Last month I wrote about a hand from the final session of the 2005 LM Pairs at the fall Nationals in Denver, where Ed Schulte and I had a 69% game and came in third overall in the event.  This month's hand is from the first final session, where we had an average session.  I picked up the following hand:

Vulnerable vs. Non-vulnerable, there were 3 passes to me.  I had my first decision now.  I could open 1NT (good 14 to an average 17) or I could open 1Spade.  You play a style where you frequently open 1NT with 5-card majors.  What would you do?

The hand is a bit too strong to open 1NT, as it has choice values with a 5-card suit.   In IMPs I would want to show my full strength and therefore be less likely to miss a game and I would open 1Spade.  But we were playing matchpoints, and I wanted to declare the hand from my side of the table.  If I open 1Spade, partner could easily bid 1NT and now the weaker hand will likely be the declarer and I will have the opening lead coming through my wonderful tenace holdings, instead of up-to-them.  I decided to risk potentially missing a game by slightly underbidding, and I opened 1NT.  I felt that being declarer was more likely to gain matchpoints than the likelihood of missing a game.  My choice of opening bids was a calculated risk.

Partner bid 2§, I bid 2ª, and he bid 2NT inviting game in notrump.  He may or may not have 4 hearts in this auction.  If I were minimum, I would pass his 2NT bid.  Anything that I bid accepts the game try, so I bid 3ª to show a maximum and 5 cards in spades.  And now I was shocked when partner passed.

This was the hand:

What do you think of partner's bidding?

With a total of 22-25HCP, partner clearly could have chosen to pass 1NT.  While game is possible, 2NT could also be in jeopardy.  In matchpoints I could have easily passed with his hand, and missed the good game.  In IMPs, I would have made the same bid that he did.  He did have prime honor cards in the major suits, a 5-card suit that could produce a lot of tricks, and the ten of clubs.  With 8 prime points and 2 possible entries to running a 5-card suit, I would clearly invite game in IMPs. 

After I showed a 5-card spade suit and game-acceptance values, he now devalued his 5-card diamond suit.  The 5th spade made it more likely that I would not be able to use his diamond suit for tricks -- either we would be subject to fast losers in hearts or clubs, or I would not have enough diamonds to be able to use his diamond suit.

My partner would never open 1NT with 17HCP and a 5-card major.  Instead he would open 1Spade and rebid 2NT over 1NT (showing 17+ to 19 HCP).  So, he believed that I held a maximum of 16HCP.  And he made a very close judgement call and passed me at 3Spades.

I would have chosen to bid 4Spades with his hand.  In support of spades I value his hand as worth 9 points ( 8 nice HCP and 1 point for ruffing value).  Opposite a partner describing a hand worth around 16 or 17 points, I would go to game.  But, it is a very close judgement call.  One can easily disagree with many of our bids in the auction, but one cannot say that any of them are clear-cut errors.

This shows a type of problem that occurs in a new partnership.  Ed and I had only played in one event previously, and we were far from ever discussing this type of situation in matchpoints.  Who knows if we would ever discuss this situation in bidding philosophy if we hadn't had this hand?

Anyway, I was playing in 3Spades and my LHO (Ira Hessel) led the §7 (3rd and 5th best).  I played low from dummy, and my RHO (Bob Hamman) thought for at least a minute, and played the §Q.  I won the §K.  Now what?

I want you to take some time to think about your line of play.  I wonder if you will guess what I played.

From Bob's hesitation, and the fact that his partner would not underlead an ace in this auction, I knew that he held the ace-queen of clubs.  This is not an unusual play for a high quality player.

Let's discuss Bob's play of the queen at trick one.  Playing 3rd best from even, and low from odd, from the lead of the §7 he knew his partner began with either a 3-,4-, or 6-card suit.  The lead of the 7 could not have been low from a 5-card suit.  And he knew that I did not open 1NT with a void in clubs, therefore his partner began with either 3 or 4 clubs.  Therefore, I had to have 2 or 3 clubs, perhaps with the king.  He knew that he would not lose any club tricks by playing the queen at trick one.  And, if the queen won at trick one, he would know that his partner held the king.  Then, he could attack in hearts, to set up heart tricks for the defense, by leading through my heart strength, while he still held a likely spade stopper controlling the hand, and keeping the club ace as an easy entry to his hand, so he could keep on attacking in hearts.  It was not an obvious defense, but one very expected from a former world #1 ranked player.  It seemed like a percentage action to him.

