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Surrey 195 for 6 (Roy 58, Curran 50, Qais 3-28) beat Kent 191 for 5 (Cox 54, Blake 50*) by four wickets
A full house crowd of 30,000 at the Kia Oval lapped it up as 25 sixes in all were struck as Surrey, with 14 of those blows in their 195 for 6, hunted down Kent's 191 for 5 with nine balls to spare.
It was Surrey's tenth win from 13 group games, with one match rained off, and both Laurie Evans and Will Jacks also made solid contributions with the bat as Kent's bowlers simply could not defend what seemed a challenging total.
Alex Blake had earlier entertained the packed stands with 50 not out from 25 balls included four sixes and two fours, but even his hitting paled besides the extraordinary strokeplay of Roy and Curran.
Fast bowler Matt Milnes, who finished with the painful figures of 3-0-48-0, felt the full force as Roy took three successive and almost contemptuous leg-side sixes and then a four from his second over, the sixth of the innings, which cost 24.
And, when Milnes was recalled for the 17th over, Curran twice smashed him straight for six and also pulled him with whiplash force for another six over deep square leg as 19 more were plundered from it.
Both Curran and Roy hit five sixes, with opener Roy also striking five fours before he was bowled by spinner Qais Ahmad in the seventh over.
Aaron Hardie pulled Grant Stewart for six in 15 on debut, before being run out failing to answer Curran's call for two, and Qais later removed both Jamie Overton and Curran in his final over to end up with a creditable 3 for 28. But, even though Kent tried seven bowlers, the fit-again Darren Stevens strangely did not bowl at all and Jamie Smith ended the game by crunching Fred Klaassen over cover for four.
Kent's total was based around three sparkling innings - 41 off 29 balls by Tuwanda Muyeye and Jordan Cox's 31-ball 54 at the start, and then the explosive Blake at the end. Perhaps Blake, indeed, should have come in one place earlier, rather than at No. 5, so cleanly did he strike the ball.
Blake's most eye-catching stroke was when he skipped down the pitch to Sunil Narine, whose first three overs had cost only 12 runs, to smash the West Indies mystery spinner a long way over the wide long-on boundary for six. It was a stroke which also inspired George Linde to drive Narine back over his head for another six as the Trinidadian's final over, the 18th, cost him 14.
There were also maximums for Blake high over extra cover and square cover off Overton and Reece Topley, respectively, plus another huge blow mowed into the stands over wide mid wicket off Jordan.
Put in, Kent lost Joe Denly for 5 in the second over when allrounder Hardie, Surrey's overseas player replacement for the injured Kieron Pollard, struck with his third ball for the club to have the former England batter caught off a skier at extra cover.
But, kick-started initially by Muyeye who later in that over superbly picked up a leg-stump ball and deposited it high over the deep square leg ropes for six, the second-wicket pair played beautifully to add 75 in 6.3 overs - in the process accelerating Kent to 67 for 1 after the six-over powerplay as 24 also came off Hardie's second over, the fifth.
Muyeye pulled Hardie for six over long leg and guided the next ball behind backward point for four before Cox hit the Australian for two sixes, first flicked over deep square leg and then hammered to wide mid wicket.
A risky second run to deep midwicket in the eighth over saw Muyeye run out by Evans' sprint to the ball, pick up and throw and Cox, after hitting Overton for three successive fours in the ninth over, fell to a good catch by Roy running back at short third five overs later, when he skied an attempted big hit at Overton.
By then Jack Leaning had gone for 6, caught by keeper Smith sweeping at Dan Moriarty's left-arm spin and Stevens kept Blake company for a while before, on 13, skying Narine to Roy running around behind the bowler from mid-off.