Green’s Dictionary of Slang

1. an expert.

1896

‘’Arry on Spring-Time and Sport’ in Punch 18 Apr. 184/3: [He] bikes, a fair reglar buster. ’E is ‘a dead open and shut,’ / As the Yankees remark; and I envy ’is style.

2. (US) an unarguable, inescapable situation.

1872		G.P. Burnham Memoirs of the US Secret Service v: Dead Open-and-Shut, a pretty sure thing; a clear fact.
1908		‘Old Sleuth’ Dock Rats of N.Y. (2006) 18: His accounts will all be cleared tonight! the lads will have a dead open and shut on him.