Beer Card Rules

Somehow I've become slightly obsessed with the beer card lately. Oh yes, it must have been the extremely unlikely event of last Wednesday's beering 3 hands in a row. Anyway, tonight, I had an interesting potential beer hand. First, let's go over the rules, as I understand them:

If the following conditions are met, your partner owes you a beer:
1) You win trick 13 with the 7 of diamonds.
2) If you are declarer, you make your contract and overtricks are acceptable. If you are a defender, you defeat the contract.
3) Diamonds cannot be trumps.
4) You must take the best line of play or defense.
5) Defensive beers and beers in doubled contracts are worth 2 beers.

The beer card rules according to Paul, author of The Beer Card blog.



In the above hand, the lead was a standard 4th best 2 of clubs to the Q and my ace. Then diamond K, diamond J to north's ace, K of clubs, and another club. At this point I have 10 top tricks and would have to lose a heart trick at the end (thereby not being able to win a beer) if i simply take my 10 tricks. But this hand also presents a chance for a beer if I take a heart finesse. Taking a heart finesse will result in either making 9 tricks if it is offside or 11 tricks if it is onside. We "know" clubs are 4-4 and diamonds 2-2 so the heart finesse is still exactly 50% and therefore an equally good line of play as cashing out for 10 tricks. That is, of course, unless clubs are not 4-4. If lho has 5 clubs, taking a heart finesse is clearly superior and if lho led from a 3 card suit, cashing out is clearly superior, but I think the chances of this are extremely slim. A more common defense (north leading anything but a club when in with the diamond ace) holds it to 9 tricks (9 top tricks but declarer in matchpoints may opt for the heart finesse that could lead to down 1 or making 5), so by a matchpoint consideration, making 4 is already going to be slightly above average.

Needless to say, I discarded a high diamond from dummy on the 3rd round of clubs and took a heart finesse, soon claiming 9 tricks and a beer. Beer card issues aside, this is an interesting matchpoint strategy problem. Should you be satisfied with making 4 or go for the extra overtrick?

What is your understanding of the beer card rules? Does this hand qualify? Would it qualify only if the heart finesse wins?

U21 USBC

This past weekend I spent a lot of time watching on BBO Vugraph the Under 21 US Bridge Championships rather than the finals of the Open USBC. While the bridge for the most part was noticeably amateurish, I enjoyed it because I know almost everyone in it and want to see them play and mature and want to think that I had something to do with them getting to the 2030 USBC finals but then losing to me. ;)

The favorites - Adam Kaplan, Adam Grossack, John Marriott, Alex Hudson, Jourdain Patchett, and Jesse Stern - had no trouble winning. They are all rather established partnerships and quite experienced players and should do well in the world competition. The second place team, probably most people’s pick to be second, consisted of Zandy Rizzo, Murphy Green, Richard Jeng, and Andrew Jeng. Both teams will represent the USA in the U21 world championships in Philadelphia in October. The Rizzo team fell behind 40-0 in the USA2 final against Ricoh Das, William Dang, Mili Raina, and Angie Green but would up winning 169-90. All of the kids clearly have bright minds and a flare for the game and have potential to be very good. It is experience that was the main distinction between the top three teams. Each pair made their share of good plays but the top pairs were able to avoid bidding misunderstandings and didn’t suffer much from two very common problems of young players today.

The first common mistake is playing too fast. By junior standards, I am a slow player. By average bridge player standards, I play at lightning speed 95% of the time and then at a snail’s pace on an occasional difficult hand. There are some hands that do not require much thought but until you are sure of that, it is best to take some time and play deliberately. Even with the screens, the teams were sometimes finishing 16 board segments in an hour and a half, only about 5.5 minutes per board, while the open teams were only on board 11 or so. Time and time again, we noticed declarers playing too quickly, especially early in the hand, or defenders not pausing for a few seconds to think more about what’s going on. Then just a few seconds later they realize their mistake. Bridge players have big egos, and perhaps playing fast is just another (slightly delusional) way to show off one’s superiority to others but that’s another article. These mistakes happen at all levels – Friday, I saw Bob Hamman forget to pitch a quick loser away on an AK in dummy before leading trumps (missing the A of trumps).

