Three is a magical number. We know as much. It's not as good as seven, but I guess that's just my personal opinion.
Three works extremely well in startups as well. I've founded several startups with two other founders, and having three people there, especially in the early days, makes sensible decision-making so much easier.
In the early days of a startup I co-founded a few years ago, one of the co-founders and I would often run into philosophical differences about delivering good user experiences. We were both very good at being stubborn and liked a good discussion, so we could easily discuss the layout of a certain page and what that meant for the rest of the user experience for hours, if you'd let us.
Having a third co-founder there who can be the tie-breaker, and refocus the team if two of the founders are veering off in the wrong direction. (I also got to be that third person in some of their conversations, thankfully!)
Three can create equilibrium, especially if you find co-founders with diverse, but somewhat overlapping interests. When my co-founders Tobias, Thom and I started Infowijs, we realised that we had the perfect combination of skills. We all brought something unique to the table, but with enough interest for each other's skillsets and focus areas that we could collaborate and delegate, without losing the whole picture.
Growing as triumvirate of co-founders as your team grows can be challenging. Because there tends to be quite a lot of overlap between what co-founders do, and because those boundaries are usually not well defined initially (since that would defeat the freedom a small team provides), this can start causing tensions later on.
One way to resolve this is to let go of the notion of co-founders for your internal team structure as soon as this is possible. In most cases, one of the co-founders will automatically gravitate more towards the CEO role. For the remaining co-founders, it's helpful to be responsible for specific areas of the company, rather than having all co-founders at the top of the org chart.
This helps create clarity to the rest of your team about main responsibilities of the co-founders, who they should reach out to when, and what objectives each person is working towards.
Of course that doesn't mean that the co-founders don't all still get to be involved in other parts of the company. Being a co-founder gives you a unique opportunity to shape the role you best see fit for yourself.