8 ever 9 never vs. Restricted Choice

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Eight ever nine never – but not when Restricted Choice applies!

‘Eight ever- nine never' is a saying that says whether you should finesse a missing queen when you have 8 and when you have 9 cards in the suit. With just 8 cards you should always finesse - eight ever; but with nine cards you should play for the drop - nine never (finesse). But actually the odds for nine cards are very close and you may prefer to finesse if there was an inference that that may be working.

Restricted choice is actually a fairly complex mathematical problem and comes into play when two honours are missing and one appears on the first round of play. It's all very technical but what it boils down to in many simple situations is that if a player drops an honour on the first round then you should play his partner for the missing honour as that is more likely than one player having a doubleton honour.

Let's have an example of these two conflicting concepts: -

 West East How do you play these three suits to make all the tricks? (1) ♠ KJ92 ♠ A10754 (2) ♠ K732 ♠ A10865 (3) ♠ K932 ♠ A10865

(1) Missing just the queen and three small ‘8 ever 9 never' applies. If there was no inference
from the bidding the best play is to lead up to the K followed by the J and play the A if it is not covered. This is very slightly (2%) better than a 2 nd round finesse. Note that it does not really matter which card you lead from the West hand at trick two but playing the jack occasionally catches an inexperienced North who will ‘cover an honour with an honour' regardless.

(2) But when you are missing 4 cards including the queen and jack it's different and restricted
choice applies. You should play up to the top card that is not in the hand containing the ten (so K here). If no honour appears then you simply play for the drop. If North drops an honour then you simply have to hope it's QJ doubleton. But if South drops an honour you have a choice – play for the drop or finesse North for the other honour. It's fairly complicated mathematics but in this situation ‘Restricted Choice' takes precedence over ‘eight ever - nine never' and you should finesse.

(3) When you have both the ten and the nine then you can start by playing up to either the
ace or the king. If there was an inference from the bidding that North may be short in the suit then play to the the top honour in the East hand and then finesse South if North drops the queen or jack on the first round.

Here's an axample to demonstrate the mathematics, the actual hand is in news-sheet 288.:

 North ♠ A10864 North ♠ K972

So there are the QJ53 missing; here are the 16 possible cominations: -

 West East Restricted choice can sometimes involve very complex mathematics, but this is a relatively trivial case. There are initially 16 possible distributions between W-E for the missing cards. Each of these possibilities is equally likely. Now you have to assume that you are playing against good defenders who will always play a low card (5 or 3) randomly when holding H53 and will also play randomly when holding QJ doubleton. Suppose you play to the ♠A and a low card appears from West and an H (honour) from East. At this stage only possibilities 4,5 and 11 are possible. So the finesse is a 66% proposition. Incidentally, you can check out the play of this suit on the ‘suit play' link on this site.Enter the N-S ♠ cards and play ♠A and a small ♠ from West and an honour from East. The computer then plays the ♠10 for you and when you choose a small ♠ from West, the computer plays the finesse. 1. QJ53 - 2. QJ5 3 3. QJ3 5 4. Q53 J 5. J53 Q 6. QJ 53 7. Q5 J3 8. Q3 J5 9. J5 Q3 10. J3 Q5 11. 53 QJ 12. Q J53 13. J Q53 14. 5 QJ3 15. 3 QJ5 16. - QJ53

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