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3♦ is only suit preference despite the 3♣ rebid and is non forcing so the question then becomes: is 3NT a sensible option - you know that you may (not will) have communication difficulties. IMHO 3NT is viable owing to the ♠9 and ♥9 and I therefore applied Hamman's law. Partner is not disbarred from carrying on if he is 6-5 in the minors.

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Ok - my last regular watching of NFL was back in the early 80s (I am UK remember) and it wasn't - or if it was I don't remember - pointed out that a 2PAT was obvious before the play started. (Mind you it doesn't seem to stop a surprise one being attempted - you may gain more on the element of surprise than you lose by not having the optimum formation set up)

So P(WIN) | two touchdowns and no other scores and P(1PAT)=1.0

= P(2PAT)+ (1- P(2PAT)) * P(2PAT) * P(OT) (convert 1st or (2nd if the first fails and OT)) OR = P(OT) …. (two 1PAT) OR = P(2PAT) … (1PAT + 2PAT)

since P(2PAT) < P(OT) it is obvious that the third option is a losing one so if we exchange P(2PAT) with ‘x’ for simplicity and assume P(OT) = 0.5 we get (for the 2-point strategy to win)

x + ((1-x).x)/2 > 0.5 2x + x - x^2 > 1 x^2-3x +1 <0 - which is solved by the quadratic formula Giving x > 1.5 - sqrt(5) / 2 = 0.38 as calculated previously.

Note that (for completion of proof) if P(2PAT)>0.5 the equation must be amended to

x + ((1-x).x)/2 > x. Fortunately this simplifies to 1-x >0 which is true for all 0.5<x<1.

However given that the average american knows SFA about probability it would be pretty hard to convince them that the correct strategy had been taken, especially when it failed!

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I think that people are forgetting that if you try the 2-point conversion and it fails then after the second touchdown the opponents KNOW you will be going for the 2-point conversion. This must reduce the probability of making it somewhat. - whereas in bridge the probabilities are fixed.

Of course if the opponents know that you know what the correct strategy is in a single event then they know you will go for the 2-point conversion on the first attempt as well, thus reducing the probability of making that one.

You must therefore NOT adopt the strategy of going for the two points all the time. Although the 1-point, 2-point strategy is derided, I suspect that in game theory it must be regarded as having merit as you have the option of going for the 1-point, 1-point option as well - thus increasing uncertainty.

The exact maths is beyond me but going for the 1-point only part of the time and the 2-point the rest (in the second touchdown) must score better if only because the chance of winning is improved with the increased chance of the 2-point conversion winning.

Isn't game theory wonderful?

What I will add - it would appear that since the probability of getting a 1-point conversion, even against specialist kicking teams is virtually 100%, surely the defensive coach shouldn't put on the kicking team at all! They should just put on the regular defensive team with instructions to assume a 2-point attempt. This MUST reduce the chance of a 2-point play working to less than the chance of 1st and goal, ball on the 2-yeard line, working - which must be a lot less than 47%.

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If you have a singleton, perhaps you could have an agreement that if you throw one card from each other suit you want a trump promotion, if you throw two cards from the same suit then you want the other suit lead. If you ruff the third round then you know what to do yourself i.e. cash the Ace before declarer throws away losers.

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Leading the A♥ has the advantage that once you look at dummy you can decide whether to play spades (admittedly the most likely) or Diamonds next. Partner gives suit preference for spades and that is that.

And you're right - leading trumps is very frequently the worst thing that a defender can do, once declarer has announced a good fit. As is illustrated here - declarer draws trumps and sets up his second suit - goodbye tricks.

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Since you underbid your hand by about 4 tricks and can't do much to catch up I suppose a double would be nice - and cashing AKQJ of hearts before giving partner a club ruff (he discarded his clubs on the hearts), spade to the Ace and another club ruff even nicer.

Bidding 5♠ is a safety measure - you MAY make it or be 1 or 2 down but have stopped any double game swing.

