The title, which launched towards the end of last week, is currently sitting at the top of the free rankings in the iOS app store and also features in the top ten of for highest-grossing apps - an "incredible record", says Apple senior vice president Phil Schiller.
However, argues ArsTechnica, a download "isn't quite the same as a purchase". Super Mario Run is free to download but users need to pay "a one-time fee" - £7.99 - to unlock its full contents.
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"Most mobile games are free to download and play but charge money for extra content, power-ups, or in-game currency," it adds.
Super Mario Run is the first time a Nintendo game has been able to be played on a mobile phone. Critics praised its intuitive one-touch controls, but gamers are unhappy that it can only be played when their device is connected to the internet.
Added to that, new mode "Friendly Run", which allows players to move through levels and collect coins against others in a "non-competitive fashion", can only be played once a day over the free version and three times a day for paying users, GameSpot reports.
Super Mario Run is available on the iOS app store at the moment and is free to download. However, a one-off fee of £7.99 will be needed to unlock the full version.
Super Mario Run expected to make $71m in first month
Nintendo makes its debut on the mobile market next week, with the launch of Super Mario Run on the iOS app store – and reports say it's set to become a commercial success
Sensor Tower say the game is expected to achieve $71m (£56m) in worldwide gross revenue during its first month and $50m (£49.6m) in net revenue, excluding projections for Chinese sales.
These figures would put Nintendo's mobile game in third place for first month app growth - Pokemon Go achieved $143m (£113.4m) of gross revenue in its first month and Clash Royale took $107m (£84.9m). Candy Crush is a distant fourth, with $16m (£12.7m) of gross revenue.
Creator Shigeru Miyamoto revealed Super Mario Run during Apple's iPhone 7 keynote in September. As the game has been optimised for a mobile platform, players will be able to make Mario jump and activate unique mechanisms throughout the world by touching the screen, all while the Italian plumber automatically runs and grabs on to ledges.
PC Advisor reports that Nintendo's new platform will cost £7.99 and launch on Thursday 15 December. It adds that Android users can get their hands on the new Mario game "in 2017".
Nintendo shares soar on news that Mario is coming to iPhone
Nintendo's stock rose dramatically today after it was announced that its best-known character, Super Mario, is to make his smartphone debut with the iPhone 7. The news caused the company's shares to spike by 18 per cent, before falling back to close 13 per cent up.
Investors seem to think the Italian plumber, created by Shigeru Miyamoto in 1985, can save both Princess Peach and Nintendo. The venerable Kyoto videogame maker has struggled to turn a profit in recent years.
Miyamoto appeared in person at Apple's iPhone 7 launch in San Francisco yesterday, standing alongside Tim Cook to announce that Super Mario Run will be available on iPhones in more than 100 countries from December.
The app will be free to download but users will have pay to access the full game. A version for Android phones is also planned.
Miyamoto demonstrated the game at the iPhone 7 launch. Players guide Mario through a series of obstacles collecting coins. They can compete with each other in higher levels of the game.
The game creator said: "For the first time ever, players will be able to enjoy a full-fledged Super Mario game with just one hand, giving them the freedom to play while riding the subway or my favourite, eating a hamburger."
The wild success of Pokemon Go, created by the US firm Niantic using characters licensed from Nintendo, has helped the Japanese firm's stock this year. Investors will be hoping Super Mario Run enjoys similar popularity, says The Independent.
Shareholders have long called for a smartphone outing for Mario, Luigi, Bowser, Peach, Yoshi and the other game characters, but Nintendo had resisted the call, fearing it would have a negative impact on its core console business.
According to the Wall Street Journal, Nintendo will be hoping that the new smartphone game will act as publicity for its upcoming console, which is codenamed NX and due to be released in March.
Today's 13 per cent rise by close of trading left Nintendo's stock at its highest level since late July and added $4.5bn to the firm's value.
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