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Difference between Bet on the wrong horse and Put the saddle on the wrong horse

bet on the wrong horse—(also: back the wrong horse) base one’s plans, etc. on a wrong guess about smth.:

  • To count on the family farm as an important thing in the American future looks like betting on the wrong horse.

put the saddle on the wrong horse —(also: get the wrong pig by the tail) lay the blame on the wrong person:

  • Blaming the teacher for the lazy student’s academic failure is putting the saddle on the wrong horse.