I would possibly have bid 5♠ on the first round - after all partner might be short in clubs or have an Ace - and I wont mind seeing 6♦ appear.

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I play a version of the Schenken 2♦ - after the Ace responses you bid the next suit up (Not NT) asking for Kings, Queens, Jacks on a similar basis OR you bid NT to show a very strong balanced hand (usual responses, partner takes over) OR you bid the final contract.

Playing this way, you don't have to rebid 3NT after 2♣ to show 25 points balanced (which is too high) as you can open 2♦ and rebid 2NT over 2♥ - if partner has one or two aces and thus goes beyond 2NT in his response then there is no problem!

(There is no point opening 2NT on 19 points - if partner can't respond there is no game and if partner has a bust you are too high anyway (statistics show that 2N - p - p - p is going off 70%+ of the time))

TBH it is usually the strong balanced hand that comes up most often as you must have a suit that is self supporting (here Hearts) as you have self-agreed the suit by opening 2♦

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In a competitive auction you MUST,MUST, MUST tell your partner your fit and any other suits you have. Failure to do so, as Yuan shows, is totally losing tactics.

You get your hand type and distribution off your chest - partner (but not necessarily the oppos) knows whether there are going to be lots of tricks - double game swings and the like, or whether he can sock the oppos on strength knowing that the distributional tricks aren't there.

(I would play any NEW suit forcing a response at and above the 3 level as a fit jump or fit non jump. Cue bidding the opponent's suit at the 4 level would be a splinter)

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I play a weak NT so many (but not all) 12 points are in my ambit. My rules are:

If opening a WNT I must have an expectation of winning 4 tricks and have strength in 3+ suits if the cards lie favourably - this means that hands with QX, JXX automatically get ditched. So the hand quoted is a minimum WNT.

(Why do I need 4 tricks? If I hold 3 then someone will hold 4 - if it is my partner then he'll bid anyway, if it is not my partner then we would be going down in a contract)

In 1st or 2nd I must have a sensible rebid over any response by partner. (I realise Strong NT players will have a response of 1NT in these occasions - but do you really want to rebid 2NT on 12 points balanced after a 2-level response?)

In third I would much rather have a major if bidding on a weak distributional hand and the weaker the hand the better the suit has to be.

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C4H9SH - it would be nice if you could inform BBO about a psyche so it could track players. In this case surely 4♥ would be a splinter showing a maximum hand.

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A. Proper Communication between Partners 1. How Effected Communication between partners during the auction and play shall be effected only by means of the calls and plays themselves. 2. Correct Manner for Calls and Plays Calls and plays should be made without special emphasis, mannerism or inflection, and without undue hesitation or haste (however, sponsoring organizations may require mandatory pauses, as on the first round of auction, or after a skip-bid warning, or on the first trick).

B. Inappropriate Communication Between Partners 1. Gratuitous Information Partners shall not communicate through the manner in which calls or plays are made, through extraneous remarks or gestures, through questions asked or not asked of the opponents or through alerts and explanations given or not given to them. 2. Prearranged Communications The gravest possible offense is for a partnership to exchange information through prearranged methods of communication other than those sanctioned by these Laws. A guilty partnership risks expulsion

(part of)Law 73

Call the Director if you suspect an irregularity (after all the 2♥ bid might be natural under their system)

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After the usual briefing to the Rabbit after the cut “Don't bid a major, don't bid no trumps, always lead my suit even if you have a void” The Hog picked up the following Hand.

♠AX ♥A432 ♦QXXX ♣KX.

Not liking his threadbare heart suit he opened 1NT, maximising his chances of being declarer.

After a pass from Karapet he heard 4♥ from the Rabbit. This had to be a “Strong Partner Transfer”. “Perfect” he thought 4♠ bid and made by me - and made the obvious bid - a declarer to his fingertips.

