Source: Percentages
I found a useful summary in a bridge book the other day, and thought I’d share it with you. It’s from Sharpen Your Bridge Technique: How to Think Like an Expert by the prolific Scottish writer Hugh Kelsey. In this book, Kelsey goes well beyond what’s here; he assumes you know this stuff and uses it as a springboard to talk about how to use the information. First, though, you have to know these numbers backwards and forwards; they come up on just about every hand.

If you are missing 4 cards:

• 4 cards will be divided 2-2 40% of the time
• 4 cards will be divided 3-1 50% of the time
• 4 cards will be divided 4-0 10% of the time

If you are missing 5 cards:

• 5 cards will split 3-2 68% of the time
• 5 cards will split 4-1 28% of the time
• 5 cards will split 5-0 4% of the time

If you are missing 6 cards:

• 6 cards will split 3-3 36% of the time
• 6 cards will split 4-2 48% of the time
• 6 cards will split 5-1 15% of the time
• 6 cards will split 6-0 1% of the time

If you are missing 7 cards:

• 7 cards will split 4-3 62% of the time
• 7 cards will split 5-2 31% of the time
• 7 cards will split 6-1 or 7-0 7% of the time
There’s ways of expressing this as mnemonics (although I’ve never found them very useful). The one I’ve seen most often is “Even splits odd, odd splits even”.  That is, an even number of cards will tend to not split evenly, but an odd number of cards will tend to split evenly. Where this mostly comes in handy is:
• When you find yourself in four of a major on a 4-4 fit, take a deep breath and ask yourself how you will handle it if the trumps split 4-1 or worse, which they will do about 32% of the time — or once in three times.  In other words, every third hand you’ll have to deal with RHO or LHO having four of your trumps.  (And every tenth hand, you’ll have to deal with RHO or LHO having five of your trumps.)
• The reason for that old saying “Eight ever, nine never” — which is to say, if you have eight trumps, finesse, and if you have nine trumps, play for the drop — is not quite right.  If you have nine cards, you’re missing four cards, and four cards tend to split 3-1 half the time, as against 2-2 only 40% of the time. The reason why that saying works is mostly because it gives you a rationale for proceedings. If you don’t use it, you might get forced into trying to decide what will happen if RHO or LHO has three trumps.
• And if your 3NT contract depends on either a trump finesse or a 3-3 split in the side suit, cash three rounds of the side suit first; you’ll only get that lucky 36% of the time.
I don’t think it’s necessary to know these percentages to the exact digit; I tend to think of most of these in terms of thirds, and I tend to ignore the terrible splits (because everyone will be dealing with them and no one will be prepared). But you must know them approximately; it’s absolutely necessary, so start memorizing.

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