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Not sure what you are talking about. If 3 is natural then 4 is a cue in support and you sign off in 6 missing a club card.
Feb. 27, 2015
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If I pass with my hand what happens? Glad you asked. Usually one of the following:

-The opponents play at 3H and we concede -140 with +140 on our way, or we lose a smaller partscore swing

-The opponents play at 3H and we miss a game

-The opponents bid to 4H, which goes down, but because we have botched the bidding over 3H we take a totally unilateral phantom save, as opposed to bidding 3S earlier and letting partner make an intelligent decision
Feb. 24, 2015
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You respond with the first sentence of your post?
Feb. 10, 2015
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Let's say we make the following assumptions: When you cash the penultimate trump, West will always pitch a randomly selected diamond, and East will pitch a randomly selected club. If East does not have a club, East will pitch a heart.

Under those assumptions, cashing the penultimate trump and seeing a club discard eliminates the possibility of a 5-0 heart split.

If you agree (and I think you will) that the relative odds of 1-4 and 2-3 heart divisions are unchanged after cashing the trump, we have no quarrel. In other words, do you agree that the only significance of a club discard is to eliminate the possibility of 0-5 hearts, but other than that it has no effect whatsoever?

If we agree on that, the only further disagreement we have is whether or not the nitpicking about the 0-5 heart division, which never mattered to begin with, makes Mr. Pavlicek's analysis incorrect.
Feb. 9, 2015
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I'd have opened 1N with this.
Feb. 9, 2015
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I think you may be missing the central point here: The club plays from East do not affect the odds of the heart split because the “Last One Out” idea does not apply to voluntary discards. It does not matter that East threw a club on the third diamond.

You are correct that on the bridge hand East cannot afford to throw a heart from a 3 card holding. However, if we imagine a world in which the goal of the defense is not to beat the contract, but to get you to incorrectly guess the probability of the heart split as of trick 10, East will always pitch a heart and you will be none the wiser. (If East were to pitch a club, you could rule out 0-5 hearts) The reason this thought experiment has any value is not because of the actual hand, because clearly if hearts are 5-0 nothing matters. The point of the thought experiment is to note that unless the opponents are cooperating, you cannot draw useful inferences about the heart split from voluntary pitches. On the Pavlicek hand nothing matters, because we realized a while ago that ace another was the right play regardless of what the exact odds of success are. However, if you try to apply your line of reasoning to the typical case where you are guessing a queen, and trying to figure the exact distribution actually matters, you will find it falls short. Look at the example I posted above.

The TL;DR is that the entire premise of your analysis is that you can apply this “Last One Out” business to voluntary pitches. That is simply incorrect.
Feb. 8, 2015
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If it is not clear why the “Last One Out” does not apply to volunteered discards, consider the following deal.

KJ32
AJ97
AK2
32

AQ654
K1086
34
AK

You bid to a contract of 7S and receive the lead of a trump. For the sake of argument let us assume you cash 2 trumps, all following, and then cash the ace, king, and ruff a diamond, followed by the AK of clubs. Again, all follow. You have reduced yourself down to

J3
AJ97
-
-

Q6
K1086
-
-

Both opponents have shown 2 spades, but we know nothing about the minor suits other than neither opponent has shown out. You would agree, I hope, that it is a total guess as to which opponent has the queen of hearts. For the sake of argument, let's assume you cash both trumps and see what materializes. At this point, the outstanding cards are 5 clubs, 2 diamonds, and 5 hearts. For starters, consider the following possible discards from the opponents:

1. Each opponent pitches 2 clubs. You are still left with a total guess. In this case, misapplying the “Last One Out” yields the same answer, as it takes the “Vacant Spaces” count from 11:11 to 7:7.

2. One opponent, say West, pitches a club and a diamond, while East pitches 2 clubs. Since there are still 2 clubs out, we do not count the clubs for the purposes of vacant spaces. However, West's diamond pitch is the second to last diamond! So if we (incorrectly) apply “Last One Out,” we can count the diamonds AND the spades (but not the clubs, there are still 2 out) for the purposes of vacant spaces. West has shown 2 spades and 4 diamonds, while East has shown 2 spades and 3 diamonds. So the (incorrect) vacant space count is 7:8, and we reach the (incorrect) conclusion that we should hook East for the queen of hearts.

