Samsung's (NASDAQOTH:SSNLF) new flagship Galaxy S6 phone will come in two versions, with one sporting a dual curved-edge display, according to a recent Bloomberg report. Both versions of the phone -- developed under the codename "Project Zero" -- will retain the 5.1" main screen size of the S5 and be encased in "all-metal" bodies.

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Samsung's previous flagship, the Galaxy S5. Source: Samsung.

Will a phone with a three-sided display help Samsung fight back against Apple (NASDAQ:AAPL), which has been pushing the company out of the premium market? Or will this just be another failed experiment targeting a non-existent market?

Samsung's smartphone woes
Samsung's global smartphone market share peaked at 35% in 2013. Today, it only controls around 20% of the market, according to research company IDC.

Samsung lost market share for two main reasons. First, cheaper Chinese competitors like Xiaomi, Lenovo (NASDAQOTH:LNVGY), and Huawei launched devices with similar specs as Samsung devices at lower prices. Second, Apple's iPhone gained ground across Asia as a status symbol, and the iPhone 6 Plus nullified Samsung's key advantage of larger screens.

As a result, Samsung's mobile earnings dropped 64% year over year in the fourth quarter of 2014, contributing to its first annual earnings decline in three years.

Trying to innovate - again
In 2011, Samsung unveiled the 5.3" Galaxy Note, which bridged the gap between smartphones and tablets with "phablets." The Galaxy Note was considered a niche product, but Samsung's flagship Galaxy S3 disrupted Apple's business the following year with a big 4.8" screen, which dwarfed the iPhone 4s' 3.5" display. By the end of the year, the S3 overtook the iPhone 4S and became the best-selling smartphone in the world.

With the S3's heyday now a distant memory, Samsung is struggling to get ahead of Apple again with another game-changing innovation. Unfortunately, the answer isn't as simple as a bigger screen this time around. Over the past two years, we've seen companies put stereoscopic 3D displays, 3D cameras, and head tracking features on smartphones -- none of which have impressed mainstream consumers.

Samsung thinks curved displays, which it is also showcasing with its newer TVs, could help it regain lost ground against Apple and Xiaomi. In late 2013, it launched the Galaxy Round, a concave 5.7" phablet, in South Korea to gauge market demand for curved displays. Customers weren't impressed, and the phone reportedly only sold 10,000 units.

However, Samsung then launched the Galaxy Note Edge, which had a display that wrapped around the right side of the phone, the following year. Market reception to the Note Edge was warmer than the Round, so Samsung launched it overseas as well. Therefore, it's not surprising that Samsung is now packing curved displays on both sides of the S6.

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Samsung's Galaxy Note Edge. Source: Samsung.

The pricing problem
The problem, however, is the price of curved displays. Samsung's 32GB Note Edge costs $1,130 unlocked. By comparison, an unlocked iPhone 6 Plus only costs between $749 (16GB) and $949 (128GB). Since Samsung's previous flagship devices traditionally cost less than Apple's iPhones, even when they had larger screens, it makes little sense to suddenly sell phones at a higher price point instead.

If Samsung wraps the display around both sides for the S6 variant, its final price tag could end up considerably higher than the comparable iPhone 6, which costs between $649 (16GB) and $849 (128GB) unlocked. Since Samsung's devices arguably lack the status appeal of Apple's iPhones, selling pricier phones than Apple could be suicidal.

Gimmicks won't save Samsung now
When Samsung marginalized HTC (NASDAQOTH:HTCCY) and Sony (NYSE:SNE) in the Android market, both companies resorted to gimmicks to try to stay afloat. HTC added 3D displays, 3D dual cameras, and waterproof frames. Sony launched comically large phablets like the 6.4" Xperia Z Ultra, added attachable SLR-style camera lenses to its phones, and let users remotely play their PS4 games.

None of those gimmicks prevented HTC and Sony from being boxed into a corner. In the smartphone market, two types of companies win -- those that make premium devices with cult appeal, like Apple, and those that can sell the best hardware at the lowest price, like Xiaomi. Those that resort to expensive gimmicks like triple-sided displays are bound to be left behind as their margins crumble.

Leo Sun owns shares of Apple. The Motley Fool recommends Apple. The Motley Fool owns shares of Apple. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.