Dropping odds

Hi all

This teams season didn’t start that well for us, some bad play and equivalent results. During clubnights Hoek and I are quite in sync already, but in serious teams matches there seems to be a bit of stress and tension around. It’s difficult to score when the fragile and precious trust you’ve built up is under heavy fire. Here’s a problem Hoek had to face from a recent teams match, against the top dog from our pool. Let’s bark. Let’s play.

South
JT4
AKQ5
QT973
5

West
North
East
South
 
 
1
2
pass
41
pass
4
4
42
double
63
a.p.
 
 
 

1. Fitshowing jump
2. Cue
3. Bark!

Vulnerable against not it wouldn’t be my choice to follow on such a meager suit, then again you do have full opening values and a strong sidesuit. Too bad we don’t play ELC or Raptor.

North
6
74
AJ52
AKQT73

South
JT4
AKQ5
QT643
5

So plenty of tricks to take, but there’s this little voice coming from the speaker saying:"Houston, we’ve got a problem!" We’re missing a King. Unfortunately we don’t have time to put out a warrant or contact Homeland Security for his whereabouts. You’ve gotta find him, and find him now.

Hoek looked at the bidding sequence and divided the 14 missing points between both opponents. Without the King of East doesn’t come close to an opening bid, so the only chance is that he’s sitting naked in East’s hand. First Hoek tried to get some information by advancing the Queen, but when West smoothly played small, Hoek took a deep breath and went for the drop.

East Dealer
NS Vul
North
6
74
AJ52
AKQT73
West
853
J98632
K7
92
East
AKQ972
T
98
J864
South
JT4
AKQ5
QT643
5

Too bad. I have to agree the drop looks very appealing, but Kees worked out the odds are about 3 to 1 against the drop. Roughly there are 28,000 distributions with a bare King against 81,000 distributions with him onside (forget about nasty 4-0 splits and/or voids). Maybe it’s more a slam for me to play, I am a simple bridgeplayer, I take a finesse when I see one.

The rest of the match was solid and we had some small gains here and there, so the loss was only 14-16. But it easily could have been a (large) victory for us.

13 thoughts on “Dropping odds

  1. The calculations were made under the assumption that East held 10 HCP and 5-7 , and that West held 5-6 . In practice, all hands where East holds a singleton King, we can assume that he also holds something else, because something like AKxxxx, xx, K, xxxx seems like a pretty lousy opening to me. But even with these assumptions the finesse stands out a mile.

  2. I don’t understand these calculations. The decision to play for the drop or the finesse depends on what kind of hands East will open 1 with. So you must know the opponents biddingstyle before you can make a good decision. For me AKQxxx with nothing beside is never a 1 opener (even not vulnerable against vulnerable), so when you play against me you should play for the drop. Against Kees you should try the finesse and against Jannes you can claim on a winning finesse! :-)

  3. Anyone looked at the bidding sequence? Take the finesse. West’s bidding (first pass then 4) practically denies a spade honor, denies a 4-card spades and yet somehow he must see something positive in it. Nothing to calculate here.

  4. Thinking a bit longer about this problem and reading the comment of Frank Vindaloo, I come to the conclusion that I will play for the drop against any player and that Kees calculations with east holding 5-7 spades are wrong!
    East cannot have 5 spades, because then west will always bid (having 4 spades). And look at the west hand. Isnt’ it strange that he didn’t bid 2spades immediately over 2diamonds, now that he has the king of diamonds?
    I think any normal player with 3 spades and the king of diamonds will normally bid 2 spades. So when west has the king of diamonds, east must have (at least) 7 spades. And with AKQxxxx and nothing else I cannot believe east will open 1spade. So I will play for the drop even against Jannes.

