Either of these options are great, its all going to come down to your personal preference of learning. If you prefer to self learn then I'd say teach yourself, build up that portfolio and jump into game development. However if you're like me and you prefer someone to teach it to you then studying abroad is an amazing experience that I've heard. Just remember that it's going to take a while either way, and that your software development background is going to help you a lot.
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Either of these options are great, its all going to come down to your personal preference of learning. If you prefer to self learn then I'd say teach yourself, build up that portfolio and jump into game development. However if you're like me and you prefer someone to teach it to you then studying abroad is an amazing experience that I've heard. Just remember that it's going to take a while either way, and that your software development background is going to help you a lot.