[karlson]

Scoring: IMP

2♦*-4♦*
4♠-p

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You open 2d multi, partner bids 4d (bid your major).

Lead is a small club (one lower spot outstanding), 3rd/5th.

[nigel_k]

The ace wins when the lead is a singleton and trumps could have been played for one loser. Low wins when the ♣K is onside and trumps cannot be played for one loser.

The chance of playing trumps for no loser is 65%. Before the lead, the chance of a singleton club in West is 7.25% and the chance of the king in West is 50%.

Let's assume West would always lead a singleton club ( though he might not with Qxx of trumps).

(0.0725 * 0.65) / (0.5 * 0.35) = 0.27

So you should play the Ace if West would lead a club 27% of the time or less when holding the king, and should play low if he would lead a club more than 27% of the time when holding the king.

This is pretty close since any of the four suits could be right on the auction though he probably doesn't have an attractive trump lead. I would probably play the ace.

[Cascade]

nigel_k, on Sep 14 2009, 03:42 PM, said:

(0.0725 * 0.65) / (0.5 * 0.35) = 0.27

What are you trying to calculate here Nigel?

If 0.5 is the 50% the king is onside then I am not sure that is right as we probably won't see a low card led from Kx for example.

[pooltuna]

karlson, on Sep 13 2009, 09:18 PM, said:

Scoring: IMP

2♦*-4♦*
4♠-p

---

You open 2d multi, partner bids 4d (bid your major).

Lead is a small club (one lower spot outstanding), 3rd/5th.

Basically your question is should I worry more about a 5-1 club break or a 3-1 spade break. As the 5-1 break is more unlikely I would just finesse the opening lead. Nigel the opening leader could hold as many as 4 clubs no? And the auction may suggest an aggressive opening lead

[nigel_k]

pooltuna, on Sep 14 2009, 08:27 AM, said:

Basically your question is should I worry more about a 5-1 club break or a 3-1 spade break. As the 5-1 break is more unlikely I would just finesse the opening lead. Nigel the opening leader could hold as many as 4 clubs no? And the auction may suggest an aggressive opening lead

Half of the 3-1 breaks will be a stiff honour so we can make in those cases plus all the 2-2 breaks so that's 65% in total. We have that 65% chance if we play ♣A and we have zero chance if we hook and they get a ruff. So you can't just compare 5-1 vs 3-1.

Wayne is right that we can rule out Kx in clubs for the opening leader and this makes the play of the ace a bit better.

[655321]

I would finesse at trick 1.

I assume that Nigel's numbers represent the a priori chances of (a) Singleton club and trumps coming in for one loser, and (b) ♣K onside and 2 trump losers.

I get 4% and 17.5% for these numbers (only 5 of the 12 5-1 club breaks have West with a small singleton).

Then to adjust these numbers for the lead, I would still adjust (a) down a little - as Nigel said, with some trump holdings a singleton lead is not always attractive. Then when adjusting (b), I would say that a trump lead is basically never happening (so the choice is down to 3 suits already), and of the 50% of the time West has the ♥A, a heart lead won't be considered either. So my guess is that (of the 17.5%) West would lead a club more than 1/3 of the time even after allowing for no club lead with Kx.

It would be possible to do more accurate calculations allowing for the fact that the odds change (5-1 clubs changes the odds of 2-2 trumps, etc) but this back of the envelope stuff is often enough.