Math problem

[Fluffy]

[hv=pc=n&s=skt8432h7dcak8532&n=sa6hat92dakq98c64&d=n&v=0&b=1&a=1dp1sp2hp3cp3dp4cp4sp6sppp]266|200[/hv]

 

♥Q lead

[nige1]

[hv=pc=n&s=skt8432h7dcak8532&n=sa6hat92dakq98c64&d=n&v=0&b=1&a=1dp1sp2hp3cp3dp4cp4sp6sppp]266|200|

♥Q lead [/hv]

Guessing: ♥A. ♦AKQ, chucking ♣s. If ♦JT appear, then ♠KA, ♦ throwing last small ♣. Otherwise ♣AK. ♣ (over) ruff.

[WesleyC]

Combining your chances by testing for ♦JT or ♦JTx seems appealing at first glance, but with 8 diamonds missing, a favourable holding is very unlikely (5.7%) when compared to the chance that an opponent ruffs exactly the 3rd diamond (16.8% minus some extreme distributions) and it also opens you up to the chance of a trump promote if LHO holds 3 diamonds (23.5%) on an otherwise favourable club layout (e.g. W: CCCSS E:CCSSS).

 

Playing on clubs right away feels like an improvement. You've got a very good chance to succeed if clubs and spades are 3/2 and the long spades are with the short clubs (24.7%) and retain some chances if the short clubs are onside with the short spades (eg west holding ♣xx and ♠J5). It's also possible to scrape home if LHO holds a stiff club and 3 good trumps eg (QJx). It's hard to add all the residuals up accurately but I'd guess that overall this line is about 31%.

 

The final option is playing 4 rounds of diamonds right away which picks up the favourable diamond layouts (JTx, 4/4 = 41%) when the trumps are breaking (28% overall). You also retain chances if RHO shows out on the 3rd round of diamonds and trumps break (an extra 4.5% or so). Which makes this line (slightly) the best chance overall chance (in my opinion) at about 33%.

 

As a disclaimer, its pretty late and I might easily have missed something obvious!

[gszes]

I like the starting with diamonds. There is an additional benefit to starting with diamonds and that is we can try for 44 (38%). If rho shows out on the 4th dia we can always fall back on the club play. If rho follows we ruff with the 8. If lho overruffs we can still make if rho began with Q9 or J9. club club ruff with the ace (unless lho shows out and fails to ruff--we are probably going down) and finesse the spade T. If dia split 44 merely 2 rounds of trumps ending in dummy and play the 5th dia pitching last club. The nice part about this LOP is that we can try it (not risk free but its fairly safe 70%) and still have a strong chance of falling back on the 3S 2c distribution. As an aside if rho trumps HIGH (creating an uppercut) on the 4th diamond it is probably best to just pitch the club and hope they started with 3 trumps.

[shyams]

If rho follows we ruff with the 8. If lho overruffs we can still make if rho began with Q9 or J9. club club ruff with the ace (unless lho shows out and fails to ruff--we are probably going down) and finesse the spade T.

Wouldn't it be better to ruff with the 10? It wins when East started with QJ9, QJ7 or QJ5 -- that's a more likely scenario than West holding Q9 or J9.

[gszes]

Wouldn't it be better to ruff with the 10? It wins when East started with QJ9, QJ7 or QJ5 -- that's a more likely scenario than West holding Q9 or J9.

 

Note that in the original position I referred to RHO (east) as beginning with Q9 or J9 vs west.

 

The T holding the trick because it cannot be overruffed is a Trojan horse. Winning the 4th dia with the trump 10 (and dia not splitting 44) means we have to fall back on the original basic plan hoping for 3 trumps and 2 clubs BUT now we are hoping only east has the short clubs whereas the original plan either opp holding 3 trumps and 2 clubs would win. Using the 8 allows for a very common defensive theme (getting overruffed by the longer trumps and playing for split honors in the trump suit) and the end position means either opp can hold 3 clubs.