If you only see a choice between "Free to Play" or hosting Ads then you have a problem greater than choosing your business model. You don't value your work enough to consider it valuable enough to pay for outright. First, ponder why that is, then address that issue.
One more: because its value depends on network effects. For example, it might be a communication service, a community forum or a multiplayer game.
Free (of cost) results in more users, which makes the service more valuable for every user. Unfortunately, it also prevents the developer from capturing this value directly.
In some cases, user segmentation and price discrimination is possible (ancillary paid features) but they come with extra design and development cost.
* it's not what I want - I prefer to deliver it for free and do not plan for it to become any source of income, just to not have costs scaling with popularity
* I don't need to sell it - I'm reasonably wealthy, with a good 40h/week job and salary. This is a side project and will loose it's charm when I convert it to a business project.
* it's hard - I work on a browser-based game (no easy to implement payment options)
In other words, it needs to be free for users and possibly earning just enough to not cost me anything.
What costs? Is hosting really so expensive, or is it something else? Obviously you have invested a lot of time. Personally, I wouldn't think twice about spending, say, $10 per month to publish something where I have invested the equivalent of $100000 in unpaid developer time (and yes, I have done that, although it's strange thinking of it in money when I did it for the challenge). Maybe it's more a psychological issue (pay for giving something away) rather than the actual cost?
Oh, I hadn't figured you were making a web game. I've thought of working on one myself (that's as far as that goes however). I would consider myself lucky to have made a web game popular enough to be concerned about the cost of running it.
Please... it's so easy to just dismiss these problems as "hey you should find a better business model" when lots of very smart people have been trying for a very long time.
Free + ads vs Paid access are the only viable models today. Anything else is an offshoot of less ads with more donations or merchandise or something else but there's no real 3rd option. If there was, we would have figured it out by now dont you think?
The OP was asking for a alternative business model for his game. I suggested he had more important things to be concerned about. Did you reply to the wrong comment?
I dont think OP's question was serious, there really isnt any other business model. And how is saying there are more important things to be worried about giving an answer to his question? Obviously not everything is worth an upfront payment and sometimes freemium is the best way to gain users and sales. Why is that somehow an "issue"?