The Yahoo! directors have now turned down Microsoft’s $44.6 billion dollar offer for their company, saying it undervalues the company. It takes guts to do that when the bid represents a more than 60% premium over the price of Yahoo! stock before the offer was made. The betting is that Microsoft will sweeten the deal a bit and Yahoo! will come around. It’s hard to see how any other bid will be a match or any other business relationship will be as profitable and still get approval from regulators.

But the bettors may be guilty of a typical Wall Street crime, looking only at the numbers and ignoring the personalities involved. Yahoo! co-founder and CEO Jerry Yang doesn’t like Microsoft. It is hard to imagine him working for Microsoft. And you can say the same for many Yahoo! employees, who have been steeped in Yahoo!’s anti-Microsoft culture. Those employees represent one of Yahoo!’s major assets, and figuring out how to retain them and keep them innovated in the Microsoft culture would be one of the biggest challenges in any acquisition.

And then there’s Google. Make no mistake, Google is the raison d’être for this entire Microsoft-Yahoo! dance. Google’s incredible growth rate and its ability to generate tons of cash from advertising on its internet search pages has the rest of the universe in a panic. Other companies in media and advertising feel they are in a survival struggle while technology companies believe they are in a similar battle to remain relevant.

Interestingly, at Google they are equally obsessed. Founders Larry Page and Sergey Brin purposely set out to create an anti-Microsoft. They have provided money and other incentives in a successful drive to hire the best and the brightest off the college campus, and they have let those newly minted engineers and computer scientists do their own thing. They have created many products, many of which have the potential to compete with Microsoft’s cash cows, Office and Windows. So far, none of these new projects are making any money.

And then there is Eric Schmidt, the man Page and Brin brought in to run Google as CEO. Schmidt is a veteran of two losing battles against Microsoft, one at Novell and the other at Sun Microsystems. The weekend after Microsoft announced its plans Schmidt called Yahoo!’s Yang to offer assistance, perhaps by working a deal that would see Yahoo! outsource its search needs to Google.

Anyone with a passing acquaintance with anti-trust law would raise an eyebrow at that one, and many did. It was a particularly ironic situation since Google’s general counsel, David Drummond, published a statement that same weekend arguing that a Microsoft-Yahoo! deal would “raise troubling questions” of the anti-competitive variety.

What do we have? Lots of smoke and posturing, the latest are a formal rejection of the bid by Yahoo!, which claims it “substantially undervalues” the company; and a new churn of the rumor mill speculating on a combination of Yahoo! assets with the Internet segments of News Corp., which include MySpace, the popular social networking web site.

That makes some sense. A deal making Fox Interactive Media a part of Yahoo! in return for giving Fox a stake in Yahoo! would create a company with 35% of the online display ad market, according to ComScore. If the Fox stake in Yahoo! is set at 20%, which is the number being bandied about, it would value Yahoo! at $50, more than the value of the Microsoft offer.

What comes next? I’m sure we’ll see Microsoft make a move. CEO Steve Ballmer took his private attempts to do a deal with Yahoo! public when Yahoo! gave him the cold shoulder. He made it clear he would take his bid to Yahoo!’s shareholders if the bid was rejected. He may sweeten the offer, but $50 seems a little high even for cash rich Microsoft. Yahoo! holders may have to choose between a sure payoff in cash and Microsoft stock and the prospects of remaining independent, but with News Corp. as a big minority partner.

Any way you put the pieces together, Google will still be twice as big in terms of online advertising as any combination of the other players. At least until someone comes along with the Next Big Thing.