How accurate is Dow Jones in the prediction of stock index futures trading on that day?

It depends on the news that day. If something unexpected happens on the day shift that the future is accurate. Premarkets often be in the market falls that day. And the reverse also happens.

Consider this

In terms of accuracy, do not take any decision based on pre-market action alone. Today is a good example. The markets were in pre-market, which are noon, but how in the end the market today is unknown.