The thing about an ELO system is that it is designed to measure skill. After playing for long enough, you rating should reach an equilibrium; sometimes drifting up a little, sometimes down a little, but always around about a certain value.
If you’re getting a 1-2 points from your best scores, and losing 1-2 with your bad scores, it sounds like you’ve reached your equilibrium point. You now know roughly what your skill level is.
The only legitimate way - the only way that means something - to improve your ELO rating from there is to learn to play better.
(Now, if you regularly abandon games that are going badly, that will artificially inflate your rating, as others point out. Even that is only temporary, though. Once a player stops this practice, their rating will gravitate to that equilibrium again. More recent games matter more in an ELO system.)
So, how to improve your skill? Well, if you are rated ~500, you’re right at the bottom end of Expert. Many good players restrict their games to Expert and up, so you’ve just gained the opportunity to play with people who know the game better than you. Play with them, observe, learn. After a game is done, talk about it. There are players who will be willing to say what you missed, or describe how they knew to make a certain play. The best players (in many games, not just Hanabi) get that good through discussion and analysis in addition to play.
At 500, you should be prepared to show that you know the basics. As well as direct play clues, you should know basic finesse and reverse, and be able to respond to a bluff even if you aren’t confident enough to give one. You should know how to give a standard save clue, and when to do so. It’s you are going to attempt bluffs, you should know to only bluff the next player. You should be aware that each player is usually in the best position to clue the player who comes after them (but this is a loose guideline - you should also understand that there are often good reasons to clue out of turn, and not automatically play random cards or, worse, have a tantrum because somebody “stole” your clue); the point here is to allow your partners to clue, and not give every clue you can see just because you can see it.
To reach 600, I’d say you should be able to give a basic bluff, and you should understand long finesse. By now, you should be thinking about the consequences of your moves - “If I clue this bluff, what happens after the response?”
By 700, you should understand trash bluff. Getting to 800 is about good judgement more than individual techniques, and hopefully you can pick up advanced moves like double bluff and layered finesse somewhere in the 750-950 region.
The other thing is that increasing your rating requires demonstrating better skill consistently, and getting 25 in a basic game isn’t much of a demonstration of skill. By playing harder variants, if you still get max score or close to it consistently, you will demonstrate your skill and gain rating points faster. Be warned, though, this only works if you have the skill to back it up.
Two other points… Playing larger games tends to net points faster, although the downside is that you are relying on more people to all play well. Frankly, I think 3-player gives too few rating points for the difficulty of the game, compared to 4-player and 5-player. And 2-player is a whole other game, strategically speaking. Some players play 2-player most of the time and then are useless in 3-5 player, even if their 2-player games get them a high rating. So don’t just play 2-player if you want to be good (at anything other than just 2-player), not just be rated good. And likewise, I’m possibly not so skilled at 2-player, because I rarely play it.
