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The two-time winners, who last toured the country way back in 2002, suffered a 0-3 whitewash against the same team at home in 2009, when the West Indies Cricket Board (WICB) fielded a second-string team following a financial spat with leading players.
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But according to Shakib, that's history.
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"The West Indies did not have their main players in that series, but they are back now which makes them a very good side," he said.
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"We will have to be at our best to beat them. I am confident we can win, but for that to happen we must play good cricket."
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Bangladesh fought back after losing the tournament opener to India by 87 runs to beat Ireland by 27 runs despite being bowled out for a modest 205.
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The West Indies too bounced back in style thrashing the Netherlands by a massive 215 runs in New Delhi on Monday, after the seven-wicket defeat to South Africa in their first game.
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Shakib said Ireland's sensational win over England in Bangalore last night had thrown open the race for the quarterfinal berths.
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"It definitely makes it wide open," Shakib said. "No team can afford to lose from here."
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Unheralded Ireland stunned England by three wickets after Kevin O'Brien smashed the quickest century in World Cup history off 50 balls to help his team race past a daunting target of 328.
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"I am not sure how much tougher the Irish win will make our chances of qualifying for the quarter-finals," said Shakib.
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"It will benefit us only if we beat England next week. All I know is that we have to play well to win against any team."
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Shakib said 300-plus scores would not be easy on the slow Sher-e-Bangla wicket, despite a high-scoring tournament opener.
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"The wicket here is not that easy to bat on," he said. "I also think there will be more spin this time than in our previous two games."
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