The Rabbit fidgeted, gulped down a large cherry brandy and half a dozen chocolate biscuits. 5♣ he bid in a squeak of thunder.

The Hog was alarmed - the Rabbit rarely made a slam try for the good reason that he rarely made 12 tricks, however, the Hog thought, he must be relying on me, as usual, to make a couple of extra tricks with my play. One could hardly blame him.

The response was obvious - bidding 5♥ showing the A♥ would calm the Rabbit down and emphasise the diamond losers. Even the Rabbit would realise that the Hog didn't have Diamonds.

The Rabbit passed! Papa turned to the Kibitzers and said “Obviously the Rabbit has been dozing again and playing in a 5-level cue bid won't be a good result for them. If I double they'll bid 5♠ which means that I lose both the benefit of the misunderstanding AND that the Rabbit won't be playing the hand - always look ahead” - and passed.

Meanwhile the Hog was, as usual, berating the Rabbit. “Why did you pass? Didn't you hear my bid? Don't you know what it means? And at a cost of 2 champagne bottles a hundred as well!”

Holding ♠Q9X ♥Q87 ♦A543 ♣JXX the opening lead stood out a mile - the A♦ - on which the Rabbit dropped the Jack

Looking at dummy a switch to a suit headed by a Queen looked too risky - although it seemed to matter little whether the contract went 5 Down or only 4. The safest option seemed to be to continue Diamonds.

The Rabbit won with the King, Played the ♥K on which, to Papa's shock Karapet discarded.

The Rabbit counted the hearts - the Queen was missing and there was probably another one left and put down his hand.

“Finessing against the QH, 2 clubs, club ruff, 1 Spade, 2 Diamonds he said, putting down ”♠QX ♥ KJTXXX ♦KJ ♣AXX

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Perhaps partner has

♠Ax ♥AXXX ♦AJXXX ♣ XX - Some people might want to make a forward move with a hand so endowed with controls - 6♥ looks a fair bet opposite ♠KXX ♥KQJTXX ♦KQX X

This is a version of John Portwood's rule: When 1NT is a possible bid - make it! (TIC)

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I always like to think in terms of tricks - partner has about 4 of them (maybe a bit more if a super fit) so unless you can see 7+ tricks in your 14 point hand you should bid 5♥. Of course KJTXXX is now worth 5 tricks - with partner's super accept - so if you can see three more (quite likely) then you should bid 4NT asking for Aces.

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No - we play a ‘strong 12’ to a ‘poor 15’ (notionally 4 - 4.5 playing tricks). At the low level the honours have to be working well together - typically sequences and good intermediates, at a high level we have the ‘Aces and Spaces’ type hands. i.e. not much filling in the suits.

Partner will always invite on the 10-12 hands providing he, too, can see a source of tricks. So we can reach 22 point 3NT hands - but these will be hands where one suit at least will be pretty solid for 4 (or 5) tricks.

(I think I have been doubled once in the last 12 months using this method - the greatest risk of being doubled is that it happens so rarely that partner might forget the wriggle:))

With a good 15 we'll rebid 1NT or 2NT as appropriate.

John Portwood

John Portwood

John Portwood

So P(WIN) | two touchdowns and no other scores and P(1PAT)=1.0

= P(2PAT)+ (1- P(2PAT)) * P(2PAT) * P(OT) (convert 1st or (2nd if the first fails and OT)) OR

= P(OT) …. (two 1PAT) OR

= P(2PAT) … (1PAT + 2PAT)

since P(2PAT) < P(OT) it is obvious that the third option is a losing one so if we exchange P(2PAT) with ‘x’ for simplicity and assume P(OT) = 0.5 we get (for the 2-point strategy to win)

x + ((1-x).x)/2 > 0.5

2x + x - x^2 > 1

x^2-3x +1 <0 - which is solved by the quadratic formula

Giving x > 1.5 - sqrt(5) / 2 = 0.38 as calculated previously.

