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Math Problem


kfay

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Came to a stalemate with karlson on this one until he ran a sim. I'm still not convinced.

 

[hv=pc=n&s=sak83hak9da53cj64&n=s7hqt75dkqt62cak3&d=s&v=0&b=11&a=6dppp]266|200[/hv]

 

LHO leads the J, RHO follows with the 6 and you win the ACE.

 

You lead a low , LHO pitches the 2.

 

Line A) You Play RHO to be 3253:

T3: A

T4: K (pitch a club)

T5: ruff

T6-7: AK

T8: K

T9: ruff

T10: Q from:

 

[hv=pc=n&s=s3h9da5c&w=shdc&n=shqtdktc&e=shdj987c]399|300[/hv]

 

Line B ) You play RHO to be 2353 or 3352

T3-4: AK

T5-7: Q, K, A

T8: K (RHO drops the Q, LHO does or doesn't drop the 10)

T9: ?

 

[hv=pc=n&s=s83hda5cj&w=shdc&n=shtdqt62c&e=shdj987c]399|300[/hv]

 

What do you ruff in dummy? Opponents play optimally.

 

 

What's better, Line A or Line B? What's the best play at the diagrammed position in line B?

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I agree with Cascade as regards dealing probabilities. Given the trump break,

3253 is over 14%

2353 is under 10%

3352 is under 12%.

 

However, there is a restricted choice argument that in the last case LHO might well discard a club from 5305, whereas in the first case with 5404 the defender has little choice because of the excellent bidding. So if I chose line 2 I'd tend to ruff a club.

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Line B is definitely wrong, because of Line C:

 

Play as in line B, but win the third heart in the North hand.

If East is 2452, ruff the last heart, cash DA, and ruff a black card with the 6.

If hearts are 3-3, lead the last heart, which LHO has to ruff. Overuff with the ace and guess what to ruff in hand.

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Any computation that ignores inferences from the lead is not enough.

 

Not to mention that any computation ignoring the bidding. I mean, 6-P-P-P was clearly not the sequence. If RHO has has only two spades, then LHO started with six of them and might have overcalled in any number of scenarios, especially with a void in trumps (and thus 6-4-3-0 shape). So, a REAL auction makes 3-card spades to the right probably a fair bet.

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