The second major problem players in this phase of learning where people know enough to think about many possibilities but not enough to realize that most of the possibilities are so unlikely to actually happen is that they just bid too much, particularly without having a fit. By the same token, the same players that bid too much without a fit don’t bid enough with a fit. Having a fit with partner in a way, gives you a license to be more aggressive as there is some safety in going to higher levels – it means the opponents probably have a fit and can make more, and taking tricks, whether in NT or a suit, is just easier when you don’t have singletons opposite KJTxx. This is something that one must learn from experience. There are few life lessons that we can just accept from other people telling us – we have to go make the mistakes ourselves to learn. Learning when to quit bidding can be a hard lesson to learn. After going down in 3NT on misfitting hands several times, one slowly learns. Bidding NT is rarely a good way to “rescue” partner from a misfit. Pass and get out while it's still relatively inexpensive is usually best. Occasionally, you’ll get a favorable lie of the cards or have an unexpected club fit and it will work well, but more often than not, passing partner in 2S in a 6-0 fit is the best thing you can do. This is why I don’t like the idea of playing new suit non-forcing opposite partner’s weak two. There’s no reason to think partner will have better support for you than you have for him and you may only be getting yourself a level higher. Hands usually play better in the long suit of the weaker hand anyway. Plus, passing partner without a fit and making him suffer a hopeless contract has a side benefit of making him think twice, then three times, then not at all, about preempting on a T high suit or open 3C on a 5 bagger. There is a reason so few world class bridge players are young and it’s not because young people aren’t as smart or talented – we can’t learn from other people’s mistakes nearly as well as we learn from our own and it takes time to make mistakes (or, if you prefer, gain experience) and improve our neural network of card sense and bidding sanity.

I remember Richard Jeng finding a nice endplay in the last match to score an overtrick in 3S, I believe. Kaplan made a few impressive declarer plays – the play in a 4HX contract Saturday was pretty interesting. There were others, too, but those are two that stuck out in my mind the most. I could go back and write about specific hands but unless someone wants to pay me, I’m not quite that motivated to write about hands that don’t directly involve me, so I’ll leave that to the Bridge Bulletin and Bridge World writers for now. :)

Beer Opportunities Galore

So, I beered two more times tonight. This first one wasn't terribly easy and took some cooperation from puffy. They conceded before the hand was up but I had it all set up to win the next lead in my hand, ruff the diamond 10, cash dummy's two top spades and come to hand with whichever entry was left. But this would not have been possible if serapuff hadn't so graciously covered my J with the A at trick 6. And at the end, ruffing out the Q from Raphael's hand seemed very likely given the 9 falling from him earlier. And even if I wanted to take a ruffing finesse, it would risk the contract. The bidding and early plays kind of mark Raph with the Q, too, because with the Q in addition to the 14 point already shown, puffy probably would have opened 1NT. So, that's number 7 in about 120 hands this week. In a hand a couple of boards this one, I had an easy beer chance in 5H, but they sacrificed at 5S. A couple of hands later I thought I might get another beer in 4H when we had KT87 opposite Q9x, but the defense went SK, DA, D ruff, CA, D ruff :(



Then, playing money bridge with a robot, I was in 4S here. I'm not sure my line was absolutely the best (I think it was) but it certainly worked this time. This is an interesting declarer play problem. I decided the best line was to take the ace at trick one, cash the ace of spades and the AKQ of clubs, pitching my heart. If someone ruffs with a spade honor, I'm probably in good shape to make. And if clubs are 3-2, I'm probably in good shape. Maybe the best line is to pay ace and another spade immediately, trying to hold it to 3 losers - 1 each in spades, hearts, and diamonds. And when the spade K falls stiff, does that change things? I think it makes it more likely for the person with 4 trumps to have a stiff or void in clubs and therefore might be more in favor of trying to draw trumps. But that only works if lho led a stiff diamond and rho has no entry, highly unlikely, if you assume lho would find the play underlead the heart ace. And I'll need to lead diamonds off dummy at some point to finesse for the 9 if they split 4-1. Eh. too many things to think about, so I went with the gut of drawing 1 trump, cashing Q-K-A of clubs. They ruff, cash DK, D ruff, ruff the H, pull last trump, end of story and taking the last trick with the D7 is easy.

Canape System Win

This hand, from the Under 21 US junior trials today, shows a system win for canape. Granted, this hand is a bit lighter than I would open but the point is still there. After a 1H opening by north (John Marriott, in this case), east cannot bid NT like he would over a normal 1D opening so the choices are X and 2C, and I think he chose correctly. Then west, with 9 points and 4 card support, could make a limit raise, but given the wide range of the 2C bid and the insinuating double from south, I do not disagree with the simple raise.  Anyway, 3NT was reached fairly easily at the other table after a 14-16 1NT opening, and I think it would be equally reachable after 1D opening and 1NT overcall.