  5. What you are actually saying is that without the diamond king, east does not really have an opening bid. If you assume likewise that any west with spade support would show it (certainly if he can bid 4 Hearts later), then the distributions that east can hold are: 7 spades, 1-2 hearts, 1-2-3 diamonds, 1-2-3-4 clubs. A 7-1-1-4 distribution seems to stand out a mile if he does not have the diamond king (why else would he open 1 Spade). There are 7 x 3 x 15 = 315 such hands (for any 7 card spade suit).
    If he holds the diamond king (which still needs to be singleton to win) he still seems to be 7114 (if not, somebody needs to explain to me why west introduced his 5 card heart suit). Again, for any spade suit there are 7 x 15 = 105 hands. Admittedly, he does not really need the spade queen anymore, but that will not increase the odds with 300 %. So we still finesse.
    Afterwards, we will be surprised by the actual distribution, but that is not our problem

  6. KJ’s reasoning matches mine at the table closely.

    In addition, if West has a 2-6-3-2 distribution without the diamond King, he could still bid 4H. His partner rates to have either a couple of hearts or extra spade length.

    So, East will open normally with the diamond King and might preempt without it, while West doesn’t need it. It fits. Of course, the King singleton isn’t a big chance, but if it’s not it doesn’t matter what you do.

    I’m suprised. The odds will always favor the King with length, so according to these calculations, you can never play for the drop.

  7. The odds will only favour the drop if you can rule out the king in the other hand.
    Or maybe if you know that there is a huge difference in High Card Points. I thought that 10 points was large enough, but now I think it will be more something like: the opponents have 26 points, with at least 23 on your right. Not willing to do the exact calculation though.

  8. You can never rule out anything for sure. If West is known to hold 23 HCP, you should say there’s a 95% chance he holds 23 points. Of the remaining 5% East would bid 95% of the time, which he didn’t, so we’re 99.75% certain.

    Each of your distributions needs to be augmented with the likelihood of the EW bidding. For the hand above it could go: 50% East will preempt, of the remaining 50% West will bid 2S 75% of the time, resulting in 12.5% that this distribution exists.

    I’m fairly certain this alters your calculations significantly, and the finesse no longer “stands out a mile.”

  9. Let’s assume you don’t know anything about the diamond distribution. Let X be the probablitiy that East has the King. If East had the King it will be a singleton in 1 in 8 hands. So:
    Probability the drop works=1/8X
    Probabilty the finesse works=(100-X)
    The drop is than in favor for X=88.9%
    If you take a probability range for X, say from 60%-100%. Averaging over the range, the drop will work 10% of the time, while the finesse works 20% of the time. This is caused by the fact that the higher X becomes, the larger the chance is that both will fail. People who are in favor of putting the King in East, are thus of the pessimistic kind.

    Now to calculate X while looking at the missing honors. If you put East on 10-14 points http://www.automaton.gr/tt/en/OddsTbl.htm tells you X=79%. This is with the assumption that there is a 50% chance that one King is spades, and 50% that it is diamonds. So X is probably a lot lower than 79%.

    So, in summary, always take a finesse. Or throw out some womanly instincts, feel which of the opponents is more tense and thus know where the King is. When playing against Jannes, I would give him a deep look in the eye and the truth will lie there.

  10. No one is arguing that you cannot calculate some odds based on card and point distributions. But you’re disregarding information, viz. the bidding. It makes some distributions more or less probable than the normal mathematical odds suggest. Something with a different probability density function, I guess; I’m out of my league there.

    (And the only bridge player I know who feels his oppenents is Dennis. And they do get tense.)

  11. I have only calculated that the bidding gives you a 90% security that West has the King. This is never that likely, see also Vindaloo’s comment. And with a probability density function… the weight of that one has to lie far above 90%, because the chances for the drop don’t increase as fast to the 100% as the chances of the finesse do to the 80%.

    Not that I would think anything like this at the bridge table…

  12. I don’t understand anything about these mathematics calculations. I only think that if east has seven , he must have the king of for his 1 opening. Which east opens 1 with a 7-x-x-x with AKQxxxx and nothing more than two Jacks??? In my opinion nobody.
    But my play will be decided by the bidding by the opponents on the boards we already played against them. I don’t understand the biddings above and probably will not have understand the biddings on the boards before. So then the finesse will be favourite. But not against normal brigeplayers.

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