With Australia made to bat first in Southampton, Smith walked in at 82-2 after opener David Warner was out for 43, caught at deep midwicket. Smith hit 116 off 102 balls, including three sixes and eight boundaries.
He was out, caught and bowled by medium-pacer Tom Curran on the penultimate ball of the innings. Australia made 297-9, and England was dismissed for 285 with three balls left. The top seven England batsmen made starts, but only James Vince (64) and stand-in captain Jos Buttler (52) scored more than 40.
At the Oval, Ross Taylor hit 71 and Kane Williamson 67 as New Zealand reached 180-4 in the 38th over to overhaul India's 179 all out in the 40th over. India, which chose to bat first, was 115-8 until Ravindra Jadeja hit 54 and combined with Kuldeep Yadav for 62.
New Zealand fast bowler Trent Boult took 4-33 in 6.2 overs and medium-pacer James Neesham 3-26. Virat Kohli was bowled by medium-pacer Colin de Grandhomme on 18, beaten by a ball which cut in late. The warmup results are unofficial as they're 13-a-side ODIs.
On Sunday, Bangladesh and Pakistan meet in Cardiff, and South Africa face the West Indies in Bristol.
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