Easter problem

[Gerben42]

Here's an interesting slam hand from last weekend, worth thinking about.

 

[hv=d=s&v=b&n=s632hk853dakt94c5&s=sakqj75h4d83cak74]133|200|Scoring: IMP[/hv]

 

Auction at the table:

 

1♠ - 2♦

3♠ - 4♣

4♥ - 4NT

5♦ - 6♠

 

6♠ was a good try as 3♠ shows a good 6-card suit at least. With 7♠, slam should be cold, with only 6 it is at worst 50/50.

 

A trump is led, RHO following suit and you take the Ace. How do you continue and why? (Think about the subtitle hint)

[whereagles]

I think I know what you mean with that hint, but I'm not sure that's best :P

[Finch]

I don't think this is particularly easy, by the way, though I know what I think the best line is.

[hrothgar]

Answer hidden

 

 

Regardless of what you do, I think that you need to lead a Heart to the King from the get go. Admittedly, this is going to let the opponents the option of leading a second round of trump, but this can't be avoided. Equally significant, I don't think that you can properly evaluate most of the lines unless you know if the King of Hearts is onside.

 

Personally, I'd lead a Heart to the King at trick 2. I'm hoping for one of the following

 

1. The Ace of Hearts is onside. I can ruff one club and discard a second on the king of Hearts

 

or

 

2. The Ace of Hearts is offsides but East doesn't have a Spade to return

 

or

 

3. Spades break 2-2 so I can cross with the six of Spades and I can pickup the Diamond suit for one loser

 

or

 

4. Spades break 3-1 / 1-3 and I can drop the QJ of Diamonds

 

This looks to be (roughly) 73%

 

 

 

[jocdelevat]

I need to ruff the 2 clubs with the remaining 2 trumps in dummy. for that to happend i play ace club then smal club. play ace and k diamonds then ruff with j spade a diamond. ruff the second club. play heart. taking out the reamining trumps with k and q and we home.

[hrothgar]

I need to ruff the 2 clubs with the remaining 2 trumps in dummy. for that to happend i play ace club then smal club. play ace and k diamonds then ruff with j spade a diamond. ruff the second club. play heart. taking out the reamining trumps with k and q and we home.

From what I can tell, this line requires that

 

East and West both have 3+ Clubs and East and West both have 2+ Diamonds. (If not, there is going to be an over ruff followed by a Heart loser).

 

The good news is that the odds that Clubs break increases the odds that Diamonds break. I ran a quick monte carlo that suggests that this line is ~69.6%

 

Here's where things get a bit complicated:

 

I ran another simulation to study how often you can pick up the Diamond suit for no losers. (Basically, Diamonds break 3-3 or the break 4-2 and you can drop QJ). If the Diamonds are behaving well enough for for you to ruff two rounds of Clubs, then you're going to be able to pick up the Diamond suit for no losers something like 55% percent of the time.

[Gerben42]

So many mathematics thrown at this hand!

 

I posted it here as there are some very simple ideas that can be applied by B/I:

 

 

 

LINE 1: If you try to ruff clubs you need to play 3 rounds of clubs and 2 rounds of diamonds before playing another trumps and hope no one overruffs. In a way you put all your eggs in one basket.

 

LINE 2:

 

Instead if you play a heart to the King, you win when the Ace is onside (basket 1).

 

If the Ace is offside, maybe RHO does not have a Spade left to return (basket 2, which is bigger than you think since... most players don't lead a trump singleton for good reason!). In this case you can try LINE 1 from this point.

 

Now if RHO does have a Spade to return (now they are 2-2 unless LHO really led his singleton trump in trick 1) you can try to play Diamonds for no losers (basket 3).

 

Better to try for 3 chances than one, even though as Richard suggests, the 1 chance is reasonably large (70%).