We will be looking at an introduction to the most fundamental Declarer Play skills. Count, Count, Count is of course the highest priority Declarer skill as it is in every phase of Duplicate, but there are a few other basic Declarer Play skills you must have. We ll first look at Distribution I call it Split Odds, which is an estimate about how Defenders holdings in a suit might be distributed: 4 3 3 3? 5 4 3 1?, etc. It s the 2 nd most important Declarer Skill you need to know well - after Counting. Even if it fails for you on any hand, it will fail for all other Declarers as well, so you haven t lost anything: lose but still get an average on a board. Sound good? Win on every hand? No. But win a majority of the 189 hands you declare in the next year? Yes. That s why it s so basic, like Counting. If you hold 8 Diamonds between your hand and the dummy, split 5 3, how are the opponent s 5 Diamonds likely to be split? There s no one way or always answer or guaranteed way to know, of course. But if you know the odds for such questions - and they are quite predictable - then in the long run you re going to beat other Declarers who don t know what the odds are, or don t use them. Know and Go with the Odds is a sound Declarer Play Plan winner. Here it is. One of the other things we ll learn early is that Finesses are the last things you should look for; not the first things in your Declarer Play Plan. Why? A Finesse is a 50% odds play, right? Wouldn t you rather have a 68% odds chance? And even if a 68% play fails, you may still have the 50% odds finesses available. Which makes more sense? Successful Declarer Play is based on a Sequence of plays over the whole 13 tricks, starting with your best chances. Take your best chances for extra tricks in the right sequence, with Finesses generally being last. Pg. 1 Bob McConnell, 2018
Split Odds Estimating: In the table below is everything you will ever need to know about Split Odds. (It s also called Percentages or Suit Distribution). The odds don t add up to 100% in each cell because I have left out 10% or lower odds splits to make it simpler. Below, I ll reduce it all to one sentence. (Copy the table: put it in your CCard.) DISTRIBUTION of DEFENDERS CARDS 2 cards will split 1 1 52% 2 0 48% 3 cards will split 2 1 78% 3 0 22% 4 cards will split 3 1 50% 2 2 40 % 5 cards will split 6 cards will split 7 cards will split 3 2 68% 4 1 28% 4 2 48% 3 3 36% 4 3 62% 5 2 36% To be certain you understand exactly what this table is telling you, look at the cell that says 5 cards will split. If defenders hold 5 Clubs, however they split, you hold 8 of them. If yours are split 4 4, there s no chance for more than 4 tricks, unless they are trump. But if they re split 5 3, how many tricks might you take? Maybe 5? Look at 5 Cards will split. 3 2 (68%) means there will be 3 Clubs in one defender s hand, and 2 Clubs in the other defender s hand, about 68% of the time. Not 100%, but 68%, which are great odds more than 2/3 of the time. They will be 4 1 about 28% of the time a little over 1/4 of all 5-card split hands. And they could be split 5-0, but the odds of that are so small you shouldn t normally consider it. Do you see any pattern to help you memorize this table? There is one clear pattern: look at the odd-numbered holdings of 3 & 5 & 7 cards. The split odds are, respectively, 78%, 68% and 62% in favor of as close to even as possible. Odd card distributions split as evenly as possible, with odds of at least 62%. Pg. 2 Bob McConnell, 2018
