【Advantage】 , 【Handicap】 , 【Allowance】 , 【Odds】 and 【Edge】 denote a factor or set of factors in a competition or rivalry giving one person or side a position of superiority over the other.

【Advantage】 is the general term, and implies superiority of any kind.

the adult, with trained powers, has an immense 【advantage】 over the child in the acquisition of information
—Eliot

A 【handicap】 is something, typically an artificial 【advantage】 , designed to equalize competition; thus, in golf, the 【handicap】 assigned a player is the difference between the average of a certain number of his best scores and par for the course; for instance, if the player’s best-score average is 75 and par is 72, his 【handicap】 is 3, and when he plays in a 【handicap】 match the player is allowed to deduct three strokes from his total score.

An 【allowance】 is an advantageous 【handicap】 stated as a deduction of some sort. In horse racing an 【allowance】 is a deduction from the weight that the rules require a horse to carry, granted to a horse considered to be at a disadvantage.

【Odds】 usually implies a material 【advantage】 as in strength, numbers, or resources. It is often used of such an 【advantage】 possessed by the opposite side.

• managed to beat the 【odds】 against him
  —O’Leary
• the peculiarly British quality . . . of sticking out against 【odds】
  —Contemporary Review

【Advantage】 is often stated as a difference, 【odds】 as a ratio.

• one boxer has an 【advantage】 of ten pounds in weight
• one army has 【odds】 of two to one over the other

【Odds】 may also denote an equalizing concession made to an inferior competitor; it then differs from 【handicap】 and 【allowance】 in that the concession is made by the superior competitor and not assigned by a third party.

• each side feels that it cannot allow any 【odds】 to the other
  —Bryce

【Edge】 may be an equivalent of 【advantage】 or 【odds】 but usually implies a slight but decisive superiority.

• here we have the 【edge】 on our rivals, not only because of our superior location, but also because we are reputedly reckless about reducing prices
  -Publishers’ Weekly