He has also represented Spain at the World Cup of Pool on multiple occasions, partnering fellow Spaniard Francisco Sánchez Ruíz in the events.

[3] During the 2006 event he survived the group stage, before defeating Jörn Kaplan and Lee Vann Corteza but was eliminated in the round of 16 by Rodolfo Luat.

[8][9] At the 2015 WPA World Nine-ball Championship, Alcaide won against Chu Bingjie and Hesam Abdulaziz in the group stage to qualify for the knockout round, before winning over Yang Ching-shun and Toh Lian Han.

Alongside fellow Mosconi Cup debutant Imran Majid, the pair defeated Earl Strickland and Johnny Archer.

[16][17] Two years later, at the 2019 World Pool Masters – a field made up of previous winners – Alcaide once again won the event beating Alexander Kazakis in the final 9–8.

[19] At the 2023 Mosconi Cup he made the winning pot as he defeated Shane Wolford to seal an 11-3 victory for Europe at the Alexandra Palace.

[21] Alcaide repeated this performance, losing only to eventual winner Dennis Orcollo and win the bronze medal at the 2011 WPA World Eight-ball Championship.

[26] In March 2019, Alcaide competed in a professional snooker ranking event when he took part in the 2019 Gibraltar Open after successfully qualifying, where he lost 1–4 to David Gilbert in the first round.