Balancing Doubles in Canape

Another thing I’ve been thinking about is what does a balancing double in a canapé system show. Like 1D-(2C)-P-P-X? In standard, you would tend to have almost any non-freak hand without length in clubs. Maybe 3-4-4-2 or 4-4-4-1 or 4-3-5-1 shape, possibly even 3-3-5-2, and it could be an absolute minimum. In canapé, when 1D guarantees having not exactly 4 in either major, but guarantees an unbalanced hand, double as takeout doesn’t make a whole lot of sense. None of the 4 hand shapes I mentioned above are possible after a canapé opening. I mean, 4-3-5-1 is a possible shape but with 4 in the suit already bid, so 5-3-4-1 in this auction would be a possible holding. Do we really want to suggest that partner bid either major when we are 5-3?

 

But using insinuating doubles (basically negative doubles that only guarantee 3 in unbid majors) and negative free bids (1D-(2C)-2M = constructive w 5+), the need for opener to show any sort of major suit length when it is passes back to him isn’t so important. Perhaps it should be a penalty double but that doesn’t make sense because on the hands where you will want to defend 2CX, partner will have made an insinuating double. Maybe it should imply canapé with 5 in the suit below the overcaller’s suit plus tolerance (2 or 3) in the other suit. So, after 1D-(2C)-P-P, X can be 5-2-4-2 or 5-3-4-1 or 5-2-5-1. And After 1S-(2D)-P-P, X = 5 clubs (4-3-1-5 or 4-2-2-5). I think I’m gonna go with the latter for now. I think.

System Win

Whenever you’re playing a non-standard system, you’re bound to have situations where your system either leads you to a good or bad result, simply as a result of the system you play. The most common one that people are familiar with is the system wins and losses of playing a weak NT. You may win some boards when you open a weak NT simply because it’s more difficult for the opponents to compete and find their fit. By the same token, you have some system losses when your side misses our on a 4-4 major suit fit that the field may get to via 1m-1M-2M while your auction is 1NT-all pass.

 

I recall very few instances when canapé has produced a system loss. There was that one time Sean opened 2C on 4 small clubs with 6 hearts to the AKQ and got to play 2C while anyone else has no problem getting to hearts. While it is a fun opening bid (11-16 hcp with 6+ clubs OR 4 clubs and a 5 card major), disasters like this can occur because responder needs more values to bid over it than over a 1minor opening. Anyway, 6-4’s with a clubs probably should be treated as one suiters unless the 6 card suit is really weak.

 

Last weekend Sean and I played a good bit, really getting the grasp of the Polish club canapé concoction I started last Wednesday. And despite 8 clear-cut errors (almost all defensive) over 2 sessions at the club, we had a combined 64.5% score. A lot of that can be attributed to the several system wins we had.  Right-siding the NT, although that is pretty much just luck, opening canapé which prohibits LHO from making a takeout double, having the opponents make offshape takeout doubles of our canapé openings that land them in opener’s best suit (this happens more than you’d expect), having sound 2M openings that put us in a better place when deciding how to act over interference and being able to make better game decisions, are among the system wins. But we do play a 15-17 NT and the 1C opening usually is a weak NT so those auctions tend to be very normal.

 

I was playing another canapé system with Shaz on Sunday, which I actually liked as well. 1M openings are exactly 4 cards unbalanced, 1D is canapé or balanced min or balanced max, 2M is 5+ and 2m is 6+, 15-17 NT, strong club, I think.

 

One hand I particularly liked from Saturday with Sean this heart slam:

 

x

Txxxxx

AKxx

KT

 

AKTxx

AKJx

x

Qxx

 

Our auction: 1C-2D-(3C)-3S-4H-5H-6H

Not a terribly scientific auction but it got the job done.

1C was 12-14 bal, or 17+ unbal, or 18+ bal

2D was 8+ w/ long diamonds or 4D and a 5+ card major, the least efficient bid in our system

3S natural, confirming a 17+ hand

4H longer hearts than diamonds, probably 6 in this case

5H do you have a club control

6H yes

 

In 2/1, you’d have a hard time getting to slam, I expect. The auction would surely start: 1S-1NT-(3C)-3H. North won’t feel comfortable bidding anything but 4H because now the lead is going right through his club king.

