user1752: Assume that the phone is one of today's high-end phones, e.g. the Samsung Galaxy S6. Also, assume that the match is a classical time limit match.

user825: Magnus Carlsen was beaten by his own chess app, but it wasn't a serious game and he did it for a presentation. I don't think that game meant anything. While I don't have data for the World Champion, I'm quite certain one of the former world women chess champions was overwhelmed by my iPhone mobile chess app. I also got similar reports for grandmaster over FIDE 2600.
To appreciate the power of a mobile chess app, we should review the match between Deep Fritz and Kramnik in 2006. According to the wikipedia, the machine had two Intel Core 2 Duo CPUs. Wikipedia states the CPUs have clock speed of 1.06 GHz to 3.33 GHz. The wikipedia also states the latest Apple A8 chip has clock speed of 1.1 GHz to 1.4 GHz. Please keep in mind clock speed is a very rough guide to performance. Anyway, the Apple iPhone is at least competitive to an Intel Core 2 Duo in terms of raw clock speed. It has been reported the older Apple A7 chip has performance close to desktop. You should be assured the latest Apple A8 chip can give any grandmaster a challenge. 
Let's take a look at the unofficial rating list for Android chess engines. While the rating scale is not related to the FIDE rating, it's hard to believe Carlsen will have an easy time against Komodo 9 on Galaxy 6, which has a rating of 3239 in the list.
Apart from the hardware, the engine algorithm has improved dramatically since Kramnik's match. We now have access to everything that a super chess engine should do; just look at the source code of Stockfish. Back in 2006 when the match was played, all of the strongest engines were closed source.
The version that Kramnik played was a 32 bits engine. This is a bit embarrassing in today's standard. The stronger mobile chess apps (including my own) are now 64 bits.
We don't have any concrete data because no grandmaster has played a serious match against a mobile phone (because there is no money involved). What we can do is infer from historical data, software improvement and rating list. I am confident Carlsen will be beaten by the strongest mobile chess app on the app store.
Finally, while Carlsen is the best player against human players, he's probably not the best player against computers. For example, Carlsen's usually trick; pushing hard in a drawn endgame would not work against a computer. Computer engine will never blunder and will never crack.

1752: <p>Assume that the phone is one of today's high-end phones, e.g. the Samsung Galaxy S6. Also, assume that the match is a classical time limit match.</p>
 825: <p>Magnus Carlsen was beaten by his own chess app, but it wasn't a serious game and he did it for a presentation. I don't think that game meant anything. While I don't have data for the World Champion, I'm quite certain one of the former world women chess champions was overwhelmed by my iPhone mobile chess app. I also got similar reports for grandmaster over FIDE 2600.</p>

<p>To appreciate the power of a mobile chess app, we should review the match between Deep Fritz and Kramnik in 2006. According to the <a href="https://en.wikipedia.org/wiki/Vladimir_Kramnik#Deep_Fritz_match">wikipedia</a>, the machine had two Intel Core 2 Duo CPUs. Wikipedia <a href="https://en.wikipedia.org/wiki/Intel_Core_2">states</a> the CPUs have clock speed of 1.06 GHz to 3.33 GHz. The wikipedia also <a href="https://en.wikipedia.org/wiki/Apple_A8">states</a> the latest Apple A8 chip has clock speed of 1.1 GHz to 1.4 GHz. Please keep in mind clock speed is a very rough guide to performance. Anyway, the Apple iPhone is <em>at least</em> competitive to an Intel Core 2 Duo in terms of raw clock speed. It has been <a href="http://appleinsider.com/articles/14/03/31/analysis-affirms-apples-a7-processor-closer-to-a-desktop-cpu-than-regular-mobile-chip">reported</a> the older Apple A7 chip has performance close to desktop. You should be assured the latest Apple A8 chip can give any grandmaster a challenge. </p>

<p>Let's take a look at the <a href="http://chesstroid.blogspot.be/2015/06/rapidroid-reloaded-june-2015-komodo-9.html">unofficial rating list</a> for Android chess engines. While the rating scale is not related to the FIDE rating, it's hard to believe Carlsen will have an easy time against Komodo 9 on Galaxy 6, which has a rating of 3239 in the list.</p>

<p>Apart from the hardware, the engine algorithm has improved dramatically since Kramnik's match. We now have access to everything that a super chess engine should do; just look at the source code of Stockfish. Back in 2006 when the match was played, all of the strongest engines were closed source.</p>

<p>The version that Kramnik played was a 32 bits engine. This is a bit embarrassing in today's standard. The stronger mobile chess apps (including my own) are now 64 bits.</p>

<p>We don't have any concrete data because no grandmaster has played a serious match against a mobile phone (because there is no money involved). What we can do is infer from historical data, software improvement and rating list. <strong>I am confident Carlsen will be beaten by the strongest mobile chess app on the app store.</strong></p>

<p>Finally, while Carlsen is the best player <em>against human players</em>, he's probably not the best player <em>against computers</em>. For example, Carlsen's usually trick; pushing hard in a drawn endgame would not work against a computer. Computer engine will never blunder and will never crack.</p>
