Alcinas started competing in PDC Europe events in 2010. After reaching the quarter-finals of a Players Championship in Haarlem in June 2010, he qualified for the European Championship via the PDC European Order of Merit. He was defeated 6–3 in the first round by Mark Walsh, despite hitting a 160 checkout to go 3–2 ahead. Alcinas is an accomplished soft-tip darts player and won the 2010 Soft Tip NDA World Championship.

He teamed up with Carlos Rodríguez to represent Spain at the 2010 PDC World Cup of Darts. They defeated Japan in the first round, before knocking out the top seeds England (represented by the world's top two players, Phil Taylor and James Wade) 6–5 in the second round. In the group stage, they lost to Wales but defeated the United States and Scotland to qualify for the semi-finals, where they were whitewashed 0–4 by the Netherlands.

Alcinas qualified for his first PDC World Darts Championship in 2011. He lost 0–3 to James Wade in the first round.

Alcinas reached his first Players Championship final in January 2011, losing 4–6 to Ronnie Baxter in Halle, Germany. He qualified for the 2011 UK Open, defeating Mareno Michels in the first round before losing 0–4 to Michael Mansell in the second round. He also qualified for the 2011 European Championship, where he lost 2–6 to Kim Huybrechts in the first round.

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