart slam (bridge puzzle)
Post by rmsgrey on Jul 15^th, 2007, 1:04pm

on 07/15/07 at 12:11:57, 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...

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Jul 15^th, 2007, 6:11pm

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.

Title: Re: Small heart slam (bridge puzzle)
Post by Three Hands on Jul 16^th, 2007, 7:18am

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...)

Title: Re: Small heart slam (bridge puzzle)
Post by rmsgrey on Jul 16^th, 2007, 8:22am

on 07/16/07 at 07:18:38, Three Hands wrote:

What if E fails to co-operate and holds up the QC until the 4th trick?

Title: Re: Small heart slam (bridge puzzle)
Post by rmsgrey on Jul 16^th, 2007, 8:35am

on 07/15/07 at 10:53:01, 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?

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Jul 16^th, 2007, 10:06am

on 07/16/07 at 08:35:15, 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.

Title: Re: Small heart slam (bridge puzzle)
Post by Margit on Jul 16^th, 2007, 11:41am

Does this make when west has
a 0 4 9 0 distribution ?

ie. 4 (known) hearts and the rest diamonds.

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Jul 16^th, 2007, 11:44am

on 07/16/07 at 11:41:36, 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.

Title: Re: Small heart slam (bridge puzzle)
Post by Margit on Jul 17^th, 2007, 5:30am

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.

Title: Re: Small heart slam (bridge puzzle)
Post by Three Hands on Jul 17^th, 2007, 6:46am

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.

Title: Re: Small heart slam (bridge puzzle)
Post by rmsgrey on Jul 17^th, 2007, 7:30am

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...

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Jul 17^th, 2007, 9:30am

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.

Title: Re: Small heart slam (bridge puzzle)
Post by Margit on Jul 17^th, 2007, 9:46am

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)

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Jul 17^th, 2007, 1:55pm

on 07/17/07 at 09:46:06, Margit wrote:

(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.

Title: Re: Small heart slam (bridge puzzle)
Post by Margit on Jul 19^th, 2007, 4:59am

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 :-)

Title: Re: Small heart slam (bridge puzzle)
Post by ThudanBlunder on Sep 10^th, 2007, 9:23am

A nice warm-up exercise, Aryabhatta. ;)

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.

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Sep 10^th, 2007, 1:16pm

It was in hard for a reason ;)

In your puzzle, do you want the defense to cooperate? or are you looking for best play (double dummy) from both sides?

Title: Re: Small heart slam (bridge puzzle)
Post by ThudanBlunder on Sep 10^th, 2007, 1:36pm

on 09/10/07 at 13:16:36, Aryabhatta wrote:

In your puzzle, do you want the defense to cooperate?

Yes.

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Sep 10^th, 2007, 3:56pm

Some more clarification needed:

You want N/S to make 10 tricks with clubs as trumps and of the 10 tricks, South should make 6 (and hence North should make 4)?

Title: Re: Small heart slam (bridge puzzle)
Post by ThudanBlunder on Sep 10^th, 2007, 4:41pm

on 09/10/07 at 15:56:42, Aryabhatta wrote:

You want N/S to make 10 tricks with clubs as trumps and of the 10 tricks, South should make 6 (and hence North should make 4)?

Yes.

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Sep 12^th, 2007, 3:01pm

This looks like a toughie.

Expect me to ask you for a hint soon... :P

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Sep 14^th, 2007, 11:56am

Any hint will be appreciated.. (but please hide it)

Thanks.

Title: Re: Small heart slam (bridge puzzle)
Post by ThudanBlunder on Sep 14^th, 2007, 5:52pm

on 09/10/07 at 13:16:36, Aryabhatta wrote:

It was in hard for a reason ;)

[hide]The 1st 5 tricks are alternately spade and heart ruffs won by North and West.[/hide]

Title: Re: Small heart slam (bridge puzzle)
Post by ThudanBlunder on Sep 19^th, 2007, 4:20pm

on 09/14/07 at 17:52:32, ThudanBlunder wrote:

[hide]The 1st 5 tricks are alternately spade and heart ruffs won by North and West.[/hide]

[hide]...and East underruffs each time.[/hide]

Title: Re: Small heart slam (bridge puzzle)
Post by Margit on Sep 24^th, 2007, 10:10pm

TB, are you sure about the hints?
With East doing as you hinted then
the first 5 tricks used 5 times 2 clubs.
Plus the 4 in South hand make 14?

