Your idea has no value. The value is in the execution.
No one is going to steal your idea.
No one is interested in your half-made game, and until very late in development, your game isn't publishable anyway. It might be a 6.5/10 game up until the last 10% of its development time, before finishing as an 8/10 game. Even if someone stole your game in its entirety, they'd have to keep working on it.
People think their own ideas are brilliant, and that's what they want to work on — not your silly game.
The reality is that game theft is basically non-existent, and the few rare cases were theft of already-published, successful games.
A publisher who stole an amateur designer's game would instantly be ruined by the bad publicity.
Work with other people on your game, all the way through. Start with people you know well, and build up to playing with random gamers, via the internet. You'll feel much more comfortable with this, once you get to know a few people. I don't just post my game for anyone to download and play, but many people do. A future publisher might not approve of that level of publicity, so I wouldn't necessarily go that far.
What you gain from other people's input is crucial. Even if there was a real chance of my games being stolen this way, I'd still do it. There is almost no way to develop a great game in secret.
Don't get a patent. A patent or NDA (non-disclosure agreement) marks you out as a laughable newbie, and publishers would likely reject your game on this information alone. You also can't patent ideas; only specific text, pictures, and explicit concepts.
As such, you can legally make a game very similar to an existing game. Your "Scrabble but with numbers" game is legal, though most publishers aren't going to be interested in it.
Designers are constantly making games that are similar to, or evolutions of previous games. This isn't even frowned upon. You just need to make sure you're adding something new, or the game won't be interesting enough to publishers and players.
Don't make a game that specifically uses an existing brand. You are not going to be able to get the rights to My Little Pony or Star Wars. Those companies will go to established professionals if and when they want a game. If you really like an existing brand, you can very easily create your own fantasy world, that's clearly inspired by that world.
"Dinosaur Island" is clearly a Jurassic Park-themed board game, even though it doesn't say so.