Note that (for completion of proof) if P(2PAT)>0.5 the equation must be amended to

x + ((1-x).x)/2 > x. Fortunately this simplifies to 1-x >0 which is true for all 0.5<x<1.

However given that the average american knows SFA about probability it would be pretty hard to convince them that the correct strategy had been taken, especially when it failed!

John Portwood

Of course if the opponents know that you know what the correct strategy is in a single event then they know you will go for the 2-point conversion on the first attempt as well, thus reducing the probability of making that one.

You must therefore NOT adopt the strategy of going for the two points all the time. Although the 1-point, 2-point strategy is derided, I suspect that in game theory it must be regarded as having merit as you have the option of going for the 1-point, 1-point option as well - thus increasing uncertainty.

The exact maths is beyond me but going for the 1-point only part of the time and the 2-point the rest (in the second touchdown) must score better if only because the chance of winning is improved with the increased chance of the 2-point conversion winning.

Isn't game theory wonderful?

What I will add - it would appear that since the probability of getting a 1-point conversion, even against specialist kicking teams is virtually 100%, surely the defensive coach shouldn't put on the kicking team at all! They should just put on the regular defensive team with instructions to assume a 2-point attempt. This MUST reduce the chance of a 2-point play working to less than the chance of 1st and goal, ball on the 2-yeard line, working - which must be a lot less than 47%.

John Portwood

John Portwood

And you're right - leading trumps is very frequently the worst thing that a defender can do, once declarer has announced a good fit. As is illustrated here - declarer draws trumps and sets up his second suit - goodbye tricks.

John Portwood

John Portwood

John Portwood

Bidding 5♠ is a safety measure - you MAY make it or be 1 or 2 down but have stopped any double game swing.

I would possibly have bid 5♠ on the first round - after all partner might be short in clubs or have an Ace - and I wont mind seeing 6♦ appear.

John Portwood

John Portwood

Playing this way, you don't have to rebid 3NT after 2♣ to show 25 points balanced (which is too high) as you can open 2♦ and rebid 2NT over 2♥ - if partner has one or two aces and thus goes beyond 2NT in his response then there is no problem!

2N = 20 - 22

2♣ .. 2!NT = 23-24

2♦ .. 2!NT = 25-26

(There is no point opening 2NT on 19 points - if partner can't respond there is no game and if partner has a bust you are too high anyway (statistics show that 2N - p - p - p is going off 70%+ of the time))

TBH it is usually the strong balanced hand that comes up most often as you must have a suit that is self supporting (here Hearts) as you have self-agreed the suit by opening 2♦

John Portwood

You get your hand type and distribution off your chest - partner (but not necessarily the oppos) knows whether there are going to be lots of tricks - double game swings and the like, or whether he can sock the oppos on strength knowing that the distributional tricks aren't there.

(I would play any NEW suit forcing a response at and above the 3 level as a fit jump or fit non jump. Cue bidding the opponent's suit at the 4 level would be a splinter)

John Portwood

If opening a WNT I must have an expectation of winning 4 tricks and have strength in 3+ suits if the cards lie favourably - this means that hands with QX, JXX automatically get ditched. So the hand quoted is a minimum WNT.

(Why do I need 4 tricks? If I hold 3 then someone will hold 4 - if it is my partner then he'll bid anyway, if it is not my partner then we would be going down in a contract)

In 1st or 2nd I must have a sensible rebid over any response by partner. (I realise Strong NT players will have a response of 1NT in these occasions - but do you really want to rebid 2NT on 12 points balanced after a 2-level response?)

In third I would much rather have a major if bidding on a weak distributional hand and the weaker the hand the better the suit has to be.

In 4th I apply the rule of 15.

John Portwood

♥X ♣AJ9 opposite

♥AKJX

There is also the possibility that just 1 spade ruff is needed ending with

♠X ♥X ♣AJ9 opposite

♥AKJX ♣X with Yuan having to hold ♠Q ♥QXX ♣KQ as his last 5 cards.