This is an absurd conclusion. It means that if one opponent is 2245 and one opponent is 2344, you manage to ALWAYS go down. The person who holds the queen of hearts just pitches a diamond and a club, while the other pitches 2 clubs. You will then finesse into the person who pitched a diamond.
Feb. 8, 2015
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Your analysis of the Pavlicek deal is not correct. This “Last One Out” does NOT apply to cases where the opponents VOLUNTARILY pitch the second to last card from worthless cards. In fact, the reason this “Last One Out” business even works to begin with is that when both opponents have followed suit and there is only one card outstanding, it must be the case that one opponent has involuntarily exhausted their holding in the suit. IOW, you are no longer dealing with volunteered information.

However, if one wishes to PROPERLY analyze such problems, the correct approach is to actually work out the odds of all relevant distributions. Trying to parse all the rules for when you can and can't apply Vacant Spaces to various types of information is NOT an example of “Simple Probability,” it is an example of needlessly complicated probability.

The (correct) approach is to use combinatorics to compute the relative odds of West's 1273, 1174, and 1075 distributions. If you do this, you will find the results in Pavlicek's adjusted 5:9 table.

If you were to cash another trump, you give yourself no unique information about the hand. Assuming that the defenders do not care about the bridge hand, but merely want to lead you astray as to the relative odds of various heart holdings at trick 10, West will ALWAYS pitch a diamond and East will ALWAYS pitch a heart, and you will be none the wiser.
Feb. 8, 2015
Nate Munger edited this comment Feb. 8, 2015
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It goes all pass with partner holding x xxxx QJ10xx xxx.
E holds Jx AQJxx xxx Qxx. W holds Qxx Kxxx x KJxxx. Who is to blame?

On a side note, let's say you opened 1S. What's your bid now? Are you happy about it?
Feb. 7, 2015
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Why are people praying deeply and hoping for miracle layouts on the second board? You're off a trump but if we assume 3-2 trumps you are a favorite to establish diamonds and only lose the trump.

IMO the only question is do we ruff a diamond before drawing some trumps, which is necessary if RHO has 3 trumps and 2 spades (or 3 and can pitch on the diamonds) and diamonds don't split (otherwise after AK of trumps, top diamond diamond ruff, spade ruff, diamond ruff, RHO overruffs dummy and cashes a club) or do we cash the AK of trumps, which is necessary when LHO is 2-2 in the reds with 1 diamond honor.

My intuition is to try ruffing a diamond first.
Feb. 7, 2015
Nate Munger edited this comment Feb. 7, 2015
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Why do you want to destroy your entries to establish the diamonds? Basically any time crossruffing works you can establish the diamonds. If trumps are 3-2, you are set if diamonds are 3-3, diamonds are 4-2 with the shortness holding 3 trumps, or the diamond shortness is on your right. If diamonds split, you can even handle 4-1 trumps with a stiff honor on your right.
Feb. 7, 2015
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My partners are always VERY sympathetic and plus it makes for a good story.
Feb. 5, 2015
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David above is 100% correct about the proper way to analyze such hands. He is also correct that this is a bit of a pain to do at the table. Phillip Martin has an excellent rule of thumb https://sites.google.com/site/psmartinsite/Home/bridge-articles/the-majority-rule .
Feb. 4, 2015
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Yes, and it is not close.

You have 24-25 HCP as a side, vulnerable at IMPs, and you hold a 5 card suit and 3 tens. Of course, you don't need all of the above to bid 3NT.

Alternatively, the poll results (will) provide adequate justification for 3NT.
Feb. 3, 2015
Nate Munger edited this comment Feb. 3, 2015
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On the last one I would “discard” a trump on the spade to put a heart through.

EDIT: Sorry I'm a moron thought I was defending 3C for some reason
Jan. 30, 2015
Nate Munger edited this comment Jan. 30, 2015
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I would fake a reverse to 2 if we had not discussed this auction.
Jan. 29, 2015
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I lead first because I know it is a pet peeve for some people but it strikes me as silly that people blame this for slow play. It takes like 5 seconds to write the contract and you can think+write at the same time.

Also, I know that people can think during the auction etc but I actually prefer for people to pause briefly before leading to avoid telling the table that your lead does not require further thought.
Jan. 29, 2015
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This is very obvious.
Jan. 18, 2015
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Yes. If you cash the clubs first then East must keep hearts. If you do not cash the clubs, then East must keep spades. However, the contract can always be defeated.
Jan. 15, 2015
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Defend. There are 12 tricks and no squeeze for 13. On the diamonds, East must be sure to keep the clubs (clearly) and the SPADES to stop a double squeeze around hearts, or the contract can make.

EDIT: As pointed out below, the above assumes declarer doesn't touch clubs. If they cash 3 rounds, East should keep hearts.
Jan. 15, 2015
Nate Munger edited this comment Jan. 15, 2015
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