Triple Squeeze

Last night I was playing on line and my opponent claimed 3NT making to speed up the game, but dummy commented on his failure to try for any overtricks and I soon realized that he would surely make more than 3 - if he just cashes his winners in a reasonable way, I could be squeezed. Claim was rejected and he went ahead and executed the triple squeeze, now double-dummy.

Dealer: West Vul: none		Gideon
		♠	A863
		♥	AQ632
		♦	T6
		♣	93
Andre				Shaz
♠	97			♠	542
♥	JT87			♥	954
♦	K32			♦	Q954
♣	AK62			♣	J85
		Howard
		♠	KQJT
		♥	K
		♦	AJ87
		♣	QT74

West	North	East	South
1♦	2♥	Pass	2NT
Pass	3NT	Pass	Pass
Pass

1♦ was either a 10-15 canape opening or a balanced 11-14 or 18-19. My opening lead was the ♠9. Declarer has 8 top tricks and after winning the opening lead in hand, played a diamond to the T and Q. A diamond back would have prevented any overtricks. If he finesses either the 8 or the J, I win and can cash out, but even if I don't cash out, I can't be squeezed because I no longer have to guard diamonds. And if he goes up with the ace, I also can't be squeezed because when the squeeze card is played (the 4th spade), he won't have an entry to both the heart threat and the diamond threat cards.

In reality, Shaz played the ♣J, which I agree with, covered and won by me. And I returned a low club, sadly not finding partner with the 10. So the ♣9 was Howard's 9th trick, but now with this ending and me being marked with all the remaining high cards from the bidding, it's a fairly easy squeeze to execute to make 4. Declarer cashes the ♥K and the rest of the spades, ending in dummy. Before the play of the last spade, here's the situation.

Dealer: Vul:		Gideon
		♠	A
		♥	AQ63
		♦	6
		♣
Andre				Shaz
♠				♠
♥	JT8			♥	95
♦	K2			♦	954
♣	A			♣	8
		Howard
		♠	T
		♥
		♦	AJ8
		♣	T7

I clearly cannot discard a heart for that gives dummy 2 extra heart tricks. I can't discard a club because that would make declarer's 10 and 7 good and he surely has the ♦A to get back to his hand. So I part with the deuce of diamonds and hope that partner happens to have the suit stopped. On the AQ of hearts, declarer discards 2 clubs, and then the ace of diamonds. Partner holds on to the 954 of diamonds and takes the last trick, our 3rd defensive trick. I suppose this is what you call a triple squeeze.

Psyching with a GIB: Bad Idea

This psyche by my opponent led to an incredibly bad result. He was in 3rd seat for the 1S opening. This led to the robot bidding 4S, doubled and down 8. He managed to take 2 tricks - the diamond ace and spade queen. +2300 to me.

Opening Bid Frequencies

Do you know the probability that you'll a strong NT hand? And how much more likely is it that you'll be dealt a balanced 12-14 instead of a balanced 15-17? Everyone likes opening 1NT because auctions after that are usually pretty easy and it makes it hard to interfere.

Now that my computer program can now reliably open the bidding and reliably make responder's first call in standard, canape precision, and canape polish club, I ran some simulations to see how frequently each opening call is used. Well, it can respond when the opening bid is 1C or 1NT. Looking at only the north hand in 200,000 deals, a 1NT opener was dealt 4.05% of the time while a 12-14 NT was dealt 9.07% of the time. In standard bidding, 42.89% of the hands resulted in some opening bid, 7.61% of which were preempts or weak 2 bids. In canape precision and canape polish club, only 39.73% and 39.44% of the hands were opened. This is almost entirely attributable to the more constructive weak 2 bids that I have adopted for use with canape - something on the order of 8-11 hcp with 2 of the top 4 honors instead of the 5-10 range that I used for a standard weak 2. Thus, in the canape systems, 4.12% of the hands were opened with some sort of a preempt.

