In the process of seeking a patent on a domino-style game, I found a game with a lot of physical likeness to mine. That game was patented around 1950. Can I still file a patent since that patent has expired and our games have significant differences on playing method and number of tiles?
An expired patent does not affect your ability to file a patent application, but it certainly could affect your ability to actually get a patent.
The information in the expired patent is in the public domain and you are only entitled to receive a patent if your game is "novel and non-obvious" compared to other games that already known.
The period of exclusive rights that come with a patent is the reward we, the public, give an inventor in exchange for the inventor teaching us something we didn't already know or couldn't have easily come up with on our own. If "we" already know about a game that is the same as (or obviously similar to) the game you came up with, then you haven't taught us anything deserving of that reward.