Applications for the shares close at 4.30pm on Tuesday, so anyone with an online dealing account can still decide whether or not to jump.
The Royal Mail will come to the stock market a week later on October 15 at a price supposed to be somewhere between 260p and 330p a share, depending on market conditions. But spread-betting firms were this week predicting a price of 340p, which would mean fewer shares for the minimum £750 subscription which investors must make.
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That suggests strong interest in the float, with reports that institutional investors have made offers which would buy up all the stock - which could mean all applications will be scaled back, though in past privatisations smaller applications have sometimes been allowed in full.
The smart money appears to be attracted by the prospect of a dividend yield of at least 6.1%, along with signals from the company that it is on track for strong profit growth. That could offset the seemingly negative effect of an industrial action threat by the Communication Workers' Union to coincide with the flotation.
It was also reported this week that the new company may land a huge windfall from the sale of a 13-acre former mail centre site which could be worth £500 million to developers.
Fund managers, however, have warned that the windfall should not be used to help Royal Mail shore up its pension scheme ahead of transferring the scheme and its liabilities to the government.
Stuart Dyer, chief investment officer at online broker rplan, said: "You may be lucky and experience an immediate windfall if Royal Mail shares trade on the stockmarket above the issue price and you sell rather than hold, but this 'stagging' approach is usually for more experienced investors prepared to take a loss."
He said backing an individual share carried individual company and sector risk.
"Investments are usually better considered for longer periods of time - there is a lot of political will towards making the Royal Mail flotation a success, which should help things go well initially.
"But questions remain around the long-term future of Royal Mail, such as the threat of industrial action, branch closures, low current profit margins, and the changing shape of postal deliveries as people send less mail and order more online.
"What's more, market conditions today are quite different from the British Gas or BT flotations three decades ago. Investors buying into Royal Mail should do so with their eyes open."
Stuart Welch, chief executive of TD Direct Investing, said: "Do your own research first. Make sure you read the company's prospectus, along with the pricing notification. While there is no guarantee of success, knowledge and understanding is the right start to making your own investment decisions.
"Secondly, consider how buying these shares will impact both your short and long-term investments and financial goals. Think about timing and consider whether you are looking for income, via dividends, or growth, via an increase in the share price."