In standard (opening 1C with 3-3, 1D with 4-4 or 5-5, and the longer suit otherwise), 1D was the most frequent opening bid at 8.72% with 1C not far behind at 8.20%. In both canape systems, 1C was overwhemingly the most frequent opening bid. I am somewhat surprised by this. In the Canape Polish club system, 1C is opened with all balanced 12-14s, balanced 18+, and all hands over 17 hcp (not using the variation that it could be 15-17 with 5+ clubs) so it makes sense that 1C would be opened 15.13% of the time. And of the hands opened 1C, 59.93% of them are of the balanced 12-14 variety. This would suggest that if you're defending against the Polish club, it's probably best to treat it as natural (2+) since if you have a good hand as LHO, it only increases the probability that the 1C opener has the balanced minimum.. Behind this, 1D, 1H, and 1S (which all have exactly the same requirements with the suits switched) and 1NT (15-17) are all opened between 3.80% and 4.18% of the deals. 2C isn't far behind at 3.54%. The requirements for opening 2C are basically the same as for 1D/H/S but sometimes we may suppress the 4 card club suit and treat the hand as a major one-suiter. In canape precision, where 1C is opened on all 16 hcp hands, that bid is made 11.48% of the time. This still seems a bit high to me but I can't find a flaw in the programming and don't feel like doing the math to determine if this is what it's theoretically supposed to be (even though that math isn't all that hard).

Another thing I was interested in looking at is how frequently the responses to 1C are used. These looked at only the south hand on the deals that 1C was opened. In the Canape Polish club system, 1D, which is 0-7 (but not 0-4 with a 6 card major) or 8-11 blanced, was bid 62.60% of the time. 1H/S/NT are all used about equal around 7.5%. In Canape Precision, the 1D response (0-7, but not 0-4 w/ 6M, OR 13+ 4441) is made 54.49% of the time. 1S at 15.43% is clearly the next most common response because it is a balanced 8-10 or 14+. hmm.

Polish Club Canape

Yesterday I felt inspired to tweak our system (the canape precision system Sean and I use) by introducing a two-way 1C opening and to incorporate canape into the responses and rebids to a 1C opening. So, after brief discussions with Shaz and Bryan, I set out to write up a system that would accommodate these things, not to be played with them but. I used no reference material and I don't think these system notes now look anything like any other system but I do have it so that auctions follow basically the same form as our canape structure for the minimum opening hands. After a couple of hours, I had a couple of pages of sequences that made sense at the time but for all I knew could be quite horrible. Then a couple of hours at the partnership bidding table and we realized this actually makes a lot of sense and allows us to bid the big hands in much the same was as we do the intermediate ones.

There are 2 downsides that I see. Opening NT is 15-17. Okay, not really a downside. It's just totally normal while nothing else in this system (when we get to open the bidding) is normal. and the auction 1C-1D-2D is too difficult to handle. In this case, opener is 17-21 with long diamonds or (4 diamonds and a longer side suit), a lot like our 1D opening which is 11-16 with long diamonds or (4 diamonds and a longer suit). Responder could have up to 11 if balanced, 7 if unbalanced, and may be fearful of bidding on without significant values. We may find ourselves in an inferior diamond fit when everyone else has no problem getting to the 5-3 or 5-4 major suit fit.

Our 1D through 2C opening bids are basically the same as before, but now the max is 16 hcp instead of 15 - they all are one-suited in the suit bid or 4 in the suit bid with a longer side suit. 2D is still mini-roman, now 13-16 instead of 12-15. 2M openings are 8-12 with a 6 card suit. 1NT is 15-17 instead of 12-15. the big change is that 1C is now either 12-14 balanced OR 18+ balanced OR 17+ unbalanced instead of any 16+.

There are a couple of big upsides in that it's fun and the opponents may not know how to react. I suppose most will or should treat it like a natural 1C, but I don't really know. I don't recall every actually playing against anyone playing a Polish club system.

District 7 GNT

While I was struggling through the Sunday Swiss at the Greenville sectional en route to a medicore 9th out of 42, the finals of flights A and C GNTs were going on in the same room. Jon Rice, Doug Dey, Lance Shull, and Audrey Ventura won flight A, no surprise to me. What is surprising is that their average was clearly less than half any other team in the flight A event except mine, yet their average age was still at least double the average age of the flight C winning team. In fact, the finals of the flight C event featured 8 players with a maximum age of 15, all from the Atlanta area. So congratulations to Richard and Andrew Jeng, Murphy Green, and Zandy Rizzo on demolishing the flight C competition.

Bridge Etiquette - Asking About Opponents' Bids

So, this weekend at the D7 GNT Flight A qualifying was not a very memorable experience. One round, however, in the sectional Swiss that we qualified for by placing 8th in the 10 team round robins Saturday, was rather humorous. And it's a good lesson in how not to act at the bridge table. The pair at first seemed to be reasonably experienced.