While Bob took time analyzing his defense, I spent time analyzing his hand.  If I was in his position in third position at favorable vulnerability with the diamond king and the §AQxx(x), that I would open the bidding with 1§.  Even with only 9HCP, I would want to get a lead-directing bid in, and at the same time, throw the opponents into a defensive auction (overcalling and takeout doubles) instead of a free unopposed auction.  I don't know if Bob Hamman would open that hand, but it certainly seemed likely to me.  Furthermore, even if he would not open that hand with 9HCP, he probably would open if he held 10+HCP, and therefore if he held the diamond king, he would not hold the spade queen, the heart queen, or the heart jack.  Restricted choice makes any of those holdings very unlikely.  Therefore, I concluded that around 95% of the time the diamond king was offside.

Now, if the diamond king is offside, how do I want to play the hand?

Maybe now you can envision the card that I played at trick 2.  I led the diamond queen!  I was hoping that my LHO would assume that I did not have the ace -- that certainly seemed likely to him.  What competent declarer would lead the diamond queen from the ace-queen?  That is certainly a strange decision, especially so early in the play of the cards.  A normal declarer would take a normal finesse in diamonds with that holding.  And, if this was the hand, then my LHO made the correct play:

In this fictitious situation, if West wins the diamond king at trick two, he lets me set up dummy's diamonds with two more diamond ruffs, and I will eventually get to discard a heart loser on the diamonds while East ruffs with a natural trump trick.  West must duck the diamond king to prevent this situation.

But I had fooled West.  This was the actual hand:

After I led the diamond queen and West ducked, I proceeded to make 11 tricks on the hand.  I cashed the diamond ace, played a spade to the king, ruffed a diamond, and led a heart to the ace, and trumped another diamond.  I now led a club, and eventually trumped a club in dummy.  With 2 diamond ruffs, I scored 6 trump tricks (5 in my hand and a club ruff in dummy), 2 hearts, 2 diamonds, and 1 club. 

I also want to discuss table presence at the table.  I did not think more than around 20 seconds before leading the diamond queen.  I had already done my thinking when Bob was making his calculations.  I think that if I had thought for 2 minutes before leading the diamond queen, that my LHO might have suspected my trap.  I certainly did not take a lot of time before making what seems like a very unusual play, and that should help the likelihood of success.  I don't think my LHO opponent knew me, so he had no good reason to expect me to make a strange-looking play, especially in a normal tempo of play.  Furthermore, my LHO did not know at this point that his partner held the club ace, which made it more likely to him that his partner held the diamond ace.  Making a play like this at trick 2 puts a lot of pressure on the opponents.

We had a bad score, because we had missed the game.  But we did save 40% of the matchpoints by scoring +200 on the hand (30 1/2 matchpoints out of 77 possible).  This was an undesired situation -- finding a way to steal an extra trick to still get a below-average score.  Fortunately, a 40% score did minimize the damage that we suffered on this board.

That score was part of an average session in the first final session of the finals of the LM pairs. Sometimes you have to fight hard to just score average, and sometimes you have lots of luck and score well.  But it is a good example of how you have to fight for every trick you can get.  It turns out if we had bid the game, we would have come in second overall.

One reason that I chose this hand for my January hand of the month, is because I wanted to consider if I still agreed with my strange looking play.  I did not want to take a lot of extra time to think about it at the table.  With this forum I can take lots of time to consider if I made a good play or not.  And, in my analysis, my lead of the diamond queen is much more likely to be successful than taking a diamond finesse.  I cannot calculate precise odds of this situation, but I would guess that my LHO would not win the diamond king about 30-50% of the time, which is much more likely than my estimated 5% chance that the diamond king was onside.  So, I like my play.

