On their two previous trips to the Caribbean, the Sri Lankans have walked away empty-handed - losing 1-0 on both occasions in series of the same length.
But there is heightened expectation that they can achieve their first series victory in the Caribbean on this trip, when they take into consideration the relative strength of both sides.
"As a team, we have been playing some really good cricket and our Test record speaks for itself, and we have been competing away from home which has been an issue for us," said Sri Lanka captain Mahela Jaywardene.
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"We are just going to do what we do best, and we are going to concentrate on what we have to do.
"We have been playing well, but there is still room for improvement, so there are a lot of challenges in front of us, and our goal is to confront those challenges, improve ourselves, and keep moving forward.
There is also a second objective for the Sri Lankans in this series - and it is to enhance their record away from home.
Two drawn