The following hand isn't very exciting from a play standpoint, but it illustrates an important point in duplicate rules which wouldn't come up in a rubber game.
Board #23 from last week's student game: Dealer S, both sides vulnerable.
S: J752
H: 8542
D: AK2
C: T4 S W N E
S: A6 S: K93 ----------------------
H: J76 H: KT3 1N(1) 2D X!(2) --
D: QJ653 D: 984 2H -- 2S --
C: A52 C: 9763 3S -- -- --
S: QT84
H: AQ9
D: T7
C: KQJ8
(1) 12-15 HCP.
(2) Alerted and explained as a transfer to hearts.
North-South's agreement is that the double shows hearts, but North
forgot this and doubled, intending it as takeout (showing the majors).
South alerted the double, explaining it as a transfer to hearts when
East asked (immediately following the alert), and bid 2H. Realizing
what happened, North corrected to 2S; South raised and the auction was
passed out.
North then called the director: does he have to inform the opponents that he forgot an agreement? The answer is no. East-West are entitled to know what North-South's agreement is, but the fact that North forgot it is private. (After all, South doesn't know what's happening either.) If a player makes a habit of forgetting a particular agreement and his partner is aware of it, then the opponents have a right to know, but this was not the case here. North played the hand, losing two spades, a heart, and a club, and scored 3S making 3.
There is, however, a problem with what happened. North realized that his partner took his bid to show hearts, and then used that information to decide what to bid next. If you remember an agreement on your own later in the auction, that's fine, but here North's memory was sparked by South's alert, and then by South's answer to East's question. Information gleaned from answers your partner gives the opponents (or from your partner's alerts) is UNAUTHORIZED. Simply put, it was illegal for North to bid 2S on this auction.
(The rule may seem silly, but it makes sense. East should not be penalized for asking a question. If East had kept quiet, North would never have known, so it isn't fair for North-South to do better simply because East wants to know what a bid meant. That said, it's usually advisable NOT to ask the opponents what their bids mean until after the auction if you're not going to bid (say, if the opponents are bidding to a slam and you have nothing). Such a question can't help you, so you might as well delay asking it until it can no longer help the opponents.)
So, what happened to the above hand? The director decided that, without the explanation, North would probably have passed his partner's 2H bid. The next step is to assign a bridge score to the hand by figuring out what would have happened had they played 2H, giving the non-offending side (East-West) credit for very good play and the offending side credit for normal play. It is clear that East-West can get 4 tricks (two spades, a heart, and a club), and a fifth trick is easy (for example, if they start off with two spades and a spade ruff), so 2H makes at most two. The remaining question is whether it goes down?
If the defense starts with 2 spades and a ruff, it's easy for declarer to make; he forces out the ace of clubs when he first gets in, and then takes a heart finesse, throwing the dummy's low diamond before letting the defense in in hearts. If the defense attacks diamonds to begin with (the director has to assume West will start with the Q, and follow up with the J, pinning the T in South's hand), South has to be more careful, holding off playing trump until it's safe, but it's reasonable to assume a player of South's ability would get that right. So, the result was changed to 2H making two. (Since the other table was in 1D by West, making one, this constituted a difference of one IMP in the final standings; the nearest two places were separated by 28 IMPs, so none of it ended up mattering.
(One final note: there is an exception to the above rule. If the non-offending side does something really stupid, the director can choose not to give them an adjustment. Thus, while 2S can be held to two if the defense attacks hearts, it is not reasonable to expect them to find such a non-intuitive play. If, however, East-West had let 2S make 4 somehow (say, by crashing the trump honors), the director could score the East-West field with the result 2S+4, but the North-South field with the result 2S+2. And, if no bridge result can be assigned, the director can simply give the offending side an average minus and the non-offending side an average plus. (At IMPs, these are +/- 3 IMPs per comparison; at match points, average minus is 40%, average plus is 60% or your average (whichever is higher).)