SPLIT ODDS. No. But win the majority of the 1089 hands you play in this next year? Yes. That s why Split Odds are so basic, like Counting.

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Helena Mosley
5 years ago
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1 Here, we will be looking at basic Declarer Play Planning and 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 basic Declarer Play skills you must have... and those are what we re going to look at here: The Odds of Defender s Card Splits. We ll first look at Distribution what we call Split Odds, which is understanding about how defenders holdings in a suit might be distributed: 4 3? 3 3? 4 2? 2 2? etc. It s the 2 nd most important Declarer Skill you need to know after Counting everything. Even if it fails on any one hand, it will fail for all other Declarers of that hand as well, so you haven t lost anything: that s a good thing - lose but still get an average on a board. Sound good? Yes. Win on every hand? No. But win the majority of the 1089 hands you play in this next year? Yes. That s why Split Odds are 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 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 who fail to use them in Declarer Play. Know and Go with the Odds is a sound Declarer winner. Do it on every hand you declare. One of the other things we ll learn is that Finesses are the last thing you should look for; not the first thing to look for in your Declarer 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 sometimes, you will still probably have the 50% odds Finesse available toward the end of the hand. 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: if they re there on the first trick, why won t they be there on the 12 th trick? Pg. 1 Bob McConnell, 2019

2 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 every cell because I have left out 10% or lower odds splits to make it simpler. Later, I ll reduce it all to one sentence. One! DISTRIBUTION of DEFENDERS CARDS 2 cards will split % % 3 cards will split % % 4 cards will split % % 5 cards will split 6 cards will split 7 cards will split % % % % % % To be certain you understand exactly what this table is telling you, look at the cell that says 5 cards will split (between defenders hands). If defenders hold 5 Clubs, however they split, you and dummy hold 8 Clubs. If yours are split 4 4, there s no chance for more than 4 tricks, unless they are trump, of course. But if they re split 5 3, how many tricks might you take? 5 hopefully? 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 statistically. Not 100%, but 68% of the time, which are great odds for you. They will be split 4 1 about 28% of the time a little over 1/4 of all 5-card split opponent hands. And they could be split 5-0, but the odds of that are so small you don t even have to consider it. (4% or so?) I have emphasized high percentage splits by bolding the top split odds in each box. Do you see any pattern to help you memorize this table? There is one clear pattern: look at the odd-numbered holdings of 3 or 5 or 7 cards. Those 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%. Great! Pg. 2 Bob McConnell, 2019

3 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 odds that you do. 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 so probably in other suits as well. Don t use it blindly: Count! Count! Count! Summary: Odd numbers of defender cards split close to even most of the time and Even numbers split not evenly about half of the time and evenly about 38% of the time. Remember this one sentence and you know what the whole table says. Some good news: Split odds are often cumulative, meaning you can add the odds together with two different suits 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. So what? What if you need only 4 Hearts tricks to make your contract, not all 5? Remember the odds (38%) for a 3 3 split of 6 cards and remember that you have an 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? A 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 a total of 86% odds to take 4 Heart tricks. How does 86% odds of taking 4 Heart tricks sound? Sounds like a winner to me. Pg. 3 Bob McConnell, 2019

4 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 sure side entry for the 5 th Heart, you should duck an early Heart trick (e.g., deliberately lose the first one) to guarantee 4 Heart tricks with 86% odds. Simple. There are other common split cases, if you are conscious of cumulative possibilities. 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 under the Ace or King; don t try a finesse: Why is that with only 40% odds for a 2 2 split? Because this is not about odds for any 4-card split: you are looking for only 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%, for total odds of at least 52.5 %. So, go ahead and play 9 ever; 8 never confidently. 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 bit better than 40% odds, right? But now you know why technically and logically. Figure the following problems out from the opening lead. Pg. 4 Bob McConnell, 2019

5 What Are the Odds? - How would you go about playing these hands? 1 74 A T742 2 J A AT AQ T8 4, K lead 4, Q lead 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 AK A92 A AQ4 K AQJT 52 3 NT, K lead 3 NT, Q lead 3 NT, 8 lead 6, Q lead 62 A743 AKT9 AKQ AJ AK K AQ3 K76 Q84 KQJ AKQT8 A 73 AQJT9 ===================================================== 9 AQ J76 Q643 AT72 10 AK KJ3 KT9 11 T92 A53 7 AQT AQ A9 6, K lead 5, Q lead 4 ; K lead 4 ; Q lead J952 AKQ AT KQ AQT AKJ87 T64 T82 KJ KJT864 A65 AQ 72 Pg. 5 Bob McConnell, 2019

6 Answers: 74 A 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. Why Clubs? 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 another entry. J A ; 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 Diamond or Club loser on the J. ======================================================= AT NT, 3 Q5 AKQ5 AQ86 AKQ #3. Your Spade stopper is gone on the 2 nd trick, so what s left? You are in the dummy only once, with just 8 winners. Do you play on Hearts to split or take the Diamond finesse? You can t do both because of Entry problems. Odds of a 3 3 Heart split are 36%; while odds of the Diamond finesse working are 50%, so take the finesse. AQ T8 3NT, 3 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. Pg. 6 Bob McConnell, 2019

7 AK #5. 8 winners with 2 chances for another trick: if the Spades split 3 3 or you can finesse twice in Diamonds. 3 NT, K 3 NT, Q Again, you only need to win only 1 of 2 Diamond finesses for 9 tricks. 62 A743 AKT9 AKQ 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 A92 A8654 AJ AK K #6. There re only 6 top winners, meaning you need 3 more tricks. There re 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. Take it. # East opened 1 Spade; you bid AQ NT and partner went to 3 NT. K9652 AQJT West has? HCP? NT, 8 You have 8 top tricks and 8 Diamonds with the K and 6, Q Q. AQ3 K76 Q84 KQJT East has the AJx so don t try to set up Diamonds. Instead, lead low from dummy toward your Q. If East takes her A, you ll have 4 s, 2 s and 3 s. If she ducks the low Diamond, take the Q and start Clubs for 9 tricks. AKQT8 A 73 AQJT9 #8. Win the lead, collect trump in 3 rounds, (90% odds) and then what? Maybe lose 2 minor suit finesses? Possible, but dumb. 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 trumped in dummy. Pg. 7 Bob McConnell, 2019

8 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. AK KJ3 KT9 6, K 5, Q J952 AKQ AT KQ AQT #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. ======================================================== 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%. AQ A9 4, Q lead 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 brings your odds to 84%. Pg. 8 Bob McConnell, 2019

DECLARER PLAY TECHNIQUES - I

DECLARER PLAY TECHNIQUES - I 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