user3885: I play regularly long games (60min each) with Droidfish/Stockfish the depth is always close around 21.
From time to time I overlook taktical flaws in my moves, obviously playing on worse positions against an engine makes no sense, so I take my move back. Technicaly the engine does the same, when it changes the evaluation.
That being said I most of the time end up in endgames that are drawn.
With black I have trouble drawing the game but I eventualy will.
With white I might have a edge, but the engine just always can hold a draw, somehow blockading the position to force a repetition.
I am a very positional player and i guess that is the reason I get these draws, because I mostly avoid taktical positions. NOTE: I am not going for totaly closed positions, I am playing normal positional chess.
I do not think I can beat the engine with black that would be asking for to much but I will try with white.
I play the Benko Opening wih white (1.g3).  
If you are curious here is the last  game I played with Droidfish: 
[fen ""]
1. g3 d5 
2. Nf3 Nf6 
3. Bg2 c6 
4. O-O Bf5 
5. d4 g6 
6. a4 Bg7 
7. b3 O-O 
8. Bb2 e6 
9. Nbd2 Nbd7 
10. c4 Re8 
11. Rc1 Rc8 
12. Nh4 Bf8 
13. Nxf5 exf5 
14. e3 Qa5 
15. Nf3 Ne4 
16. cxd5 cxd5 
17. Ne5 Rxc1 
18. Qxc1 Qd8 
19. Nd3 Bd6 
20. Ba3 Ndf6
21. Bxd6 Qxd6 
22. Qc2 Qa3 
23. Rc1 h5 
24. Qb2 Qd6 
25. Ne5 Kg7 
26. b4 Re7 
27. f3 Ng5 
28. Kf2 Ne6 
29. h4 Rc7 
30. Rxc7 Qxc7 
31. Bf1 Nd7 
32. Nd3 Nf6 
33. a5 Ne8 
34. Qc1 Qxc1 
35. Nxc1 Nd6 
36. Nd3 Nc7 
37. Ne5 Ne6 
38. Nd7 Nf8 
39. Nc5 Ne6
40. Bd3 b6 
41. Nd7 bxa5 
42. bxa5 Nb7 
43. a6 Nbd8 
44. Ke2 f6 
45. Kd2 Kf7 
46. Kc3 Ke7 
47. Nc5 Nc7 
48. Kb4 Nc6+ 
49. Ka4 Nd8 
50. Bb5 Nde6 
51. Bf1 Kd6 
52. Kb4 Nf8 
53. Bd3 Nfe6
54. Bb5 Ng7 
55. Nb7+ Ke7 
56. Bd3 Nge6 
57. Nc5 Kd6 
58. Nb7+ Ke7 

It went some moves on but ended in a repetition.
I am not really a fan of 1.e4 or sicilian type positions.
I kinda got the opinion that you can not really beat the engine in a long positional game in contrast to human players because the engine makes very few inaccuracies.
I guess the most chances are in a complex middle game. (I would still like them to be positional, maybe mixed with taktics)
I couldlnt really find any good (human vs engine) games where the engine was in trouble.
I will take a look now at recent engine games stockfish lost maybe that will give me a clue how to beat an engine beast.
Maybe in the mean time you will have some usefull ideas, because that is what we are the best in (for now).

