Gudas played in the Czech Extraliga with HC Kladno during the 2008–09 season. Gudas was selected by the Everett Silvertips of the Western Hockey League (WHL) in the first round of the CHL Import Draft with the 20th pick. After going un-drafted in the 2009 NHL Entry Draft, Gudas was invited to the Los Angeles Kings training camp that year but was not offered a contract. He then joined the Silvertips that fall. He had a strong season with the Silvertips, posting 7 goals, 30 assists, and 151 penalty minutes. His play for the Silvertips paid off when he was selected by the Tampa Bay Lightning in the 2010 NHL Entry Draft with their 3rd-round draft pick. Gudas participated in the 2010 Lightning developmental camp that ran from 10–14 July. On 8 August 2010, the Lightning announced they had signed Gudas to a three-year entry-level contract.