I made a spreadsheet the last time I was mortgage shopping, and the break even point on buying points was five or six years then, too, regardless of how many you bought. Keep in mind that it still makes sense to buy down more if you are going to carry the same loan longer, due to the additional payoff after the break even point.
But shop thoroughly. Some of the quotes I got were far enough below other ones to more than offset the points difference. I got a rate variance of about 1.25% between my lowest and highest rate quote, after accounting for their bullshit fees. Sometimes lenders are looking to round out a portfolio with a specific LTV or credit score in order to hit their ratings metric, and will this offer you a sweeter deal to have your business immediately.
Lenders will always be a step ahead of you in this game. They have already done the math in more ways than you know even exist, but you still have some information they don't have. Like your own future plans of staying there forever, and what other offers you have received.
I had three different lenders tell me over the phone that the best quote I had received was fake and that nobody could possibly offer me that rate and fee structure. They had all kinds of BS reasons why I should pay more. I told them they could beat the quote or I'd shop elsewhere. They all backed out eventually, and I got the good deal I had been promised that nobody else thought was real. You just have to keep calling them back every time you get a better quote, to give them a chance for your business. It was a hard few days work, but saved me tens of thousands of dollars.
I worked with about seven different lenders. Some dropped out in the first 24 hours, three held on to the end vying for my business. It was a (very) local independent broker who came through in the end, but they sold my loan off almost immediately to one of the big national banks.