Andrew:

Odd numbers break evenly, even numbers break oddly

More Ditties BridgeCast this week from Level 3. BridgeCast is Andrew's monthly subscription service, join him as he presents a daily deal. To find out more click here. Taken from Andrew's "Rules, Acronyms and Ditties" book which is, providing the inspiration, for his current series of Level 3 daily videos on BridgeCast.

If you are missing an odd number of cards in a suit, they rate to divide as evenly as possible. Seven missing cards rate to split 4-3; five missing cards rate to split 3-2; three missing cards 2-1.

If you are missing an even number of cards in a suit, they do not rate to split evenly*. Six missing cards are more likely to be 4-2 than 3-3; four missing cards are more likely to be 3-1 than 2-2.

Why? There are two ways a suit can split 4-2: four on your left and two on your right; or two on your left and four on your right. There is only one way a suit can split 3-3. The same argument applies to 3-1 versus 2-2.
*A 1-1 split is slightly more likely (52%) than 2-0.

Six	Five	Four	Three
3-3 36% 4-2 48% 5-1 15% 6-0 1%	3-2 68% 4-1 28% 5-0 4%	2-2 40% 3-1 50% 4-0 10%	2-1 78% 3-0 22%

Six

Five

Four

Three

3-3 36%

4-2 48%

5-1 15%

6-0 1%

3-2 68%

4-1 28%

5-0 4%

2-2 40%

3-1 50%

4-0 10%

2-1 78%

3-0 22%

Do bear in mind that these are the à priori numbers and often there are clues pointing in a particular direction. Say an opponent leads the two of a mediocre suit v your 3 NT; he has just four cards there and probably no other four- card suit (it would be stronger): ergo his shape may well be 4333. Or say an opponent leads a two v your 3 NT then turns up with a singleton in another suit; he is probably 4441 (he’d have preferred to lead from a five-card suit)

South Deals
None Vul

♠	A 8 5 2
♥	A K 10
♦	10 8 2
♣	7 6 3

♠	K J 10
♥	Q 7 5 3 2
♦	7 4
♣	Q J 9

N
W		E
S

♠	Q
♥	9 8 6 4
♦	A 9 6 5
♣	K 10 4 2

♠	9 7 6 4 3
♥	J
♦	K Q J 3
♣	A 8 5

West	North	East	South
			1 ♠1
Pass	4 ♠2	Pass	Pass
Pass

Dubious but satisfies Rule of 20 (high-card points + lengths of two longest suits reaching 20).
Poor shape, but good controls. Three-and-a-half Spades really.

4 ♠ by South

Lead: ♣ Q

On our deal West led ♣ Q v 4 ♠, declarer winning ♣ A and facing a two-way choice.

Line A: Lead ♥ J over to ♥ AK throwing one club, then play ♠ A and another. On a 2-2 trump split, the opponents will score just one trump, ♦ A and one club. You will go down if trumps are not 2-2.

Line B: Lead and run ♥ J at trick two. If it loses you are down (at least one). If ♥ J wins, cross to ♠ A, cash ♥ AK discarding both losing clubs and now you can afford a 3-1 trump split and two trump losers. Ignoring the number of undertricks (and ♥ Q being doubleton), you should choose Line B because it gives you a 50% chance of success (West holding ♥ Q). Line A relies on a 2-2 trump split – and a missing even number of cards does not rate to split evenly.

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Odd numbers break evenly, even numbers break oddly