In an interesting question here, @Masclins asks how two twins who can each experience and perceive everything the other is sensing or thinking might be able to exploit their ability. I want to ask a question where the psychic ability is much more limited in some respects but is precognitive.
Imagine that a single person has by a great deal of application developed the skill of sometimes being able to send himself a small amount of information back from a short time in the future.
By a "small amount of information", I mean on average less than a single bit. So if in the future he chooses a playing card at random - perhaps using a quantum random number generator - and then looks at it, he can with a slightly greater than evens chance predict correctly right now whether the card will be red or black. Similarly if without telling our subject an assistant decides that red corresponds to an appreciation of the British pound against the Swiss franc and black to a depreciation, and at a future time he checks how the currency market has moved and then gives the subject a card to look at accordingly, the subject can predict its colour with a similar chance of success.
If he could always predict the card colour correctly he would be sending a whole bit of information, but by "sometimes" I mean he can only do it correctly 53% of the time1, and moreover he can only manage to repeat the precognition, even at that level of success, at least a week after the last time he did it.
And by a "short time in the future" I mean no more than 30 seconds.
To restrict the conditions even more, let us assume our subject does not have access to a vast quantity of money. So for example he cannot invest a million pounds each week selling or buying Swiss francs for British pounds according to the card colour he perceives precognitively. Nor can he offer his services to a person who can stake large amounts.
How might he use his precognitive ability to amass wealth?
Edit: please note that this question is not the same or even nearly the same as this other one. The ability I am supposing is probabilistic. There is no possibility of chaining perceptions together as is suggested in the most popular answer to that question, because the ability only works (probabilistically) 30 seconds into the person's own future and only at intervals of at least a week. The second most popular answer is also not applicable, since again the ability works probabilistically with a success rate of only 53% and the person does not have access to big money. Basically his edge is very small, this is clear in the question, and it is signalled in the word "slight" in the title.
1 Technically the average number of bits of information he sends per prediction is 0.00260, so he would have to do it 385 times to send a single bit. For details of how to calculate that figure, click here. The point is that the ability is not only probabilistic but very weak. But it is no less real for that.