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India now trail New Zealand by 39 runs going into fourth day.
The 32-year-old Test specialist had played only one of the seven games that the Capitals have played so far, finishing his four overs wicketless for 26 runs against Sunrisers Hyderabad in Abu Dhabi.
Sammy had expressed anger upon realising the meaning of the word 'kaalu' which he says was used to refer to him and Sri Lanka's Thisara Perera when the pair played for SRH in the Indian Premier League.
The leg-spinner took out Shreyas Iyer (17), Shikhar Dhawan (34) and Rishabh Pant (28) as Delhi Capitals suffered their first loss.
"If you need to play in the Test series or any red-ball cricket, you've got to be on the flight in the next three or four days. If you aren't, then it's going to be tough," said the Indian head coach.
Rohit, who is recovering from a hamstring injury he suffered in the ongoing IPL, was left out of the India squad for the Australia tour on a day when he hit the nets for Mumbai Indians, sparking speculation on his fitness status.
The two have been ruled out of the two Tests against Australia and are also doubtful for the remaining two after it was conveyed to the BCCI that the duo will require close to a month to be match fit.
The Indian captain said he was kept in the dark about deputy Rohit Sharma's hamstring injury and believes the opener should have travelled to Australia to boost his chances of playing the Test series against Tim Paine's men.
Ishant, playing for Delhi, had twisted his ankle on his followthrough while bowling against Vidarbha in the Ranji Trophy on Monday.
India's senior-most pacer hurt his ankle badly while spearheading the Delhi attack against Vidarbha.
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