I've comprehensively researched the requirements of publishers, and found the following:
First and foremost, most publishers are looking for games with novel mechanics and themes. They want a good game, but they also have to be able to sell it. Many have a box on their submission form, asking "why is this game novel?"
The easiest games to get published are "wide appeal games" — games that anyone can and would play. These games have light strategy, easy turns, and short playtimes (like 10-45 minutes.) They have simple rules (two pages or less), that are explainable in a few minutes. These games have almost no text, and gameplay that doesn't require you to think too hard. The game should focus on a single, simple activity.
A wide appeal game prioritises ease of play over almost everything else. If it's not easy to understand and play, it's not a wide appeal game. This will usually mean sacrificing strategic depth and/or replayability. The Depth:Complexity ratio here is extreme.
The theme should be strong, simple, fun, and not a niche interest. Things like fantasy, sci-fi, and war are not wide appeal. Nor are dry things like trading, history, or industry.
Randomness is much more acceptable in wide appeal games. Excitement and fun take precedence over strategy and fairness.
Despite all this, publishers are not looking for shallow novelties. They expect a bit of depth, and as much replayability as possible.
A much smaller number of companies want meaty strategy games that come in a big box.
Radlands is a strategy card game. It originally had a futuristic theme, and it's not hugely novel. It was extremely hard to get this game published, despite being a great game. I almost ran out of publishers.
Publishers are overwhelmingly not looking for some specific themes and types of games.
I've looked through the requirements of dozens of publishers, and compiled the following list of the things publishers overwhelmingly don't want:
Like Chess or Poker, or anything that includes their components. These are extremely dull. No publisher is interested in this.
Collectible card games like Magic, with packs of random cards you trade with friends, are instant death. Put all the cards needed to play into a box instead, so the customer can get the whole game without trading, collecting, and spending a fortune.
Games where you start with a bad deck, and add cards to it to improve it. They can be very dry, and tend to be very high in work. Most importantly, there are just too many of these. Never jump on the latest fad, or even the fad before that.
These are games like checkers, which have no theme. No matter how hard they try, a publisher can't sell a game about cones hopping over cubes. This is easily fixed, however. Just add an appropriate and attractive theme for your game, and come back.
These games only have appeal to the mass market, and the mega-companies that make such games don't accept submissions. A few word games do get published, but it's a very small number. You'd better have something unique to offer. "Scrabble 2", or "Box of Quiz Cards #981345987" isn't going to cut it.
These tend to be 90% education, and 10% game. These are not games. Go to an education provider.
Roll a die, and move that many spaces. This type of game is obsolete, and will be dismissed instantly.
This fad is not appealing to everyone, and has already been done to death.
A very small number of publishers will accept war games. You're going to need to know your stuff, because this is a niche and hard-core market.
If you can make your game more publishable, by changing its theme or mechanics, you should consider doing so.