ADDENDUM

Now, I will examine my estimation of the diamond king being offsides about 95% of the time, and my estimation that my LHO will duck the king some 30-50% of the time.  I welcome any mathematician to come forward with any corrections to these calculations.

I will assume correctly that Bob held the Ace-Queen of clubs, without the Jack of clubs. 

I will make two similar calculations using high card points (HCP) as a guideline for what hands Bob would open in third seat.  FIRST I will estimate that he will always open any hand that has 11 HCP in third seat at favorable vulnerability, that he will open hands with 10HCP about 70% of the time, and that he will open hands with 9HCP about 40% of the time.  THEN I will estimate that he will always open any hand that has 11 HCP, open hands with 10HCP 75% of the time, and hands with 9HCP 50% of the time. 

While I don't know if these are accurate estimations for this player, it is about as good an estimation as I can make.  In the modern expert game, experts open the bidding with far less than was done traditionally.  I will show the two different sets of calculations to estimate the fragility of making such estimates.

Given that he has 6HCP in clubs, it is possible for him to have diamond king and only 9HCP when he does not have the spade queen, heart queen, or heart jack.  When the cards are dealt, if it is given that he has the club ace-queen and diamond king, then the odds are 13-to-10 that his partner will be dealt the spade queen.  And if that happens, then the odds are 12-to-10 that his partner will also be dealt the heart queen.  And if that happens, then the odds are 11-to-10 that his partner will also be dealt the heart jack.  What this roughly means is the odds of him being dealt the diamond king and not any of those other 3 honors is about 9.4% of the time (10/23 times 10/22 times 10/21).

For him to have 10HCP, he could not have the spade queen, nor the heart queen, but would have the heart jack.  When the cards are dealt, if it is given that he has the club ace-queen and diamond king, then the odds are 13-to-10 that his partner will be dealt the spade queen.  And if that happens, then the odds are 12-to-10 that his partner will also be dealt the heart queen.  And if that happens, then the odds are 12-to-9 that he will also be dealt the heart jack.  What this means is roughly 8.1% of the time those other 3 honors are divided that way when he holds the diamond king and club ace-queen (10/23 times 10/22 time 9/22).

So, in the first estimation, if he holds the diamond king, he would not have opened the bidding: 9.4% of the (60%) times he held 9HCP, an additional 8.1% of 30 percent of the time he holds 10HCP, and an additional 8.1% of 30% of the time he holds 11HCP.  5.64% plus 2.43% = 8.07% of the time he would not have opened the bidding.

In the second estimation, he would not have opened the bidding 9.4% of the 50% of the time he held 9HCP, plus and additional 8.1% of 25% of the time that he held 10HCP.  4.7% plus 2.02% = 6.72% of the time.

So, in the first estimation he will hold the diamond king 8.07% of the time, and in the second estimation he will hold the diamond king 6.72% of the time.  My general estimations at the table of 5% that he would have the diamond king were fairly close.

Therefore, if he would follow those estimated guidelines, then he would open the bidding about 7% of the time that he holds the diamond king -- therefore if his partner will duck the diamond king more than 7% of the time when I lead the diamond queen at trick 2, then I made the right play.  And since I estimated roughly that he would duck the diamond queen when he held the king around 30-50% of the time, then my decision to play the hand the way that I did was a clear-cut decision.

It is hard to know accurately how often my LHO would duck the diamond queen when he held the king.  My bridge sense told me that he would usually beat the queen with the king, especially if he began with only 3 diamonds.  But, if he held 4 diamonds or more, then he might duck the king at least half the time, depending upon the quality of the player.  A novice would just take the winner, while an expert would frequently duck.  If he would always win the diamond king when he was dealt 3 diamonds or less, and if he would win the diamond king 30% of the time when he holds 4 or more diamonds, then he would be ducking the diamond king 35% of the time. (This rough estimation is assuming he and his partner were both dealt 4 clubs.  If he only held 3 clubs, then it is slightly more likely that he would duck the diamond king.)

At the table, once I estimated that Bob held the diamond king only about 5% of the time, then I was confident that I was making the right play.  I am happy to see my follow-up calculations back up my decision.