user3885: I just won today with black against Droidfish/Stockfish-5 depth 21.
[fen ""]
1. d4 Nf6 
2. c4 e6 
3. Nc3 Bb4 
4. e3 b6 
5. Bd3 Bb7 
6. Nf3 O-O 
7. O-O Bxc3 
8.bxc3 c5 
9. Nd2 Nc6 
10. Rb1 d6 
11. Bb2 e5 
12. f3 Nd7 
13. d5 Ne7 
14. Ne4 Qc7
15. Qe2 h6 
16. Nf2 f5 
17. e4 f4 
18. Bc2 Ng6 
19. Ba4 Nf6
20. Qc2 Nh5 
21.Rbe1 Ne7 
22. Nd3 g5 
23. Nf2 Nf6 
24. Qe2 Kh8 
25. Bc2 Rg8
26. Qd3 Rg7 
27. g4 Ng6 
28. Qe2 Rag8 
29. Nd3 Bc8 
30. Rf2 Rh7 
31. h3 h5 
32. Rh2 Kg7 
33. Qd2 Rgh8
34. Ree2 Nh4 
35. Ne1 hxg4 
36. hxg4 Bxg4 
37. fxg4 Nxg4
38. Bd1 Qd7 
39. Ba3 Nxh2 
40. Rxh2 g4 
41. Rh1 Kf8 
42. Kf2 g3+ 
43. Ke2 g2 
44. Rg1 Qh3 
45. Qd3 Qh2
46. Kf2 Rg7 
47. Bc1 Rg3 
48. Qe2 Rf3+ 
49. Qxf3 Nxf3 
50. Bxf3 Qg3+ 
51. Ke2 Rh1 
52. Rxh1 Qxf3+ 
53. Nxf3 gxh1=Q 
54. Ne1 Qxe4+ 
55. Kd1 Qxc4 
56. a4 Qxa4+
57. Nc2 f3 
58. Be3 Qc4 
59. Kc1 Qxc3 
60. Bf2 a5 
61. Be3 a4 
62. Bd2 Qd3
63. Be1 a3 
64. Bh4 Qf1+ 
65. Kd2 f2 
66. Ke3 Qc1+ 
67. Kxf2 Qxc2+
68. Ke3 a2 
69. Kf3 a1=Q 
70. Kg4 Qg6+ 
71. Kf3 Qf1+ 
72. Bf2 Qd1+ 
73. Ke3 Qgd3
# 0-1

Well, you can see multiple things that might help to defeat Stockfish:
(Should help you against humans, too. ;-)

Do not give the engine any kind of counterplay.
Such positions are more likely to be found in closed games.
Keep pawms on the board, do not exchange to much of them.
Create imbalanced positions e.g Bishop/Knight exchange, double pawns etc.
the plan is to play a long game.
Play very sound openings.

It is possible to win ;-)

user2429: While it is extremely difficult for a human to beat the top chess engines, many of the mobile engines (like Driodfish) are still beatable. 
I will consider Driodfish 1.53 since that's the one currently installed on my Android phone and is similar to the one the OP is using. 
Engines are very good at tactics, so humans cannot realistically hope to beat them there. However, engines don't "understand" strategy. The top engines can cope with this because they simply think way too deep and can tactically compensate for lack of strategic understanding. They also have good evaluation functions. However, the weaker mobile engines still lack in this area. 
So the way to beat these engines is to achieve those kind of positions where strategically you have an edge at the cost of some temporary tactical disadvantage (like material). Engines can often be lured into such positions. For instance, consider this game I just played with Droidfish 1.53. At the cost of a pawn (temporary tactical disadvantage), I was able to secure a very strong advantage for myself many moves later. The computer failed to see this when it went for the material advantage - 
[FEN ""]
[White "Wes"]
[Black "Droidfish 1.53"]

1. d4 d5 2. c4 c6 3. Nc3 Nf6 4. e3 e6 5. Nf3 Nbd7 6. Qc2 Bd6 7. g4 Nxg4 
8. Rg1 h5 9. h3 Qf6 10. Be2 Nh6 11. e4 Bb4 12. Bg5 Qg6 13. Bd3 dxc4 
14. Bxc4 Qh7 15. O-O f6 16. Bxe6 fxg6 17. Nxg5 Qg6 18. f4 Bxc3 
19. bxc3 Qf6 20. f5 Nf8 21. e5 Qe7 22. Bxc8 Rxc8

Droidfish 1.53 itself now evaluates this position as a clear advantage for White. 
As great a player as Garry Kasparov himself employed this strategy in some of his games against the top engines of that time. 
Garry Kasparov vs Deep Junior 2003, Round 1, 1-0
  [FEN ""]
  [White "Garry Kasparov"]
  [Black "Deep Junior"]
  [Date "2003"]     