Now look at even numbered splits: 4 cards and 6 cards. Even card distributions split unevenly about 50% of the time (3 1 or 4 2) and they split evenly 36% to 40% of the time (2 2 or 3 3). (Let s call that 38% to simplify remembering it.) But 38% vs. 50% isn t terribly different odds. Go for 38% odds when there s no better odds elsewhere. Don t think they will split evenly most of the time: it s not true, but, once again, all declarers playing the hand will have the same issues. SPLIT ODDS WHEN THERE HAS BEEN OPPONENT BIDDING. When defenders bid, you know specific things about Shape and HCP in the bidders hand. If East opens 1 and you declare in Hearts, are 7 missing Spades split 4 3 as our table indicates? Of course not. East has at least 5 Spades, so the Split Odds Table is off in Spades, and therefor possibly in other suits as well. Don t use it blindly: Count. Summary: Odd numbers of defender cards split close to even 62% of the time and Even numbers split not evenly about 50% of the time and evenly about 38% of the time. Remember this one sentence and you know the whole table. Some good news: Split odds are often cumulative, meaning you can add the odds together with two plays to maximize how many tricks you might take. An example: Suppose you and dummy hold 7 Hearts, split 5 2, including the Ace, King and Queen. That means defenders hold 6 Hearts. Since that s an even number, your odds of a 3 3 split are only about 38% to pick up all 5 Heart tricks by playing them off the top. But what if you only need 4 Heart tricks to make your contract, not 5? Remembering the odds (38%) for a 3 3 split of 6 cards, also remember the additional 48% odds of a 4 2 split. If you only need 4 Heart tricks, not 5, to make your contract, what are your total odds of winning 4 Heart tricks? An even 3 3 Heart split gives you all 5 tricks, plus the 4 2 Heart split gives you additional 48% odds to take 4 Heart tricks, for total 84% odds to take 4 or 5 Heart tricks. How does 84% odds of taking at least 4 Heart tricks sound? Sounds like a winner to me. Pg. 3 Bob McConnell, 2018
But there s another vital factor you must consider for safely collecting at least 4 Heart tricks. ENTRIES. If you have a clear side entry to the 5 Heart hand to collect the 5 th Heart trick, you are safe. But if you only need 4 Heart tricks to make your contract and don t have a safe side entry for the 5 th Heart, you should duck an early Heart trick (e.g., lose the first one deliberately) to virtually guarantee 4 Heart tricks with 84% odds. Often, you have 9 trumps, missing the Queen. The Split Odds table shows 40% odds for a 2 2 split, dropping the Queen, and 50% odds for a 3 1 split. But bridge books say 9 ever; 8 never meaning play the Ace and King to play for the drop of the Queen with 9 cards in the suit; don t try a finesse. Why is that with only 40% odds for a 2 2 split? Because this is not an issue about odds for any 4-card split: you are looking for one specific card the trump Queen. So, of the 4 missing cards, as you see in the table, you have 40% odds of a 2 2 split plus you have the possibility of the Queen being a singleton in a 3 1 split. This is an extra 1/4 of 50% odds, for total odds of 52.5%. So, go ahead and play 9 ever; 8 never. This is why bridge books say 9 Ever; 8 Never, even though they don t explain why. 52.5% isn t always or usually, but it s a good bit better than 40% odds, right? Now you know why, technically and logically. Pg. 4 Bob McConnell, 2018
What Are the Odds? - A Quiz: Now that you know all about Percentages of Splits of defenders cards, ( Split Odds ), how should you plan the Play of these hands? The contract and opening lead are between the hands. Answers follow on the next page. 1 74 A64 9653 T742 2 J52 432 A84 9765 3 AT 762 743 98652 4 AQ532 842 954 T8 4 Spades, K 4 Hearts, Q 3 NT, 3 lead 3 NT, 3 lead AQJT98 95 AQJ AQ AQ AQJT97 K97 A3 Q5 AKQ5 AQ86 AKQ 74 A65 AJT AKQJ9 5 AK743 652 54 982 6 876 93 A92 A8654 7 74 AQ4 K9652 873 8 7642 983 AQJT 52 3 NT, K lead 3 NT, Q lead 3 NT, 8 lead 6 Spades, Q 62 A743 AKT9 AKQ AJ AK K8764 9732 AQ3 K76 Q84 KQJT AKQT8 A 73 AQJT9 East opened 1 Spade; you overcalled 1NT. Pg. 5 Bob McConnell, 2018
9 AQ J76 Q643 AT72 10 AK7 7652 KJ3 KT9 11 T92 A53 7 AQT983 12 AQ3 742 86543 A9 6 Diamonds, K 5 Diamonds, Q 4 Spades; K 4 Spades; Q J952 AKQ AT8752 - - KQ AQT9764 8532 AKJ87 T64 T82 KJ KJT864 A65 AQ 72 Answers: 74 A64 9653 T742 #1. You have only one Entry to the dummy, so you can take only one of the 3 available finesses Spades, Diamonds or Clubs. Which do you take? Does it matter? Yes. CLUBS first. Why? If it succeeds, you ll have no Club loser; if another finesse works, you ll still have a loser in that suit because of lack of entries. J52 432 A84 9765 4 ; K 4 ; Q AQJT98 95 AQJ AQ AQ AQJT97 K97 A3 #2. Again, a loser in each suit and only one entry to dummy. But, as usual, a finesse is the wrong plan anyway. Win the K in hand. Play the A and Q, forcing out the K. Then, after drawing 1 trump, go to the A and pitch a loser on the J. Pg. 6 Bob McConnell, 2018
