[lamford]

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IMPs. West leads the four of spades, third and fifth to the jack and ace. You play the two of clubs to West's ten, your five and East's king. East returns the eight of spades to your ace and West's five. Now you play the three of clubs and West plays the jack. Your play? And would you have played differently if the clubs had gone:
a) West plays the queen then the ten, and East the king on the first round
b) West plays the jack then the ten, and East the king on the first round
c) West plays the ten then the jack, and East the queen on the first round
d) West plays the jack then the ten, and East the queen on the first round
e) West plays the ten then the queen, and East plays the jack on the first round?

[nige1]

lamford, on 2014-October-09, 01:48, said:

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IMPs. West leads the four of spades, third and fifth to the jack and ace. You play the two of clubs to West's ten, your five and East's king. East returns the eight of spades to your ace and West's five. Now you play the three of clubs and West plays the jack. Your play? And would you have played differently if the clubs had gone:
a) West plays the queen then the ten, and East the king on the first round
b) West plays the jack then the ten, and East the king on the first round
c) West plays the ten then the jack, and East the queen on the first round
d) West plays the jack then the ten, and East the queen on the first round
e) West plays the ten then the queen, and East plays the jack on the first round?

I think that there are 4 relevant cases ..

• W: JT or TJ E: K. W can hold JT or QJT
• W: QT. E: K. W can hold QT or QJT
• W: TQ. E: J. W can hold QT or KQT
• W: TJ or JT. E: Q. W can hold JT or KJT

W has 6 ways of playing QJT but 2 each with JT or QT, so, when E plays the K, going up A is a 2/3 shot.
The other cases seem about 50-50 except that there's a case for going up A anyway ...

• When the A is right, it's worth an extra trick and
• Vacant-space inferences from the play imply that W is slightly less likely to hold 3 cards in ♣s

[lamford]

nige1, on 2014-October-09, 06:04, said:

I think that there are 4 relevant cases ..

• W: JT or TJ E: K. W can hold JT or QJT
• W: QT. E: K. W can hold QT or QJT
• W: TQ. E: J. W can hold QT or KQT
• W: TJ or JT. E: Q. W can hold JT or KJT

W has 6 ways of playing QJT but 2 each with JT or QT, so, when E plays the K, going up A is a 2/3 shot.
The other cases seem about 50-50 except that there's a case for going up A anyway ...

• When the A is right, it's worth an extra trick and
• Vacant-space inferences from the play imply that W is slightly less likely to hold 3 cards in ♣s

On that basis, East should only play the king when he has to. From KQ doubleton he should play the queen. Is that right, however?

[gszes]

I hate guessing I stink at it big time. This hand provides me with
a very sound alternative to the guesswork and I will try and make a case
that the spade T is leading us away from the best LOP. IMHO we should

play low to trick 1.

This play faces almost zero chance of a switch by rho (if so hold your
cards closer to your chest or get into an easier game). Even if RHO does
manage to find a switch we can always fall back on a 22 club break.

trick 2 win a top spade
trick 3 lead a club and duck
trick 4 win another top spade
trick 5 lead another club and since rho holding 3 clubs is no longer
a factor go up with the ace since you cannot make if lho began with 3
clubs and 5 spades.

This might seem like we are playing for spades to break 22 but that is not the
case at all. We are playing for 22 OR rho holding 3 clubs. This combination of
events is roughly 80% of the makeable possibilities.

rho having 3 clubs is about 34% and 75% of those times they will hold the K so
the given LOP loses outright 25.5 % of the time the remaining 74.5% has a sure
thing when lho holds the club K singleton 18.5% but the remaining 56% is to be
determined on how well we can guess. So the given LOP starts with a disadvantage
of 5.5% and it only gets worse depending on how far short of perfect one's guesswork
is out of the remaining 56%.

I agree it feels good to keep all possibilities open but when the result is guesswork
vs a clear cut choice given new information sometimes just taking the LOP with the greatest
overall chance of success is best.

[nige1]

lamford, on 2014-October-09, 11:01, said:

On that basis, East should only play the king when he has to. From KQ doubleton he should play the queen. Is that right, however?

IMO E should randomize e.g. if W plays TJ and S knows that E always plays the K from KQ, then, when E plays Q, S can confidently duck the 2nd round. Such considerations might

• Reduce the odds in favour of the drop when E plays the K. and
• Increase the odds of playing for a 3-1 break when E plays the Q.

I guess there might be more ramifications although the players seem to be stuck on tram-lines in the other variations (i.e. restricted choice arguments don't seem to apply unless W has QJT or E has KQ). Anyway this is a difficult and interesting problem. Thank you, Paul

[lamford]

gszes, on 2014-October-09, 13:07, said:

I hate guessing I stink at it big time. This hand provides me with
a very sound alternative to the guesswork and I will try and make a case
that the spade T is leading us away from the best LOP. IMHO we should

play low to trick 1.

This play faces almost zero chance of a switch by rho (if so hold your
cards closer to your chest or get into an easier game). Even if RHO does
manage to find a switch we can always fall back on a 22 club break.

trick 2 win a top spade
trick 3 lead a club and duck
trick 4 win another top spade
trick 5 lead another club and since rho holding 3 clubs is no longer
a factor go up with the ace since you cannot make if lho began with 3
clubs and 5 spades.

This might seem like we are playing for spades to break 22 but that is not the
case at all. We are playing for 22 OR rho holding 3 clubs. This combination of
events is roughly 80% of the makeable possibilities.

rho having 3 clubs is about 34% and 75% of those times they will hold the K so
the given LOP loses outright 25.5 % of the time the remaining 74.5% has a sure
thing when lho holds the club K singleton 18.5% but the remaining 56% is to be
determined on how well we can guess. So the given LOP starts with a disadvantage
of 5.5% and it only gets worse depending on how far short of perfect one's guesswork
is out of the remaining 56%.

I agree it feels good to keep all possibilities open but when the result is guesswork
vs a clear cut choice given new information sometimes just taking the LOP with the greatest
overall chance of success is best.

It might not be that difficult for East, holding three spades and two club entries, to switch to his better red suit. However, we did decide to win the first spade, and we are now faced with a tough problem after our 'error' at trick one, which we all make from time to time. And your line did not gain anyway, as East did not have three clubs, unless there are fourteen in this pack.