。
I bet him a dollar I'd sell more magazines than he would.
Literal
I [subject-が] him [than-より] magazine [object-を] many sell [thing-こと] [on-に] he [with-と] 1 dollar bet.
賭ける ('to bet, to wager') here takes several arguments: what's being bet (1ドル), what's being bet on (僕が...ことに = the proposition), and whom with (彼と). The clause [僕が彼より雑誌を多く売ること] is a nominalized wager proposition. A multilayered structure typical of formal descriptive Japanese.