maths problem

[jddons]

[hv=pc=n&s=sakt86hj97643dcj2&w=sq943hakq8d7ck753&n=sj752ht5dj862caqt&e=sh2dakqt9543c9864&d=n&v=b&b=13&a=p1d2dp3s5dppp]399|300[/hv]

IMPS.

1. Is it better to play to drop J♦ or take a first round finesse? At the table I took the view that assuming S was 5-5 in the majors he had 3 missing spaces hence the chance of him having the J were 3/13. North had 6 missing cards hence holding 4♦ seemed less likely but is this analysis correct?

2. What do you call on the east hand at your first turn? would you do differently in first seat? Whether or not to pre-empt with this type of hand seems a surprisingly common problem. Do you have ground rules for this in your partnership?

3.Result? A push in 5♦ -1 after A♠ lead.

[Cyberyeti]

That analysis is clearly not correct, S has 3 vacant spaces, but N only has 6 given that he presumably has 4 spades and 3 hearts.

 

Our opps played 3N-3 when they didn't get the diamonds right

[Tramticket]

If you assume from the bidding that South is likely to hold 10 cards in the majors and North is likely to hold 7 cards, then the important cases are:

 

Taking the finesse succeed over playing for the drop if North holds all four missing diamonds = (6/9)x(5/8)x(4/7)x(3/6) = 11.9%

Playing for the drop succeeds over taking the finesse if South hold the Jack = 33.3%

 

It is clearly right to play for the drop.

 

Of course South might be 6-5 (as in this deal) or even 6-6. You can re-perform the maths for these cases, but it will be correct to play for the drop.

[Cyberyeti]

 

Of course South might be 6-5 (as in this deal) or even 6-6. You can re-perform the maths for these cases, but it will be correct to play for the drop.

 

Not true unless my calculations are wrong:

 

For 6-5 it's pretty close, finesse 7x6x5x4/9x8x7x6 = 5/18 = 27.78%, drop 2/9 = 22.22%

 

For 6-6 it's not close, finesse 8x7x6x5/9x8x7x6 = 5/9 = 55.56%, drop 1/9 = 11.11%

 

You now need to work out the chance of 5-5 vs 5-6 or 6-6/5-7/6-7, I suspect 5-5 is more likely by enough that the drop still wins.

[jammen]

I would always open 5♦ and then play it like the Hog. Trump the high spade lead and then play four rounds of diamonds. East can beat you by returning a ♥ but that is very unlikely. Trump the spade return and play off all your trumps save one. In the six card ending: [hv=pc=n&s=sh2d4c9864&w=sahj976dcj&n=sq9hakq8dc&e=sjht5dcaqt]399|300[/hv]

 

On my last trump West is squeezed out of his club as I pitch dummy's losing heart. I then cross to the A♥ and throw West in with the 9♠. West is now forced to play a ♥ to the good dummy, so I lose no ♣ trick and make my contract.

[Tramticket]

I would always open 5♦ and then play it like the Hog. Trump the high spade lead and then play four rounds of diamonds. East can beat you by returning a ♥ but that is very unlikely. Trump the spade return and play off all your trumps save one. In the six card ending: [hv=pc=n&s=sh2d4c9864&w=sahj976dcj&n=sq9hakq8dc&e=sjht5dcaqt]399|300[/hv]

 

On my last trump West is squeezed out of his club as I pitch dummy's losing heart. I then cross to the A♥ and throw West in with the 9♠. West is now forced to play a ♥ to the good dummy, so I lose no ♣ trick and make my contract.

 

Its easier to follow if you don't rotate the diagram. Quite a neat double dummy solution (you need to cash two hearts before throwing west (original south) in.

 

I suspect that north (original west) is more likely to return a heart than you think :)

[jammen]

Thanks for the tip, I didn't realize that I had rotated the hands. I should clarify that when you play four rounds of trumps you cannot play them from the top or the dummy is squeezed. After A diamonds reveals the bad split lead the 10 diamonds pitching a club from dummy. A spade or trump back now produces the six card ending, while a heart return is down two (except when declarer is 0-2-8-3 which produces the same winning ending).

[Dinarius]

With most partners, I open 2♣️ with East, rebidding 3♦️. This show 8 tricks.

 

Given North’s pass, over 1♦️ by East, I bid 4♦️with the South hand.

 

Finally, where’s the finesse? As in, if you cross to take it, you’re still minus 1, correct?

 

On the bidding, you don’t expect diamonds or hearts to break, right? So, playing for one down, by playing diamonds from the top is the better MPs strategy, no?

 

D.

[jammen]

With most partners, I open 2♣️ with East, rebidding 3♦️. This show 8 tricks.

 

Given North’s pass, over 1♦️ by East, I bid 4♦️with the South hand.

 

Finally, where’s the finesse? As in, if you cross to take it, you’re still minus 1, correct?

 

On the bidding, you don’t expect diamonds or hearts to break, right? So, playing for one down, by playing diamonds from the top is the better MPs strategy, no?

 

D.

Not to mention that you will make the contract when trumps split or the opponents misdefend.

[johnu]

Finally, where’s the finesse? As in, if you cross to take it, you’re still minus 1, correct?

 

Yes, after crossing with a heart to take a diamond finesse, you still need to get to dummy to cash the remaining heart honors unless the ♣A is onside. You could try cashing 3 rounds of hearts before taking a diamond finesse but that needs hearts to be 5-3 else North will ruff the 3rd heart, and now you need a club finesse to make.

 

The point is that you can't look at the diamond suit in isolation.

[jammen]

The club Ace has to be off or else LHO has passed with AK,A, and a void,

[Dinarius]

Am not looking at the diamond suit in isolation. Am trying to consider best MP strategy.

 

If you commit to finesse, you also commit to cashing the Hearts first.

 

On the bidding, I expect it is more likely that Hearts won’t allow you to cash them before taking the finesse, than it is that one of South’s Clubs might be a Diamond. Though I’m not a mathematician, so I can’t prove it.

 

I’m still playing Diamonds from the top.

 

D.

[gszes]

I would always open 5♦ and then play it like the Hog. Trump the high spade lead and then play four rounds of diamonds. East can beat you by returning a ♥ but that is very unlikely. Trump the spade return and play off all your trumps save one. In the six card ending: [hv=pc=n&s=sh2d4c9864&w=sahj976dcj&n=sq9hakq8dc&e=sjht5dcaqt]399|300[/hv]

 

On my last trump West is squeezed out of his club as I pitch dummy's losing heart. I then cross to the A♥ and throw West in with the 9♠. West is now forced to play a ♥ to the good dummy, so I lose no ♣ trick and make my contract.

 

This is the proper end position but I believe the proper LOP is to win the first dia (get the bad news) and immediately surrender a trick to the dia J. Playing 4 dia from the top will squeeze dummy on the 4th dia because in order to achieve your end position dummy must be able to retain at least 3s 4h and 2c when rho wins the dia J and if you play off the top 3 diamonds and THEN surrender to the J dummy can only hold 8 cards.

 

This hand allows you to safely cash 2 dia then surrender to the J but it is a bad habit that allows the opps more opportunity to card information and thus increase the odds of a heart switch.