What is the right equity percentage for a potential technical partner?

You should always give someone what they deserve. Never more and never less.

Most people don't know how to do this so they guess. They try to predict the future or they look for rules of thumb or they try other ways of guessing. Kind of like you are doing now.

The best way to determine this is to consider one person's risk relative to others.

When someone contributes to a startup company and doesn't get paid they are accepting risk. The value of that risk is equal to the fair market value of the contribution they made. For instance, if you could earn $100,000 a year doing whatever it is that you do and you do it for a startup without getting paid you are, in effect, risking $100,000 a year.

Taking risk in a startup company is essentially betting on the future outcome of the startup. If you and I bet $10 on the same hand of Blackjack we are each betting the same amount and, therefore, each deserve exactly half the winnings (if any).

So, the right way to split equity in a startup company is to keep track of what's been contributed, then perform this simple formula:

Individual Ownership (%) = Individual Risk/Cumulative Risk

The model changes over time as more contributions are made. Each day a person contribute their stake would change. This means that at any given time, no matter what changes, who joins or who leaves. Everyone always has exactly the ownership they deserve to have.

Unlike traditional models that require us to predict the future, the relative risk model is based on easily observable values in the market. Everything has a fair market value.

So, the answer to your question is simple. Add up the risk he has taken and divided it by all the risk taken by everyone (including you). Each person's share can be calculated this way and the total will always equal 100%.

On day one, before he's done anything, his ownership will be 0%. As it should be. Over time, as he risks, his % will change based on relative risk.

This is a perfect, unambiguous formula. Every other equity model lays the foundation for disputes later on. Only a relative risk model will give you the fair answer.

I've written a book on this topic, called Slicing Pie, you may have a copy if you contact me through Clarity.fm or SlicingPie.com.

If all the CTO is doing is coding software that you came up with, designed, and made previous versions of, then yes 40% is too high, and 30% even may be a bit high, as the website you cited suggests. It depends largely on how indispensable he/she is. Do they have unique skills that are uniquely contributing to the project (other than the fact that they've been there for a while and know the product well by now). If not, then you could very well have freelance programmers do the work instead, using ODesk, elance, etc. To use freelancers effectively you can use the 'Code as Cards' system developed by Amol Sarva (link to free book: http://a.sarva.co/wp-content/uploads/2014/12/2014-Dec-9-Ship-While-You-Sleep.pdf). I've worked with Mr. Sarva in the past (co-founded Halo Neuroscience with him), and the system works well once you get past the first 1-2 weeks and have stable, dependable programmers working for you. If you'd like to talk more about any of this I'd be happy to do a call.

Yeah for what you have mentioned it seems 30% is more than enough.
Now it is also important to keep in mind how important is technology going forward. If your business is totally tech dependent for example ad-tech or artitifical-intelligence then 40% is good. But if your business has considerable amount of offline work for example ecommerce, getting vendors and partners on platform then 30% is more than enough.
Finally if you are going to be CEO and other guy is CTO and he gels well with you and works with complete alignment of goal then you can consider giving him 40%. Its pretty hard to find awesome tech guys these days. And more than that if he realizes to work with you as per your plans then its very very helpful.
We can also chat in detail if you want.

Sometimes the best way to break a stalemate over equity is to agree on equal shares but give someone a faster schedule or some portion vested up front — or, conversely, agree to allocate a larger percentage but tie it to a longer vesting schedule and/or milestones. Shares aren't really "owned" until they're vested.

There's no hard and fast rule about vesting any more than there is about exact equity percentages, yet entrepreneurs often assume everyone's shares must vest according to the same schedule. Instead, I recommend taking a hard look at past, present, and anticipated future investment of "sweat equity" in the venture by each co-founder. More often than not, in my experience, someone started working first/harder/longer, quit their day job, made a critical breakthrough early on, etc. — or is expected to pull the most weight in the coming months, solve thorny technical problems, recruit vital team members, and so forth. (Yes, it's a guesstimate, but the same is true of valuation and almost every other metric at an early stage startup.)