The Tao of Gaming

Boardgames and lesser pursuits

Just lucky, I guess

Here’s a bridge problem for you (not for Jeff, but the rest of you).

spades AQT86
hearts AQ3
diamonds Kxx
clubs Kx

spades KJ975
hearts 542
diamonds AQx
clubs Ax

You wind up in 6 spades, only to discover the unlucky duplication (both hands are 5-3-3-2 distribution). LHO leads the diamond jack (strongly hinting at the ten and probably 9). Trumps break 2-1, everyone follows suit, and your opponents are experts.

I recently discovered an article on the psychological differences between (self-described) lucky and unlucky people. The experimenter couldn’t find any actual difference (testing via picking lottery numbers, and the like). Then he asked the subjects to count the number of photographs in a newspaper section.

On average, the unlucky people took about two minutes to count the photographs whereas the lucky people took just seconds. Why? Because the second page of the newspaper contained the message “Stop counting – There are 43 photographs in this newspaper.” This message took up half of the page and was written in type that was over two inches high. It was staring everyone straight in the face, but the unlucky people tended to miss it and the lucky people tended to spot it.

After reading that I was instantly reminded of Victor Mollo’s classic introduction to card play at bridge. “Card Play Technique: The Art of Being Lucky.” Look back at that hand … anyone can make the hand if LHO has the heart king. You pull trumps, and finesse the queen. If LHO has the king, you are lucky, and if RHO has it you are unlucky.

But the winning player will notice something else. If you get rid of the minor suits, you have additional chances. Pull trumps, and run the minors. New lead low towards the queen. LHO plays the 9, so you … play the Ace! If the finesse works, you’ll still have to lose one heart anyway. Come back to hand with a spade and lead low towards the queen. LHO plays the 6 this time (see below), you play the queen, and RHO wins with the King.

But he doesn’t have any more hearts to return, and leads a club, giving you a ruff and sluff for the last trick. So, the lucky player wins when RHO has a stiff King doubleton king. What if he had Kxx (or more?) Then everyone looses. I’m not sure if being open-minded and having a positive attitude will help your luck in games, but doggedly working towards your goal with a closed mind probably hurts (as in life).

And why did the expert play the 9 of hearts on the first round? If he’d played the six, you could have just ducked in dummy. Then either RHO would be forced to overtake (and either lead a heart into the AQ, or give you that ruff and sluff), or he would show out, and the finesse would be marked. He avoided giving you a sure play, and gave you a chance to go wrong. If you didn’t, he can legitimately gripe about bad luck….

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Written by taogaming

November 7, 2009 at 10:52 pm

3 Responses

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  1. Playing low on the first Heart trick (as opposed to rising with the Ace) will work if RHO has K, KJ, KT, or KJT. I assume that the play Brian outlines has a higher probability of working, but it isn’t immediately obvious, so both cases need to be checked.

    Larry Levy

    November 8, 2009 at 2:49 pm

    • ‘If RHO has a stiff King, you can’t go wrong.

      If RHO has KJ or KT, playing anything but the queen wins. (But play low means you are going to fly with the ace next time and not finesse, and odd position).

      With KJT specifically, you need to play low.

      So the low play wins against xxxx-KJT split. The Ace wins against xxxxx-Kx (where it may be KJ or KT).

      More prosaically, playing low means that if LHO wins with the 9 (RHO playing low) and leads a heart, you have to finesse or guess that RHO has the stiff king correctly. Playing Ace and then towards the queen saves you the guess.

      (I could have solved this by having LHO play the Jack, but I figured the 9 was good enough).

      taogaming

      November 8, 2009 at 5:36 pm

      • It’s actually quite close. Not only does ducking the first trick pick up KJ10 tight, it picks up any 1-6 break. (All plays pick up stiff king onside.) But you should know by then if 1-6 is possible. By the time you are down to five cards, RHO will have had to pitch a heart if he had six of them. If he has done that, there is no chance he has Kx or KJ10 tight left (assuming he’s not a generous type who likes letting opponents make hopeless slams) with the one exception that he was dealt precisely KJ109 and chose to pitch precisely the 9. (Please don’t say, “but LHO played the 9.” This is a semi-restricted choice situation, which is quite messy, so trust me when I say you have to consider this case.) You should also know something about the side suit distributions; if RHO followed to all the minor suit cards and had three trumps, for example, he doesn’t have six hearts. If he had only two trumps, he’ll have to be exactly 2632. That leaves LHO with 1147 shape; you might have heard from him at some point. You should also know if a 5-2 break is possible. If RHO has shown up with one trump and two diamonds, and each player has followed to the clubs, then a 5-2 heart break is impossible.

        The bottom line is that Brian’s play is slightly better in the abstract (the calculations are weird due to the semi-restricted nature of the H9), but that by the time you have to make the choice, it’s possible that it is either vastly better or substantially inferior.

        JeffG

        November 9, 2009 at 12:23 pm


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