I'm currently attending college and am almost finish with my Bachelors in Computers science.I plan on getting my masters in computer programming in hopes that it will help me get into game design. If not I at least will have a fallback plan in any other IT related field. I'm just curious as to how likely it is to happen for me.
You should notice that game design is nothing that is necessarily related to programming. It also applies to board games, card games and every type of game, computer games being one of these. It's a different field and being a good programmer doesn't mean you're a good game designer. However being a programmer already can help you becoming a good game designer because as such you have to have knowledge about what's possible in game development.
I'm currently on the same path working towards my masters degree in media informatics and thinking about how to get into the games industry. Unless you want to be an indie you don't have to master both programming and game design.
Either way start making games with one of the popular engines out there. You will have to be the programmer and the game designer at the same time. Make a lot of games. Most of them will suck but you'll become better and better. Ragarding your question if it's going to happen it won't just happen. You'll have to make it happen and it's not going to be easy.
Let's talk about my experience. I did a diploma in game design, cool right? Then I did a year of games design at degree level, super cool. And then my dreams kinda ended there. I found getting work in the game industry extremely difficult and I had qualifications that were intended to allow easier access into the industry. I ended up with an apprenticeship in software development, a real turn around.
But I still have this spark of games design and development in me, so I took to making my own game. I made a really bad Flappy Bird clone to start with (to get used to GameMakers engine) then took to Unity and Unreal, and found what I enjoyed to work with (which was 2d games with GameMaker.)
I am now working with a company and making assets for games in GameMaker, as well as working on my own project. It will be slow, but this way you have an income, you can live comfortably but also enjoy what you love to do. Making games is fun, but you don't simply make a game, you craft it, mold it from your creativity.
When I visited Ubisoft in Newcastle, one of the designers told me "Never make a game the people want, make a game you want... people will soon realize it's what they wanted all along."
To sum it up
Follow your dream (if it is your dream.) But just be careful, and put your heart into a game you want, and just work on it. If you need help with anything, or a direction to go with creating your first indie game, just ask.
Hope this helps.