  1. d4 d5 2. c4 c6 3. Nc3 Nf6 4. e3 e6 5. Nf3 Nbd7 6. Qc2 Bd6 7. g4 dc4 
  8. Bc4 b6 9. e4 e5 10. g5 Nh5 11. Be3 O-O 12. O-O-O Qc7 13. d5 b5 
  14. dc6 bc4 15. Nb5 Qc6 16. Nd6 Bb7 17. Qc3 Rae8 18. Ne8 Re8 19. Rhe1 Qb5 
  20. Nd2 Rc8 21. Kb1 Nf8 22. Ka1 Ng6 23. Rc1 Ba6 24. b3 cb3 25. Qb3 Ra8 
  26. Qb5 Bb5 27. Rc7

Garry Kasparov vs X3D Fritz 2003, Round 1 1/2-1/2
  [FEN ""]
  [White "Garry Kasparov"]
  [Black "X3D Fritz"]
  [Date "2003"]

   1. Nf3 d5 2. c4 c6 3. d4 Nf6 4. Nc3 e6 5. e3 Nbd7 6. Qc2 Bd6 7. g4 Bb4 
   8. Bd2 Qe7 9. Rg1 Bc3 10. Bc3 Ne4 11. O-O-O Qf6 12. Be2 Nf2 13. Rdf1 Ne4 
   14. Bb4 c5 15. cd5 ed5 16. dc5 Qe7 17. Nd4 O-O 18. Nf5 Qe5 19. c6 bc6 
   20. Bf8 Kf8 21. Ng3 Ndc5 22. Ne4 Ne4 23. Bd3 Be6 24. Be4 de4 25. Rf4 Bd5 
   26. Qc5 Kg8 27. Rgf1 Rb8 28. R1f2 Qc7 29. Rc2 Qd7 30. h4 Qd8 31. g5 Ba2 
   32. Re4 Qd3 33. Rd4 Qe3 34. Rcd2 Qe1 35. Rd1 Qe3 36. R1d2 Qg1


3885: <p>I play regularly long games (60min each) with Droidfish/Stockfish the depth is always close around 21.</p>

<p>From time to time I overlook taktical flaws in my moves, obviously playing on worse positions against an engine makes no sense, so I take my move back. Technicaly the engine does the same, when it changes the evaluation.</p>

<p>That being said I most of the time end up in endgames that are drawn.
With black I have trouble drawing the game but I eventualy will.
With white I might have a edge, but the engine just always can hold a draw, somehow blockading the position to force a repetition.</p>

<p>I am a very positional player and i guess that is the reason I get these draws, because I mostly avoid taktical positions. NOTE: I am not going for totaly closed positions, I am playing normal positional chess.</p>

<p>I do not think I can beat the engine with black that would be asking for to much but I will try with white.</p>

<p>I play the Benko Opening wih white (1.g3).  </p>

<p>If you are curious here is the last  game I played with Droidfish: </p>

<pre><code>[fen ""]
1. g3 d5 
2. Nf3 Nf6 
3. Bg2 c6 
4. O-O Bf5 
5. d4 g6 
6. a4 Bg7 
7. b3 O-O 
8. Bb2 e6 
9. Nbd2 Nbd7 
10. c4 Re8 
11. Rc1 Rc8 
12. Nh4 Bf8 
13. Nxf5 exf5 
14. e3 Qa5 
15. Nf3 Ne4 
16. cxd5 cxd5 
17. Ne5 Rxc1 
18. Qxc1 Qd8 
19. Nd3 Bd6 
20. Ba3 Ndf6
21. Bxd6 Qxd6 
22. Qc2 Qa3 
23. Rc1 h5 
24. Qb2 Qd6 
25. Ne5 Kg7 
26. b4 Re7 
27. f3 Ng5 
28. Kf2 Ne6 
29. h4 Rc7 
30. Rxc7 Qxc7 
31. Bf1 Nd7 
32. Nd3 Nf6 
33. a5 Ne8 
34. Qc1 Qxc1 
35. Nxc1 Nd6 
36. Nd3 Nc7 
37. Ne5 Ne6 
38. Nd7 Nf8 
39. Nc5 Ne6
40. Bd3 b6 
41. Nd7 bxa5 
42. bxa5 Nb7 
43. a6 Nbd8 
44. Ke2 f6 
45. Kd2 Kf7 
46. Kc3 Ke7 
47. Nc5 Nc7 
48. Kb4 Nc6+ 
49. Ka4 Nd8 
50. Bb5 Nde6 
51. Bf1 Kd6 
52. Kb4 Nf8 
53. Bd3 Nfe6
54. Bb5 Ng7 
55. Nb7+ Ke7 
56. Bd3 Nge6 
57. Nc5 Kd6 
58. Nb7+ Ke7 
</code></pre>

