Green’s Dictionary of Slang

shoestring v.

[‘one hauls oneself up by one’s shoestrings’]

(Aus.) to increase one’s bets from a small to large amount.

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[Aus]C. Crowe Aus. Sl. Dict. 72: Shoestring, rising from a small bet to a large amount.

In compounds

shoestring gambler (n.)

(US) a criminal gambler who gradually bets more heavily and thus entices his victims to lose increasing amounts.

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[UK]Mirror of Life 23 Nov. 15/3: ‘Get up, [Buffalo] Bill. We've been done by a shoe-string gambler. Get on your outfit and let's corral the — ’.