The prospect of becoming a stock market millionaire can seem exciting, but it need not be daunting. In fact, I think one can aim for a million simply by buying and holding a limited number of well-known and long-established blue-chip shares.

What it takes to go from zero to a million

If one seriously wants to become a stock market millionaire, it takes not just ambition but also a practical plan.

Putting in just a few quid and hoping to stumble on some miraculous once-in-a-generation share will not cut the mustard, I reckon.

Not only is a proper investment strategy required — so is capital. It takes money to make money.

That means that, while it is possible to start with zero, a disciplined regular saving plan is a helpful tool to provide money to invest.

Everyone’s financial situation is different and that will affect how much any one person can invest in their share-dealing account or Stocks and Shares ISA. But the short of it is, the more one puts in, the faster one can aim for a million.

Why doing less can earn more

Imagine an investor puts in £800 each month and was able to grow their portfolio value at a compounded value of 5% annually by investing in 50 leading shares.

Doing that to aim for a million, the investor would be opening the champagne after 38 years.

But imagine if they bought just the 7 or 8 best-performing of those 50 shares and achieved a compound annual growth rate of 10%. They would be a millionaire in 26 years. At 15%, it would take just a couple of decades.

How the top shares perform will vary over time. But the same principle always applies: the best-performing few shares in any group (say, the FTSE 100) over a given time period will outperform the rest.

That can speed things up, perhaps significantly, as in the path towards a million.

That is just simple maths. What is not so simple, alas, is knowing (or even guessing well) which shares will be top performers in any given timeframe.

Going for great, nor merely decent

Many investors know the difference between finding what feels like a really good opportunity and a merely decent one. Great ones can be rare: Warren Buffett pins much of his success on “about a dozen truly good decisions” over many decades.

It can therefore feel tempting to invest in merely decent opportunities. But Buffett’s strong performance comes from being patient and going for brilliant chances in a big way.

As an example, consider ExxonMobil (NYSE: XOM).

I expect demand for oil and gas to stay high. For decades people have been talking about use falling – and I do see that as a risk – but so far it has been resilient, as the global population grows.

Exxon is in prime position to benefit from this. It has a more focussed portfolio than some rivals, outstanding assets, and a proven business model over many decades.

In fact, not only has it proven its business over decades, the energy major has grown its dividend annually for decades.

The thing is, although I think it is a great business the share price does not strike me as cheap. So, for now, I am watching without buying.