On board 2, LHO looks at our convention card for about 30 seconds, puts it back where I had it, and asks "Do you play 2/1?" "It's at the top of the damn card that you were just looking at." No, don't respond like that either (a simple yes sufficed).

Third board, white vs. red, it's 2 passed to me and I open a weak 2♥ on a 2-6-3-2 12 count. They somewhat rationally bid to 4♠ and go down 2.  Had I opened 1♥ they may have done 1 trick better and may have stayed out of game. Actually our teammates were making 3♥ our way so it was a 2 imp gain. Anyway, LHO was visibly upset that I had a little more than anyone else at the table expected me to have. But of course, our card is marked very light 3rd seat and very light preempts so this bid is clearly within range.

Fourth board, I open 1♣ , LHO passes, partner bids 1♥, RHO passes, I bid 2♥, LHO asks if 1♣ was natural (yes), partner bids 4♥, all pass. Not surprisingly, LHO has 6 clubs and RHO dutifully leads a ♣. Nothing really mattered on this hand and it was a push and we didn't comment on the unauthorized information given to RHO.

Next board, LHO opens 1♥, two passes, and I balance with 2♣. Partner bids 3NT and LHO jumps in his seat and noticeably shakes his head. RHO dutifully leads not a heart from Kx. Again the lead didn't make a difference and he made 5 for a push and no comment was made about the UI. Yes, on this auction, my partner tends to have something like a trap pass (with very good hearts) or a takeout double of 1♣ (and therefore probably 4 hearts) so a heart lead is often not right in this situation, but LHO's body language conveyed his bad heart suit quite clearly.

Last board of the set, LHO opens 1♦, partner doubles, RHO passes, I bid 1♠, LHO asks if the X was takeout. He competes to 3♦ and I compete to 3♠ , making. I guess there's not really any unauthorized information given by asking if it's a takeout double, it is just odd. I dunno.

Tip of the day: Be Aware of Partner's Problems

If the bidding and early plays might be misleading to partner, do what
you can to help him defend properly. A good example came up today. You
hold KQx, xxxx, xxx, Qxx. 3rd seat favorable vulnerability you open 1S
and the auction proceeds X-3S-4H-all pass. Dummy has Axx in spades and
a scattered 16. Your SK holds trick one and partner encourages. Do not
continue with the queen. Continue with a low spade so partner will not
have to guard spades. Not only does he have more minor suit cards to
protect, but he will never get the count in spades right.

GIB programming flaw

I was playing money bridge while eating lunch today. My robot had:
AKQJ, AKxxx, T, AKQ. It opens 2C, I bid 2H, which it said showed 5+
hearts and 8+ points. It bid 4NT, rkc for hearts. I bid 5D, 1 or 4.
GIB passes and I luckily go down only 1 because I was 5-5 in the reds
w HQ and DA and DJ. Needless to say, there were 13 top tricks in
hearts or nt. Cost me $23.20.

When to take a Safety Play?

Although I do have a preference for matchpoints and consider my overall style better suited for that type of game, safety plays are among my favorite kind of declarer plays. In today's hand, there are a couple of subtle options. South is in 4♥ after an uncontested auction and west leads the ♦Q.

North
♠	KJxx
♥	Jxx
♦	xxx
♣	Axx
South
♠	Axx
♥	AKQxx
♦	Ax
♣	xxx

You might be able to make it on some sort of strip and endplay but you don't know enough about the distribution and that's not really a possibility to consider. The only real way to make 5 is to draw trumps, play ace of spades and take a spade finesse. This line will make 5 when spades are 3-3 with the Q onside, an 18% chance. It will make only 3 when the suit is 4-2 and the Q is off (24%) or when RHO has 5 or 6 spades with the Q (7%). Combined, this is a 31% chance you'll go down with this line, and you'll make 4 51% of the time: 3-3 w/ Q off (18%), 4-2 w/ Q on (24%), 5 or 6 spades w LHO or stiff Q with RHO (9%). That means on average, you'll make 3.87.

Let us consider another line of play, a line that is only available on a non-club lead, for a club lead would cut out an entry to dummy. What are the percentages of playing the K and A of spades first and then leading low towards the jack? This will never get 4 spade tricks because if the Q falls, the suit cannot split 3-3, so it essentially gives up the chance of an overtrick, but does it fact make the contract more likely to succeed. This line will make 4 77% of the time: any 3-3 split (36%), any other time the Q is onside (32%), Q or QX offside (9%). You will go down 23% of the time: RHO with at least 4 spades including the Q. On average this makes 3.77 tricks, slightly worse then the previous line.