Of course with a ♥ lead through AKJ the squeeze is broken.

John Portwood

John Portwood

1. How Effected

Communication between partners during the auction and play shall be effected only by means of the calls and plays themselves.

2. Correct Manner for Calls and Plays

Calls and plays should be made without special emphasis, mannerism or inflection, and without undue hesitation or haste (however, sponsoring organizations may require mandatory pauses, as on the first round of auction, or after a skip-bid warning, or on the first trick).

B. Inappropriate Communication Between Partners

1. Gratuitous Information

Partners shall not communicate through the manner in which calls or plays are made, through extraneous remarks or gestures, through questions asked or not asked of the opponents or through alerts and explanations given or not given to them.

2. Prearranged Communications

The gravest possible offense is for a partnership to exchange information through prearranged methods of communication other than those sanctioned by these Laws. A guilty partnership risks expulsion

(part of)Law 73

Call the Director if you suspect an irregularity (after all the 2♥ bid might be natural under their system)

John Portwood

♠AX ♥A432 ♦QXXX ♣KX.

Not liking his threadbare heart suit he opened 1NT, maximising his chances of being declarer.

After a pass from Karapet he heard 4♥ from the Rabbit. This had to be a “Strong Partner Transfer”. “Perfect” he thought 4♠ bid and made by me - and made the obvious bid - a declarer to his fingertips.

The Rabbit fidgeted, gulped down a large cherry brandy and half a dozen chocolate biscuits. 5♣ he bid in a squeak of thunder.

The Hog was alarmed - the Rabbit rarely made a slam try for the good reason that he rarely made 12 tricks, however, the Hog thought, he must be relying on me, as usual, to make a couple of extra tricks with my play. One could hardly blame him.

The response was obvious - bidding 5♥ showing the A♥ would calm the Rabbit down and emphasise the diamond losers. Even the Rabbit would realise that the Hog didn't have Diamonds.

The Rabbit passed! Papa turned to the Kibitzers and said “Obviously the Rabbit has been dozing again and playing in a 5-level cue bid won't be a good result for them. If I double they'll bid 5♠ which means that I lose both the benefit of the misunderstanding AND that the Rabbit won't be playing the hand - always look ahead” - and passed.

Meanwhile the Hog was, as usual, berating the Rabbit. “Why did you pass? Didn't you hear my bid? Don't you know what it means? And at a cost of 2 champagne bottles a hundred as well!”

Holding ♠Q9X ♥Q87 ♦A543 ♣JXX the opening lead stood out a mile - the A♦ - on which the Rabbit dropped the Jack

Looking at dummy a switch to a suit headed by a Queen looked too risky - although it seemed to matter little whether the contract went 5 Down or only 4. The safest option seemed to be to continue Diamonds.

The Rabbit won with the King, Played the ♥K on which, to Papa's shock Karapet discarded.

The Rabbit counted the hearts - the Queen was missing and there was probably another one left and put down his hand.

“Finessing against the QH, 2 clubs, club ruff, 1 Spade, 2 Diamonds he said, putting down ”♠QX ♥ KJTXXX ♦KJ ♣AXX

John Portwood

♠Ax ♥AXXX ♦AJXXX ♣ XX - Some people might want to make a forward move with a hand so endowed with controls - 6♥ looks a fair bet opposite ♠KXX ♥KQJTXX ♦KQX X

This is a version of John Portwood's rule: When 1NT is a possible bid - make it! (TIC)

John Portwood

John Portwood

Partner will always invite on the 10-12 hands providing he, too, can see a source of tricks. So we can reach 22 point 3NT hands - but these will be hands where one suit at least will be pretty solid for 4 (or 5) tricks.

(I think I have been doubled once in the last 12 months using this method - the greatest risk of being doubled is that it happens so rarely that partner might forget the wriggle:))

With a good 15 we'll rebid 1NT or 2NT as appropriate.