After put in to bat by West Indies, Ross Taylor scored his 10th Test century to guide New Zealand to 307 for 6 at stumps on day one.
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New Zealand hope to go one better and get their first win in 11 matches under Hesson and captain Brendon McCullum in the second Test in Wellington.
The Basin Reserve pitch is expected to be livelier than the strip at the University Oval, which produced a high-scoring draw in the first Test, with the help of rain in the final session.
West Indies: Kirk Edwards, Kieran Powell, Darren Bravo, Marlon Samuels, Shivnarine Chanderpaul, Narsingh Deonarine, Denesh Ramdin(wk), Darren Sammy(c), Shane Shillingford, Tino Best, Shannon Gabriel.
New Zealand: Hamish Rutherford, Peter Fulton, Kane Williamson, Ross Taylor, Brendon McCullum(c), Corey Anderson, BJ Watling(wk), Tim Southee, Ish Sodhi, Neil Wagner, Trent Boult.