eye for/to the main chance, to have an

have (or with) an eye for (or on or to) the main chance

look or be looking for an opportunity to take advantage of a situation for personal gain, especially when this is financial.
This expression is taken from the use of main chance in the gambling game of hazard, where it refers to a number (5, 6, 7, or 8) called by a player before throwing the dice.
See also: chance, eye, have, main

eye for/to the main chance, to have an

To look out for one’s own best interest or for the opportunity that will be most profitable. The term is thought to come either from betting in cockfights (main being an obsolete word for cockfight) or from a game of chance called hazard, in which the main signified the number (anywhere from 5 to 9) called by the caster before the dice were thrown and chance signified the second throw of the dice, which determined the total. In any event, the expression dates from the sixteenth century, was recorded by John Lyly and Shakespeare, among others, and appeared in John Ray’s English Proverbs of 1670.
See also: eye, have, main