The Tigers surpassed their previous total of 288 runs at Zahur Ahmed Chowdhury Stadium in Chattogram.
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Mushfqiur hit 64 off 55 while Mahmudullah remained unbeaten on 64 off 43 balls with three sixes and fours.
And Tamim Iqbal and Shakib Al Hasan also hit a 50. Tamim scored 64 off 80 balls with three fours and one six while Shakib added 51 off 81 with three fours.
This was the second time when Tamim, Shakib, Mushfiqur and Mahmudulla hit a 50 in a single ODI.
Overall, it was only the third time when four or more Bangladeshi batsmen scored 50 or more in a single ODI.
However, Tamim and Shakib were slow to score in the soil of Chattogram where making runs is easier than Dhaka.
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Najmul Hossain Shanto, who is batting at number three in this series, disappointed once again. He came to the crease early as Liton Das had been removed in the first over of the match.
However, Shanto failed to capitalise the chance as he fell prey to Kyle Mayers, only scoring 20 off 30 balls. He managed to score 1 and 11 in the first two games.
For the West Indies, Alzarri Joseph was the best bowler taking two wickets for 48 runs in 10 over while Raymon Reifer also bagged two conceding 61 in 10 overs.
Debutant Keon Harding gave away 88 runs, the most expensive figure by a Caribbean bowler on debut.
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However, no team won an ODI chasing more than 286 runs at Zahur Ahmed Chowdhury Stadium. So the West Indians will have to make a record to win the last match of the series.