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All comments by Bart Bramley
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Kit is correct. In the original problem, before declarer plays a card, the chance that East has exactly one of the two missing key cards is about 2/3.

Above I had a hard time seeing the fallacy in David Burn's argument using 22 yellow cards, two red cards, and two green cards. Now I see it. We are instructed to deal West both red cards, to deal East one (random) green card, and then to deal the rest of the cards randomly. It is true that with this method, the chance that East gets the other green card is approximately 1/2. However, that's not how to count all the cases. To do so we must perform the calculation twice, once each for the possibility of East receiving one specific green card or the other. However, when we then deal out the remaining cards and count cases, we will DOUBLE COUNT the cases where East gets both green cards. Thus, there are only three “pools” of cases, one where East gets both green cards and two more for East getting exactly one of the green cards.

Kit and others were right all along. My bad.
11 hours ago
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I ignored the possibility that West has three aces for the same reason as in the original problem: No opening bid.

I maintain that the original problem and my restatement are logically comparable. Each statement of the problem assumes that there are three significant high-card holdings, of which West is known to hold at most two. On opening lead he shows you one of the holdings. In the original it is a specific holding. In my restatement it could be any of the three holdings. How does that change the subsequent calculation?

David Burn's reformulation of “restricted-choice” when East is KNOWN to have at least one of the significant cards is on point. Indeed, in his example of a nine-card fit missing king-queen, declarer makes a clear error by not playing the ace on the first round when he knows that at least one royal is offside.
April 19
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Reluctantly I find myself agreeing with David. Reluctantly, not because I have any problem with David personally, but because his solution is highly non-intuitive for me.

Here's how I convinced myself. Let's restate the problem in simpler terms. Suppose we are missing three aces. Further suppose that we know that West always leads an ace when he has one, choosing randomly when he has more than one. On the dealing there is an equal probability of West having either one ace or two aces. We will see the lead of any specific ace exactly one-third of the time. Therefore, when West leads an ace there is a 50% chance that he has no other ace, which means there is a 50% chance East has BOTH other aces.

In turn, this implies that in the original problem the chance that East holds both the K and A is approximately 50%, rather than the approximately one-third chance produced by the standard restricted-choice argument.
April 19
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Billy was a teammate when I won my first national (Men's BAM, Spring 1980), which happened to be Billy's last national win. Several years later I moved to Chicago to trade options, which allowed me to see Billy regularly on the options floor as well as at the bridge table, plus occasionally on the golf course. He was a delight in any venue, a class act all the way.
April 8
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I echo Barry's sentiments in all respects, especially the nice guy part. I first met Anders many years ago when he played in the Cavendish Pairs in New York several times (and won it once). More recently I corresponded with him on matters of esoteric analysis.

I will miss his warmth and his keen intellect.
March 22
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I have arrived. In addition to Chuck Berry's Memphis (I love the line “with hurry-home drops on her cheek that trickled from her eye”) and Dylan's Stuck Inside of Mobile (“it all seems so well timed”) I heard Big River (Grateful Dead version) and Dylan's Highway 61 Revisited. Many more songs available.
March 19
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Thanks to everyone!
And congrats to Peter and Judi! We all waited a long time for this.
March 14
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We need a vowel so we can pronounce it. And we would much rather SCUM them than SCAM them.
March 6
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My favorite method, SCuM (Shape, Color, Majors), is great for this hand. I double to show either spades and diamonds, or hearts and clubs. At my next turn I will jump to five hearts, implying a slam drive with hearts and clubs, and better and/or longer hearts (with my suits reversed I'd jump to six clubs).

If partner has a dreadful misfit (2-1 in my suits, say) she might bail and pass, but with any semblance of a fit she should prefer at the slam level. If she has the club king (you never know) she can think about seven.
March 6
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This is very sad news. Russ and I went back to the '70s when we both lived in New England. My first friend in the family was his older brother Steve (who passed away in 1985). Russ and I were variously partners, teammates and opponents on many occasions, and always friends. He was warm and amiable with a lively sense of humor and a ready smile. He was one of those people that had what I call “the twinkle”, that special look in his eye.


Judy and I will miss you, friend.
Dec. 13, 2018
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The second deal is the last board of the 2003 Bermuda Bowl. Declarer Lauria was manually playing dummy's cards because Versace had left the room to find out the status of the match. The safety play is the SPADE QUEEN, which would have guarded against declarer not noticing that LHO (Soloway) had actually played a SPADE instead of the expected heart ten.

Unluckily for Lauria, when he manually “discarded” a lower spade his RHO (Hamman) followed suit with the spade ten. Now declarer had to go down two, which meant losing the match by 1 imp instead of going to overtime with the safety play of the spade queen.

Working back to the first deal, I see that declarer on that deal must have led a black card instead of the third diamond. If I “discarded” either low spade on an actual spade lead, it's all over. The same is true if I discarded my club on a spade lead, since I will then have to lead the club after I win the spade ace. And if I discarded a spade on a club lead, declarer will win the king and cash a spade while I must now follow with my penalty card. The safety play is to discard a HEART. Regardless of the black suit led, if I correct my revoke in time we will still beat the contract whenever it can be beaten.

