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A bridge maxim is a rule of thumb cited by players in contract bridge acting as a memory aid to best practice gained from experience.[1]
There are two strategies - the finesse, which is 50-50 in both cases, and the drop, which relies upon the opponent who has the queen having only one or two (but not more) cards in the suit, and becomes more likely to succeed the more cards in the suit are held.
Lacking any further information, the maxim suggests that optimal strategy is to finesse when holding a total of eight cards in the suit, and don't finesse but play the two top cards to cause the queen to be "dropped" if nine cards are held.
Advanced players will often try to gain further information or deduce which hand holds the queen, before choosing their play. The difference in percentages is so close (the Bridge Encyclopedia states that the finesse is a 50% probability of success holding 8 cards, while the drop has a 53% holding 9 cards) that the slightest inference might influence a player to choose to finesse or to drop with nine cards.
"Eight ever nine never" refers only to when declarer can afford no loser in the suit: there are many more things for him to think about when declarer can afford a loser. For example, if the finesse would land in the hand of the dangerous opponent who can give the other opponent a ruff that declarer can't afford, with eight cards he might have to play for a "drop" by playing the ace and king then a small one to the jack. Even if the finesse would have lost, now the dangerous opponent can't give his partner a ruff, because he can't have any more trumps left (if the queen didn't fall under the ace and king, the potential ruffer can't have more than two cards in the suit).
However, it is best to use your judgment: if the bidding or previous play suggests that partner can't have the jack, 10 or 9, or enough cards for this card to be promoted (e.g. if he can only have two cards and you know declarer has the jack, his 10 will still fall under one of declarer's cards whether you cover or not) then there is no point covering, as this will only help declarer by telling him where an important card is.
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