Wednesday, March 9, 2011

Suit Combinations: 9 cards missing the KJ


I've seen this suit combination several times lately. Do you know the correct play? That's kind of a trick question. To know the correct play of this suit for a particular hand, you'd have to consider the form of scoring, the bidding, the contract you're in and how likely the rest of the field will be in the same contract, how the field will likely play this suit, and table feel.

There are 3 reasonable lines of play:
1) finesse the Q, then play the ace
2) double finesse (let the 10 ride, then let the 9 ride)
3) play the ace, then lead toward the Q

Strictly mathematically speaking, line 1 will yield more tricks on average, 4.03 tricks to be exact but will leave you with only 3 tricks in the suit 23.43% of the time (when KJx or KJxx or stiff K are offside).
Line 2 nets 3 tricks the same amount of the time it nets 5 tricks (24%) so yields 4.00 tricks on average.
Line 3, which intuitively seems bad, gets you 3.95 tricks on average but if your goal is to play the suit for 4 tricks, this is clearly the best option as only 17.2% of the time will you be held to only 3 tricks (KJx or KJxx offside).

I'm still waiting for the play of the ace to make the contract when either of the other 2 lines results in going down but even when you get a hand where you need to old that suit to 1 loser, only 6.2% of the time will it help, so in matchpoints this safety play is normally not worth the chance of risking a potential overtrick. An exception would be if you have reached a good contract that most of the field is unlikely to get to. Playnig the ace first will get you 5 tricks only 12.4% of the time while finessing the Q first will get you 5 tricks 26.6% of the time as the reward for making an overtrick rates the be same as the penalty for going down if everyone in the field is in the same contract with the same decision.

At imps, the play of the ace first is clearly a winning play in the long run (if the contract depends on losing no more than 1 tricks this suit). In the 14.2% of the time that you'll fail to get an overtrick as compared to finessing the Q, you'll lose an imp and in the 6.2% of the time that you do get an extra trick by playing the ace first, you'll win 10 or 12 imps depending upon vulnerability. Thus, on average you will win (or save) .478 imps when non-vul or .602 imps when vul.

1 comment:

  1. Addendum:

    Leading up to the A is actually a slightly better play. Although it is useless if LHO shows out if LHO plays the J then playing the Q is correct even if you were planning on playing the A.

    LHO would only play the J from J, KJ, Jx (knowing they aren't taking a trick) and in all of these cases finessing will only help [KJ tight with LHO]

    So low to the A and low to the Q again unless LHO plays the J.