(clarified last sentence)
Oct. 25, 2018
Bart Bramley edited this comment Oct. 25, 2018
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Damo:

If you're going to cite my article to support your theory, do all of us the favor of showing the deal and the specific actions you find “strange”.

Yes, I said that “off-center actions abounded” on the deal. The most glaring was a favorable third-seat weak 2 by Bobby Levin on AJ764 1087652 65. I said that Levin's call “was exotic, though his other options, including pass, would have been even more so.”

There is a world of difference between “off-center” and “incomprehensible”, which is the descriptor I would use for many of the Blue Team actions in Wilsmore's book.
Oct. 7, 2018
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West may have missed the killing defense, but he does have a perfect 13-card straight.
Sept. 9, 2018
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I'm relieved that our calculations of the relative merits of the two lines are now consistent, albeit not identical. I see that I erred by assuming that QJ would allow the suit to be set up with one ruff, which will affect my count of both lines. And my raw numbers of winning cases are lower than yours because I used factors of 2, 1, 0.5 and 0.5 for the trump holdings.

I may not have the energy to grind it through again. I'll settle for having determined that Meckstroth's (and my) instinct was correct: The 3-way combo is significantly better than the line that simply enhances one of the three ways.
June 1, 2018
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Kurt: My math is different.

I excluded deals with voids but included all other deals. I made the same assumptions about possible holdings from which the lead could be made (half of the time from J10 or J108, never from J103, even though I consider that last assumption doubtful).

Line 1: All in on diamonds. I assumed that declarer would win the A and lead a second trump, finessing the nine if possible. Then he would play AK and a third diamond, taking the ruffing finesse if plausible (2-2 trumps and RHO playing Q9 or J9), else ruffing high.

Line 2: Combo line. Win the K and play AK. If both honors fall, ruff a diamond high and hope for 2-2 trumps. If one honor falls, ruff a diamond low; then, if the other honor has fallen, hope for 2-2 trumps. If declarer survives the diamond ruff but the diamonds are not good, then cash AK, club ruff, heart ruff, club ruff; then, (a) if the A has fallen, take the most logical red-suit ruff to dummy, draw trumps and claim, or (b) if the A has not fallen but the Q has, try to cash the J and ruff a diamond to dummy.

I assumed that the defender sitting over dummy (over the diamond void) would always drop a diamond honor from any holding with both diamond honors, but that the defenders would not otherwise false-card in diamonds, as that would entail risk from many holdings (declarer's diamonds are hidden). I also assumed that the defenders would always make the most effective discard.

I found 221,725 winning layouts for Line 1, and 298,639 winning layouts for Line 2. A severe drawback for Line 1 is immediate failure when the lead is from J10 or J108. Note that the combo line does not discount the chance of setting up diamonds; that is one of THREE possibilities for success.

Moreover, even on the trump layouts that are favorable for Line 1 (10, 103 and 108), the two lines have almost identical chances of success, differing by only a few hundred cases in favor of Line 1.
June 1, 2018
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I should have included the possibility of trying for queen-third of hearts. However, playing for it compromises some of the other chances, because it requires cashing AK before ruffing the first club. If either the Q or A is doubleton, then declarer must ruff an extra red card at the end, which would not be necessary otherwise.

Nevertheless, I now think that the best overall line is: K, AK, then, if no quack, AK, club ruff, heart ruff (if queen still out, else cash the jack first), club ruff. Now, if the Q fell tripleton, try to cash the jack and ruff a diamond to dummy. If the club ace fell, ruff a diamond.

If a diamond quack falls, especially from North, it's more complicated. Testing diamonds will lose a makable contract when North has J108-xxxx-Qx-xxxx and pitches a heart on the third diamond, but if he is 3=5=2=3 you survive.

I still that Meck's combo approach, leaving two low trumps in hand, is superior to going all out for diamonds.
May 22, 2018
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I realize now that this squeeze is a variant of a guard squeeze. Imagine West with Jxx of clubs; it still works, because East can never throw a club.

In many guard squeezes declarer cannot afford to cash a side winner early, lest he squeeze the opposite hand early, but in this layout declarer could have cashed the second high diamond immediately without disturbing the ending.

The key is that declarer must be certain of the count. If so, he can always make without guessing the club queen.
May 21, 2018
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Wooldridge did make four hearts, playing as described. I was an opponent.

Inexperienced Vugraph operators made many errors throughout the early KO rounds.
May 17, 2018
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Devastating.

A great player and a greater man. A true friend. The definition of strength in the face of adversity.

Judy and I miss you dearly. Our thoughts are with Peggy.
May 14, 2018
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I agree with John. My defense seems to matter only when declarer is 6520. Partner is unlikely to have six hearts unless his trumps are strong enough to beat them, as long as I cash my two tricks. Thus, declarer has 4+ hearts and I must stop ruffs in dummy. Declarer can draw trumps and cash winners, or he can ruff a heart or two in dummy, but not both. Partner will burn up a diamond winner when declarer tries to get off dummy. I need partner to have the heart king plus either the spade ace or KQ9.
April 9, 2018
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