In other words, playing the AK first wins an extra trick (and makes the contract when the other way goes down) when east has Qx of spades (8%), and the finesse wins an overtrick when west has Qxx (16%).

So, how do you decide what line of play to take? In a matchpoint game? In imps? In matchpoints, you should consider how likely the field is to be in the same contract. In this case 4♥ seems to be an easy and normal contract to reach so you probably should try for the maximum number of tricks. In an average game, the field will take the straight up finesse and the matchpoints to be won by taking the safety play when it wins should be about equal to the matchpoints lost when it loses, relative to the straight finesse. If you decide that a significant portion of the field will be in a partscore or in 3NT making only 3, you would be even more concerned with making the contract for just making would already be a good score.

In imps, it's a little different. You don't care so much about the 1 imp you could win by making an overtrick but you care about not losing the 10 or 12 imps (Depending on vulnerability) when you go down and they make at the other table. If the probability of making an overtrick is 10 or 12 times as big as the potential gain from a safety play, then it's an even chance, but this time the ratio is 2:1. By taking the safety play as opposed to the normal finesse at the other table, you'll push the board 76% of the time, win 1 imp 16% of the time, and lose 10 or 12 imps 8% of the time, so in this form of scoring, it's clear to take the safety play.

Score of the Day: 970

+970 for 2SX making 7. This actually happened tonight on these 2 hands:

Qx
AQTxx
T8
Txxx

AKJTxx
9x
AQ95
8

The auction went: 1S-2H-P-P; 2S-P-P-X; P-P-P
West led the king of diamonds. I drew trumps, passed the heart 9, then played heart to the Q, heart A, pitching a club, diamond, covered, and won with the 7 falling from west.

In other news, playing Lebensohl and Minorwood, what is 4D in this sequence: P-2H-X-3D; P-4D?? Basically, is it invitational or Minorwood (roman key card blackwood for diamonds)? Those are pretty much the only two reasonable options. Even though 3D promises constructive values, I think there is a strong case that doubler actually just wants to invite game in diamonds. That's a hand that would probably come up more often than wanting to explore for a slam in diamonds, but 3H is available as a try for game. Advancer may still have good hearts and want to play 3NT and effectively 4D after 3H would be not accepting a game try. Maybe. I eventually agreed that 4D should be minorwood, clearly exploring for a slam. 3H would be the start of any game-try by doubler. On the actual hand tonight, I passed 4D with: xx, xxx, AQxxx, xxx. Partner had a 2 loser hand: AKQJxx, x, Kx, AKQx. Needless to say, 6S was the place to be.

Tip of the Day: Know Your System

Okay, even if you forget your system, still lead your good 6 card suit against 3NT.

Kx, Qxxx, KJTxxx, x. both vul, I opened a 3rd seat 2D, alerted as mini-roman. the auction proceeded 3C-3H-3NT-P-P-P. And I led a heart, obviously. And now declarer has 9 top tricks. Partner has Ax of diamonds and declarer Qxx. Perhaps they would have been entitled to some redress if I led a diamond but I doubt it. Perhaps they have a valid argument that I have to lead a heart on this sequence or that partner has to shift at trick 2, "knowing" that declarer has 5 diamonds but I really doubt it. The only redress I can possibly see is being required to bid 4H, but only if partner was not a passed hand. eh.

When is it too late to catch a revoke

So, if you've revoke but no one else notices, and you start the next hand, the previous result can no longer be changed. That is all.

I had: xx, KQT9, xx, AKxx. Against a good pair at the Atlanta club, Sean opened a canape 1D, I bid 1H, he bid 2H, I bid 4H. Dummy: Qx, Axxxx, QJTx, xx. LHO leads a high diamond spot. It goes A, K , 3rd diamond. I ruff with the K, draw trumps in 2 rounds, pitch a spade on the good diamond, lose a spade, ruff a spade, claim making 4. We played the next hand, after that hand, RHO begins wondering where the 13th diamond was. Apparently I had it the whole time and didn't even realize it, so we change the score to -100, which seems appropriate to me. Some discussion, not involving Sean or I takes place, rule books were consulted, and was determined that once they had bid the the following board, the previous one couldn't be adjusted.