word or term for letting someone else have a chance to win

Solution 1:

You could say you're "going easy on them".

Solution 2:

Pulling your punches To refrain from deploying all the resources or force at one's disposal

Solution 3:

One option is throw:

  1. to lose (a game, race, or other contest) intentionally, as for a bribe.

Definition no. 15 taken from dictionary.reference.com

Solution 4:

sandbagging: deliberately underperform in a race or competition to gain an unfair advantage

underplay: 1. to achieve (an effect) by deliberate lack of emphasis 2. (Cards) to follow suit with a lower card when holding a higher one

play down (to): lower one's standards (to meet the demands of someone)

(go in the) tank: deliberately lose or fail to finish (a match)