<p>It went some moves on but ended in a repetition.</p>

<p>I am not really a fan of 1.e4 or sicilian type positions.
I kinda got the opinion that you can not really beat the engine in a long positional game in contrast to human players because the engine makes very few inaccuracies.
I guess the most chances are in a complex middle game. (I would still like them to be positional, maybe mixed with taktics)</p>

<p>I couldlnt really find any good (human vs engine) games where the engine was in trouble.
I will take a look now at recent engine games stockfish lost maybe that will give me a clue how to beat an engine beast.</p>

<p>Maybe in the mean time you will have some usefull ideas, because that is what we are the best in (for now).</p>
 3885: <p>I just won today with black against Droidfish/Stockfish-5 depth 21.</p>

<pre><code>[fen ""]
1. d4 Nf6 
2. c4 e6 
3. Nc3 Bb4 
4. e3 b6 
5. Bd3 Bb7 
6. Nf3 O-O 
7. O-O Bxc3 
8.bxc3 c5 
9. Nd2 Nc6 
10. Rb1 d6 
11. Bb2 e5 
12. f3 Nd7 
13. d5 Ne7 
14. Ne4 Qc7
15. Qe2 h6 
16. Nf2 f5 
17. e4 f4 
18. Bc2 Ng6 
19. Ba4 Nf6
20. Qc2 Nh5 
21.Rbe1 Ne7 
22. Nd3 g5 
23. Nf2 Nf6 
24. Qe2 Kh8 
25. Bc2 Rg8
26. Qd3 Rg7 
27. g4 Ng6 
28. Qe2 Rag8 
29. Nd3 Bc8 
30. Rf2 Rh7 
31. h3 h5 
32. Rh2 Kg7 
33. Qd2 Rgh8
34. Ree2 Nh4 
35. Ne1 hxg4 
36. hxg4 Bxg4 
37. fxg4 Nxg4
38. Bd1 Qd7 
39. Ba3 Nxh2 
40. Rxh2 g4 
41. Rh1 Kf8 
42. Kf2 g3+ 
43. Ke2 g2 
44. Rg1 Qh3 
45. Qd3 Qh2
46. Kf2 Rg7 
47. Bc1 Rg3 
48. Qe2 Rf3+ 
49. Qxf3 Nxf3 
50. Bxf3 Qg3+ 
51. Ke2 Rh1 
52. Rxh1 Qxf3+ 
53. Nxf3 gxh1=Q 
54. Ne1 Qxe4+ 
55. Kd1 Qxc4 
56. a4 Qxa4+
57. Nc2 f3 
58. Be3 Qc4 
59. Kc1 Qxc3 
60. Bf2 a5 
61. Be3 a4 
62. Bd2 Qd3
63. Be1 a3 
64. Bh4 Qf1+ 
65. Kd2 f2 
66. Ke3 Qc1+ 
67. Kxf2 Qxc2+
68. Ke3 a2 
69. Kf3 a1=Q 
70. Kg4 Qg6+ 
71. Kf3 Qf1+ 
72. Bf2 Qd1+ 
73. Ke3 Qgd3
# 0-1
</code></pre>

<p>Well, you can see multiple things that might help to defeat Stockfish:
(Should help you against humans, too. ;-)</p>

<ul>
<li>Do not give the engine any kind of counterplay.</li>
<li>Such positions are more likely to be found in closed games.</li>
<li>Keep pawms on the board, do not exchange to much of them.</li>
<li>Create imbalanced positions e.g Bishop/Knight exchange, double pawns etc.
the plan is to play a long game.</li>
<li>Play very sound openings.</li>
</ul>

<p>It is possible to win ;-)</p>
 2429: <p>While it is extremely difficult for a human to beat the top chess engines, many of the mobile engines (like Driodfish) are still beatable. </p>

