romance is twenty times harder for gay people

About 5% of people are gay, so in any given community it's about twenty times harder for a gay person to find a partner than for a straight person.

The model is simple. Suppose you have some criteria for a potential partner: they should be around your age, your preferred gender, some level of physical attractiveness, share similar interests, etc. These criteria apply to some fraction $p$ of the population, meaning that every person you meet has a priori probability $p$ of being a potential partner. Gay people have the additional criterion that their partner must also be gay or bi; this is more or less independent of the other factors. So every person a gay person meets has probability $0.05\cdot p$ of being a potential partner (technically the 'must be gay' qualification is replacing a much less restrictive 'must be straight' filter, so a proper calculation is more like $0.05 / 0.95 \cdot p$, but this doesn't change things very much). All else equal, then, the number of potential partners within a gay person's social networks is approximately twenty times smaller than for a straight person.

Like all useful models, this one contains truth but doesn't tell the full story. There are reasons why things are better than they might appear.

• Ultimately you only need one partner. In a group of $n$ people the probability that you have no potential partners is $(1 - 0.05\cdot p)^n$, which goes to zero at an exponential rate. So in large enough groups you will have potential partners. But you need to actively filter for them.
• All else is not equal: gay people seek out gay friends and gay networks. This is one reason it's almost impossible to be gay without having it become an important part of your identity: it's close to mathematically necessary for gays to seek out gay communities. You might prefer to spend your time hanging out with fellow nerds, or rock climbers, or musicians, etc., but single gays just don't have the luxury of choosing friend groups based purely on these interests. In a large enough city you'll be able to find the intersections: gay nerds, gay climbers, etc. There will still be tradeoffs (you can only filter by so many things, so if you filter your climbing friends by being gay, you may not be able to filter by some other criteria, like living close to you, or being from the same cultural background, etc.) but the odds are better.
• Dating apps also work to filter the pool so that 100% of potential matches are gay. Again, there are tradeoffs: using them requires active effort, and gives up the other implicit filters and assumed common ground that comes from meeting people organically (there's a reason why most of my straight friends met their partners through school or friend networks). Also, any gay person using apps regularly will soon exhaust the pool in all but the largest cities. But apps are still a useful tool.
• Too much choice can be bad; constraints can be good. A naive model would suggest that people in arranged marriages should have an almost infinitely harder time forming happy relationships, since they're only ever assigned one potential partner no matter how big their networks are! But we know that in fact arranged marriages tend to be about as happy as others. You don't really have a fixed list of criteria for a partner: circumstances can bring people together, and it can be a privilege to end up in a circumstance with someone where it's common knowledge that you have no choice but to be good partners for each other.

There are also reasons why things are worse than they appear:

• Not all gay people are visibly out, so the effective multiplier is probably lower than 0.05.
• Because it's harder for us to find relationships, gay people have less relationship experience, and are on average worse at relationships than straight people who didn't have to try too hard to get practice in high school. In particular, gays are depressed at a higher rate than the general population. So the prevalence of 'boyfriend material' guys with social skills and good mental health might be lower within the 5% than in the other 95%.

Overall, the empirical rate of gay people finding happy relationships is a lot higher than the 'twenty times harder' model would suggest, though it's probably still lower than for straight people (TODO find research?). There is quite a lot of hope, but you do have to work for it by taking active steps that straight people wouldn't, like moving to big cities and finding gay communities. Objectively speaking, this will require sacrifice elsewhere, but finding love is worth some sacrifice. And you may find that the sacrifice isn't really a sacrifice after all.