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Suppose you are missing Kx in a suit. It is (exactly) 52% that the suit splits 1-1. Everybody knows that.
How about missing Q432? J65432? etc.? Will the suit run if you play it from the top?
Missing 2k cards (0<k<7) including one card of particular interest, the probability that either the suit breaks evenly or that the particular card is in the short hand is close to (51+k)%.
| k | probability | application |
|---|---|---|
| 1 | 52% | Kx |
| 2 | 53.13% | Q fourth |
| 3 | 54.01% | J sixth |
| 4 | 55.03% | 10 eighth |
| 5 | 56% | 10 missing, Ace not long |
| 6 | 57.04% | 12 missing, Ace not long |
| 7 | 58.2% | ? |