AT 762 743 98652 #3. Your Spade stopper is gone on the 2 nd trick, so what s left? You are in the dummy only once, with only 8 winners. Do you play on Hearts to split or take the Diamond finesse? You can t do both because of Entries. Odds of a 3 3 Heart split are 36%; while odds of the Diamond finesse working are 50%, so take the finesse. AQ532 842 954 T8 3 NT, 3 3 NT, 3 Q5 AKQ5 AQ86 AKQ 74 A65 AJT AKQJ9 #4. Duck the 1 st two Hearts and (hopefully) see them split 4 3, so you have only 1 more Heart loser. Do finesses in Spades and Diamonds have equal odds? Yes. You only need to win 1 of 2 Diamond finesses for 9 tricks. The odds of that happening are 3 to 1 in your favor. Only if West has both the K and Q will you lose both finesses. (The 10 is an entry to dummy.) AK743 652 54 982 #5. 8 winners with 2 chances for another trick: if the Spades split 3 3 or you can finesse twice in Diamonds. 876 93 A92 A8654 3 NT, K 3 NT, Q 62 A743 AKT9 AKQ Again, you only need to win only 1 of 2 Diamond finesses for 9 tricks. The odds of that happening are 3 to 1 in your favor: 75% odds. Only if West has both the J and Q will you lose both. Duck 2 Hearts. AJ AK K8764 9732 #6. There s only 6 top winners, meaning you need 3 more tricks. There s chances in Diamonds and in Clubs, but only in Clubs is there a chance for 3 extra tricks, if they should split 2 2. Even if Diamonds split 3 2, you ll still be short a trick, even though a 3 2 Diamond split has higher odds (68%) than a 2 2 (40%) Club split. Start with the A and another Club. Pg. 7 Bob McConnell, 2018
#7. 74 AQ4 K9652 873 East opened 1 Spade; you bid 1NT and partner went to 3 NT. West has? HCP? You have 8 top tricks and 8 Diamonds with the K and Q. 7642 983 AQJT 52 3 NT, 8 6, Q East has the AJx so don t try AQ3 to set up Diamonds. AKQT8 K76 Instead, lead low from A Q84 dummy toward your Q. If 73 KQJT East takes her A, you ll have AQJT9 4 s, 2 s and 3 s. If she ducks the low Diamond, take the Q and start Clubs for 9+ tricks. #8. Win the lead, collect trump in 3 rounds, (90% odds) and then what? Maybe lose 2 minor suit finesses? Certainly possible. But there s a 100% Play. Play the A and more Clubs until the K wins. Take the A and ruff a Heart. You then have 3 more Club winners, where you pitch dummy s 3 Diamond losers. Your Diamond loser is then ruffed in dummy. AQ J76 Q643 AT72 #9. Missing the K, J and 9. With no Spade loser, there s a safety play that will guarantee no more than 1 trump loser. Ruff the K lead and take the Spade finesse. If it wins, lead a trump from dummy and cover any honor East plays, or the T over her 9. If it loses, bang down the A, hoping for a 33% chance of a singleton K. AK7 7652 KJ3 KT9 6, K 5, Q J952 AKQ AT8752 - - KQ AQT9764 8532 #10. Pitching 2 Clubs on Spades, you could still lose 2 Clubs and the Ace. So Jettison (pitch) both Hearts for 1 less loser. Collect trump (2 rounds = 78%) then lead a Club, covering any honor from West. If it loses to East, repeat the finesse, giving you 3 to 1 chances of success. 75% odds of at most 2 Club losers. Pg. 8 Bob McConnell, 2018
T92 A53 7 AQT983 4 ; K AKJ87 T64 T83 KJ #11. Win the A and A, then a Spade finesse, losing 2 Hearts, a Diamond and the Q? Better is to play the A and K, hoping for the 68% 3 2 Spade split but assuming the Q doesn t drop. Then play Clubs, hoping for 1 or more Heart pitches before the Q holder ruffs in to collect another Heart winner. The odds of a 3 2 Club split are 68%. AQ3 742 86543 A9 4 ; Q KJT864 A65 AQ 72 #12. 4 losers possible unless the 50% Diamond finesse wins. But take 1 Spade trick first because if they split 4 0, you must take the Diamond finesse. You have 7 Diamonds; they have 6. Any 3 3 or 4 2 split will give you a discard of a loser. Odds? 48% for 4 2 plus 36% for 3 3, bringing your total to 84%. Pg. 9 Bob McConnell, 2018