In March 2014, Alcinas beat Glenn Spearing and Matthew Edgar to reach the third round of the UK Open for the first time in his career where he was thrashed 9–2 by Christian Kist. He advanced to the last 16 of an event for the first time in over a year at the seventh Players Championship courtesy of victories over Nigel Heydon, Mark Barilli and Stuart Kellett, before losing 6–3 to Keegan Brown. In the second round of the World Cup of Darts, Alcinas and Rodríguez lost their singles matches against the Dutch pair of Michael van Gerwen and Raymond van Barneveld to exit the tournament. He was knocked out at the same stage a year later this time partnering Cristo Reyes for the first time, as they lost to the Belgium brothers of Kim and Ronny Huybrechts. In individual events during 2015, Alcinas qualified for the International Darts Open and European Darts Grand Prix, but was eliminated in the first round of both. He reached the final of the South European Qualifier for the 2016 World Championship and lost 6–4 to John Michael.