What are the odds?

[silvr bull]

Conditions for this problem:

1) You are declarer in NT or a suit contract at MPs;

2) If a suit contract, the opp trumps were evenly divided and have been pulled;

3) You have transportation and timing so you can use winners you develop;

4) You need three tricks in this side suit to make your contract, or 4 tricks for a desirable over trick.

 

Dummy has 9xxx in a side suit, and declarer has AKT. RHO plays a low spot card when the suit is led from dummy.

 

Playing from the top wins 3 tricks if LHO has a stiff Q or J, or Qx or Jx, and wins 4 tricks if LHO has QJ tight.

Playing the ten first wins 3 tricks if LHO has a stiff x, or xx, and wins 4 tricks if LHO has xxx.

Other distributions of the suit give the same number of tricks regardless of the card declarer plays first from AKT.

 

With no additional information, is it better to play the ace or ten first from AKT?

Are the odds close, or is one play much better than the other?

[smerriman]

According to SuitPlay, all other things being equal, you should play low to the ten, but it's close:

 

Low to T: 8.7% of 4 tricks, 69.4% of 3 tricks, 2.781 tricks on average

 

Low to K: 3.2% of 4 tricks, 71.8% of 3 tricks, 2.750 tricks on average

 

This doesn't take into account any chances that RHO will play an honor from QJx to begin with though. And the second line takes 3 tricks more often, so this also assumes everyone else is in the same spot.

[Stephen Tu]

Easiest way is to calculate these for yourself using something like:

http://rpbridge.net/cgi-bin/xcc1.pl

 

Note there is a third possibility: cash high honor, then cross back and finesse.

 

[silvr bull]

According to SuitPlay, all other things being equal, you should play low to the ten, but it's close:

 

Low to T: 8.7% of 4 tricks, 69.4% of 3 tricks, 2.781 tricks on average

 

Low to K: 3.2% of 4 tricks, 71.8% of 3 tricks, 2.750 tricks on average

 

This doesn't take into account any chances that RHO will play an honor from QJx to begin with though. And the second line takes 3 tricks more often, so this also assumes everyone else is in the same spot.

Thanks! I guessed it would be close. Looks like low to the ten first is better at MPs where over tricks have value, but Ace first then low to the ten is better at Imps.

[silvr bull]

Easiest way is to calculate these for yourself using something like:

http://rpbridge.net/cgi-bin/xcc1.pl

 

Note there is a third possibility: cash high honor, then cross back and finesse.

Thanks! The Pavlicek site helps me to see this more clearly. Ace first, then (if W plays small) low to ten wins 4 tricks when W has QJ doubleton (1.6%), and wins three tricks when W has a stiff Q or J (2.4%), but gets only 3 tricks when W has xxx (7.2%) and gets only 2 tricks when W has Qx or Jx (13%). Playing Ace and King first is always better (or equal) when W has either honor in that suit.

 

Low to the ten first wins 4 tricks when W has no honor in that suit (23%), but gets only 2 tricks when W has a stiff Q or J or Qx or Jx (15%). To maximize winning 3 tricks without regard for a 4th trick (scoring at Imps for example), the choices below are approximately right:

 

Low to ten first: 65.8%

Ace & King first: 65.9%

Ace first then low to ten: 68.3%