Title: Re: Small heart slam (bridge puzzle)
Post by ThudanBlunder on Sep 24^th, 2007, 11:06pm

on 09/24/07 at 22:10:16, Margit wrote:

TB, are you sure about the hints?
With East doing as you hinted then
the first 5 tricks used 5 times 2 clubs.
Plus the 4 in South hand make 14?

[hide]Sorry, I meant that East underruffs North each time.[/hide]

Title: Re: Small heart slam (bridge puzzle)
Post by Margit on Oct 3^rd, 2007, 2:56am

OK. Lets take a stab at this -
[hide]
The West hand has 10 spades, 2 clubs
and one other card.
Lets make this the Diamond Ace.

Now to the clubs. We know West
has 2, East has 3, so put the remaining
4 into the North hand.

Now to the Diamonds. Lets distribute
the remaining Diamonds 4 to North
and 5 to East.

At trick 6. North leads a Diamond taken
by West.
West returns the only thing
he has, a Spade. North trumps with
his last trump. East discards a Diamond.
South discards a Heart. These last discards
are crucial.
At this stage, both North and East have
3 Diamonds.

At this stage, E/W have 3 tricks, North has
taken 4.

North leads a Heart. South trumps.
South then leads the remaining 3 trumps
on which both North and East discard
their Diamonds.
And now South has winners with the remaining 2 Diamonds.
[/HIDE]

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Oct 3^rd, 2007, 1:18pm

Nice Margit! Looks right to me.

Title: Re: Small heart slam (bridge puzzle)
Post by Margit on Oct 4^th, 2007, 8:44am

Another comment -
[HIDE]
Actually as everybody is cooperating
so to speak, West does not need to have
the Ace of Diamonds. Any diamond which is
greater than the lowest held by North and West
will do.
Eg. The 7, 6 with North and 5 with East or
vice-versa.
[/HIDE]

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Oct 5^th, 2007, 12:49pm

Here is another one. If you are a already bridge player, it would probably be easy/medium for you, depending on your skill. If you are not a bridge player or have just begun, then this puzzle would be more interesting (I hope).

Spades are trump. You (North + South) need to make at least 12 tricks. West leads to the first trick by leading the spade 2.

How will you play to maximize your chances of making at least 12 tricks?

(Note: please read the first post for the rules and meaning of A, K, Q etc)

Code:

North

Spades: A K Q 5 4
Hearts: A Q T
Diamonds: A 3 2
Clubs: A 2

South

Spades: J T 9 7 8
Hearts: 5 3 2
Diamonds: K 4
Clubs: K 4 3

Title: Re: Small heart slam (bridge puzzle)
Post by Three Hands on Oct 8^th, 2007, 12:07pm

[hide]Comes down to how the hearts break. 3 rounds of trumps clear up any ruffs, and you can ruff a club and a diamond after winning the AK in each. This leaves you with a spade and 3 hearts remaining in each hand and, by making sure you're leading from South, lead up to the 10 (or beat whatever honour West comes up with). If the 10 (or higher honour) holds, Ace (or Q if the K showed up in the last round) of hearts and a round of spades gets the 12. If East wins, they then either return a heart, in which case you win with either Q or A, depending on if the K shows up, then claim the rest, or they lead a non-heart, in which case you ruff with one hand and throw a low heart with the other, and then win the Ace of hearts and ruff a heart/lead the last spade. 13 tricks is possible if West was left with KJ of hearts, or they hideously mis-defend[/hide]

I think that's about as fool-proof as I can come up with...

Title: Re: Small heart slam (bridge puzzle)
Post by Aryabhatta on Oct 8^th, 2007, 4:05pm

Well done Three Hands. That is correct and guarantees 12 tricks. [hide] Ruffing Diamonds last ensures you end up in South hand to make the heart lead.[/hide]