E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Bilk.
To cheat, to obtain goods and decamp without paying for them.
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The landlord explained it by saying that a bilk is a man who never misses a meal and never pays a cent.A. K. McClure: Rocky Mountains letter xxii. p. 211.
To bilk in cribbage is to spoil your adversaries score; to balk him. Perhaps the two words are mere variants.