How much house will $2 million get you in the United States these days?

You could buy 25 pretty nice four-bedroom, two-bath homes in Cleveland, Ohio. Or, you could get just one modest ranch house in Los Altos, California, the most expensive real estate market in the country, according to a new survey by Coldwell Banker.

But, then again, you would probably get beat out by an all-cash buyer offering a higher bid.

Competition is fierce in today's emerging hot real estate markets because the inventory of available properties is still extremely low. In areas like Silicon Valley, though, the economy is humming and buyers have plenty of money.

Los Altos is in the middle of the action, surrounded by the corporate headquarters for Google, Facebook and dozens of other major tech companies, as are neighboring Newport Beach, Saratoga, Redwood City and Los Gatos, the rest of the top five on Coldwell's list.

As other markets heat up around the country, buyers can learn a few things from what's happening in some of the hottest places.

NEW MATH

If there is one thing Silicon Valley's techies know, it's algorithms. You're going to need one in today's top markets to figure out how far above asking you need to bid.

Sumi Kim Hachmann, a 32-year-old researcher at Quora.com, snagged her three-bedroom, one-bath house in Menlo Park last year after six months of trying. Each time she found a house she liked, she crunched the square footage and comparable sales to figure out how much to bid, refining her math each time she lost out.

She liked a fixer-upper listed at $1.1 million, and was willing to bid $100,000 over asking. Her agent told her to double that, at least. She did, but the sellers countered. The house sold for $1.4 million to somebody else

"That was definitely discouraging," Hachman says. "But it was a learning experience."

Next time, she went in with a strong offer that amounted to $1,000 per square foot, and won. Now, a year later, she's incredulous that houses in the neighborhood are going for double that.

While price is largely controlled by location and size, you need to add a premium to your offer if you need a mortgage, says Joe Brown, managing broker of a Coldwell branch in Los Altos. Bids being equal, sellers prefer all-cash because there is less risk. Price will still prevail, though, so a higher bid from a qualified buyer with a mortgage should win.

Another caveat: Keep contingencies out of the purchase agreement. Doing this is difficult for mortgage-seekers because banks typically require that the purchase price match the appraised value of the house. With prices going so far above asking, that can get tricky.

"You either ask them to put a lot more down or have them sign something that they will waive the appraisal contingency," says Ducky Grabill, a founding agent of Sereno Group realty, who is based in Las Gatos.

Grabill also suggests having the lender call the listing agent and let them know they will guarantee the financing.

LOWER EXPECTATIONS

Another strategy is to buy below your price point, says Brown. If you have the resources for a $2 million house but cannot compete with stronger buyers, then aim for $1.5 million and turn it into the house you want.

This is a modification of the old "buy the worst house in the best neighborhood" adage. But you cannot just sit on this kind of property and hope it will appreciate; you've got to renovate.

That's what Amy Bohutinsky, chief marketing officer of real estate site Zillow.com, did with her own purchase of a fixer-upper in the Seattle area two years ago.

"If you buy it with the intent of fixing it up, it can be an easier way" into a house than engaging in a bidding war, Bohutinsky says.

She also recommends expanding the boundaries of your search: considering for-sale-by-owner properties, preview listings like Zillow's "Make Me an Offer" section and "coming attractions" on listing sites.

BE READY

It is not enough anymore to show up at an open house pre-qualified for a mortgage and with a letter that sells yourself. You may need to have an engineer or other inspector come along, says Sereno Group's Grabill.

She had a client recently clinch a $2 million all-cash deal after his first viewing, but only because he was able to do his due diligence on the foundation issues immediately.

This buyer was one of those bidding down on a property. He was really in the market for more like $2.5 million, and will put the remainder of his budget into fixing it up.

"They are throwing so much more money at properties to get it. It's a little crazy," Grabill says.