The best way to increase your chances of being employed as a game developer is to get your hands dirty and actually work on the development of some small games.
You say that you are "interested in programming games", which makes me believe that you haven't developed any games, yet. I advice you to stop thinking and start doing. However, the first order of business will not be to specialize in any of those fields. Let me elaborate.
When I interview you for a job, if you tell me you are interested in programming games and your specialty is game AI, I will immediately ask you which games you worked on. If the answer is "none", I don't care about how many books you read or how you believe you are an expert in game AI. You won't be hired, period.
To obtain game development experience in a specific field such as AI, you need to seek out others that are developing games and try to get into their teams. You want specialization, remember? A generalist can develop the whole game, but a specialist needs to work in a team. However, you will again be asked for previous work for someone to trust you with the AI of their game, let's say. Even if you will work free of charge. So, it's a chicken and egg problem right there. Basically, you can't just specialize in anything with no prior game development experience.
Here's what you need to do: you need to forget about specializing and start contributing to the development of a game in any way you can. You can develop a simple game using a game engine such as Unity, or ask someone else developing a game and they will tell you what they need done. Then you'll figure it out and that will give you experience.
Once you have something to show, not only you will have a better chance of joining a team, but also you'll have a better idea on fields that you can specialize in or that you don't like to work on. Trying to make a decision right now without that experience is like marrying someone without getting to know them. You cannot know if you will hate coding game AI unless you have some relevant experience.