Tychokinesis is the ability to mentally and alter stochastic fields, which affect the chance of one event or another, thus generating good or bad luck. With this ability one could even use stochstic fields to set events into motion (as long as there is a chance of it happening anyway), causing normally-improbable things to happen, or normally-likely events to not happen. This could be positive or negative for either side.
In quantum mechanical terms, this may actually be an inversion of the observer effect, where observation of a quantum waveform causes it to collapse into a definite state. In this case, the observer - the user - seems to be able to choose which of the possible states the waveform will collapse into, bending chance to his or her will.
Of all the strategies one could think of, the most obvious would be to influence situations already in play. However, tychokinesis can also be used to charge objects, subjects or areas with good or bad luck, so that should a person or item come into contact with the charged object, they will walk along a path of causality that will initiate a sequence of unfortunate events.
One with this ability could even psychically initiate events associated with good or bad luck. Of coruse, however, you must have in mind what you would consider bad or good luck, and then your mind will bend stochastic fields in order to match whatever it is you thought of (granted that this event is possible; and greater likelihood would increase the chance of the ability working better, also).