<p><em>I will consider <strong>Driodfish 1.53</strong> since that's the one currently installed on my Android phone and is similar to the one the OP is using.</em> </p>

<p>Engines are very good at tactics, so humans cannot realistically hope to beat them there. However, engines don't "understand" strategy. The top engines can cope with this because they simply think way too deep and can tactically compensate for lack of strategic understanding. They also have good evaluation functions. However, the weaker mobile engines still lack in this area. </p>

<p>So the way to beat these engines is to achieve those kind of positions where strategically you have an edge at the cost of some temporary tactical disadvantage (like material). Engines can often be lured into such positions. For instance, consider this game I just played with Droidfish 1.53. At the cost of a pawn (temporary tactical disadvantage), I was able to secure a very strong advantage for myself many moves later. The computer failed to see this when it went for the material advantage - </p>

<pre><code>[FEN ""]
[White "Wes"]
[Black "Droidfish 1.53"]

1. d4 d5 2. c4 c6 3. Nc3 Nf6 4. e3 e6 5. Nf3 Nbd7 6. Qc2 Bd6 7. g4 Nxg4 
8. Rg1 h5 9. h3 Qf6 10. Be2 Nh6 11. e4 Bb4 12. Bg5 Qg6 13. Bd3 dxc4 
14. Bxc4 Qh7 15. O-O f6 16. Bxe6 fxg6 17. Nxg5 Qg6 18. f4 Bxc3 
19. bxc3 Qf6 20. f5 Nf8 21. e5 Qe7 22. Bxc8 Rxc8
</code></pre>

<p>Droidfish 1.53 itself now evaluates this position as a clear advantage for White. </p>

<p>As great a player as Garry Kasparov himself employed this strategy in some of his games against the top engines of that time. </p>

<p><a href="http://www.chessgames.com/perl/chessgame?gid=1260051" rel="nofollow">Garry Kasparov vs Deep Junior 2003, Round 1, 1-0</a></p>

<pre><code>  [FEN ""]
  [White "Garry Kasparov"]
  [Black "Deep Junior"]
  [Date "2003"]     

  1. d4 d5 2. c4 c6 3. Nc3 Nf6 4. e3 e6 5. Nf3 Nbd7 6. Qc2 Bd6 7. g4 dc4 
  8. Bc4 b6 9. e4 e5 10. g5 Nh5 11. Be3 O-O 12. O-O-O Qc7 13. d5 b5 
  14. dc6 bc4 15. Nb5 Qc6 16. Nd6 Bb7 17. Qc3 Rae8 18. Ne8 Re8 19. Rhe1 Qb5 
  20. Nd2 Rc8 21. Kb1 Nf8 22. Ka1 Ng6 23. Rc1 Ba6 24. b3 cb3 25. Qb3 Ra8 
  26. Qb5 Bb5 27. Rc7
</code></pre>

<p><a href="http://www.chessgames.com/perl/chessgame?gid=1269887" rel="nofollow">Garry Kasparov vs X3D Fritz 2003, Round 1 1/2-1/2</a></p>

<pre><code>  [FEN ""]
  [White "Garry Kasparov"]
  [Black "X3D Fritz"]
  [Date "2003"]

   1. Nf3 d5 2. c4 c6 3. d4 Nf6 4. Nc3 e6 5. e3 Nbd7 6. Qc2 Bd6 7. g4 Bb4 
   8. Bd2 Qe7 9. Rg1 Bc3 10. Bc3 Ne4 11. O-O-O Qf6 12. Be2 Nf2 13. Rdf1 Ne4 
   14. Bb4 c5 15. cd5 ed5 16. dc5 Qe7 17. Nd4 O-O 18. Nf5 Qe5 19. c6 bc6 
   20. Bf8 Kf8 21. Ng3 Ndc5 22. Ne4 Ne4 23. Bd3 Be6 24. Be4 de4 25. Rf4 Bd5 
   26. Qc5 Kg8 27. Rgf1 Rb8 28. R1f2 Qc7 29. Rc2 Qd7 30. h4 Qd8 31. g5 Ba2 
   32. Re4 Qd3 33. Rd4 Qe3 34. Rcd2 Qe1 35. Rd1 Qe3 36. R1d2 Qg1
</code></pre>
