Let's say I were to come up with a game, but wasn't 100% sure on what I wanted to implement. Let's also say that I could come up with efficient algorithms to solve certain problems fast. Would it be a bad thing to implement the game based on these cool algorithms(which most likely have nothing to do with the game initially) ? Or is it smarter to just apply thought and time into the original idea to make it complete ? TIA

Depends on what sort of algorithms you decide to implement. What's the specifics?

Would you try and build a house with just a hammer? What about trying to paint a picture; would you use a hammer for that?

Probably not. While the hammer is useful in some situations - like some of the tasks involved in building a house - it's not useful in all situations. Certainly, a builder doesn't look at his or her hammer and then ask, 'what can I do with this'!

Look at the problem first and then choose an appropriate solution. In terms of game design, that means you first want to develop a game concept that has merit (i.e., you think someone would want to play your game). Then, work out what sorts of things are going to happen in your game and if you decide you need AI, then decide what sort of things the AI must do. This will lead you to the correct tool (or set of tools) for that part of the job.

On the other hand...

There is nothing wrong with presenting a 'tech demo' of an algorithm or tool you have invented. You might invent a new gas-powered hammer. That doesn't mean you want build a whole house to prove that it works... you just want to nail a few peices of wood together. Thus, if what you really want is to present your tool to other people, think of a scenario that would adequately present the relevant properties of your tool and then implement this scenario.

Cheers,

Timkin