FANDOM


Hi all!

I searched for a long time a method in order to calculate the difficulty of a level in Piano Tiles 2. Personal evaluations are too subjective, depending on personal skills and impressions. So, an objective and mathematical method should be used instead.

I spent many time to find an optimal algorithm, and each algorithm I found had some pros and some cons. At the end, I believe that the following one would be a good one, and the best one among the ones selected by me, reflecting my personal impressions on the level difficulties, even if some doubts on some levels remain. Any further suggestion will be accepted.

Let me explain my algorithm (I prepared an Excel sheet with VB code in order to calculate the difficulty of each level, otherwise doing it personally would be very time consuming).

1. Value of each tile

Each tile has the following value:

  • Single tile: 1, except when placed after a double tile when its value is the value of the previous tile + 0.2
  • Long tile: 1/(value of the tile - 1)^2, for example the "+3" tile has a value of 1/2^2 = 1/4 = 0.25, the "+7" tile has a value of 1/6^2 = 1/36 = 0.02778. If placed after a double tile its value is multiplied by 3
  • The value of both single and long tiles, if immediately after a sliding tile, is multiplied by 2. For example, if a "+3" tile comes after a sliding tile, its value is 2*(1/2^2) = 0.5
  • The first double tile of a row: 4, except when placed after a single tile whose value is greater than 4. In this case its value is the value of the previous tile + 0.2
  • Subsequent double tiles (i.e. double tiles coming immediately after another double tile): value of the previous tile + 0.2
  • The last rapid tile of a sequence (last tap of a multiple tap): 4
  • Precedent rapid tiles (previous taps): 0.5 each

    Note: rapid tiles are the ones in which you have to tap the big tile many times. For example, if you have a "16" rapid tile, its value is 15*0.5 + 4 = 11.5

  • The first tile of a sliding tile: 2.5
  • Subsequent tiles of the same sliding tile: 0 each
  • A pause covering a single tile: 0.5
  • A pause covering two tiles: 1/8 = 0.125 each tile
  • A pause covering three tiles: 1/18 = 0.055555 each tile
  • A pause covering four or more tiles: 1/32 = 0.03125 each tile

The value of a tile cannot be greater than 8, i.e. if the value of a tile is greater than 8, its value is limited to 8.

2. Value of sequences

For each tile, we can associate a sequence calculated as the sum of the current tile and the 9 subsequent tiles. If a tile is one of the last tiles of a section, we use the first tiles of the next section, if a tile is one of the last tiles of the piece, we use the first tiles of the piece.

3. Calculation of the difficulty

The difficulty of a piece (up to a certain tile, for example up to the first star, or to the third star, or to the third crown. etc...) is calculated as follows:

DIFFICULTY = (A/20) + B

where:

  • A is the sum of all the points indicated in section 1 above multiplied by the speed of the corresponding tile (in tiles/second) ^ 4, until the last tile considered in the sequence under evaluation
  • B is the maximum among the following values: each value indicated in section 2 above multiplied by the speed of the corresponding tile (in tiles/second) ^ 4, until the last tile considered in the sequence under evaluation

4. Difficulty classification

Depending on the difficulty value, the following classification is suggested:

  • From 0 to 4000: Baby Level
  • From 4000 to 8000: Extremely Simple
  • From 8000 to 12000: Very Simple
  • From 12000 to 18000: Simple
  • From 18000 to 25000: Moderately Simple
  • From 25000 to 35000: Moderate
  • From 35000 to 50000: Moderately Difficult
  • From 50000 to 75000: Considerably Difficult
  • From 75000 to 100000: Difficult
  • From 100000 to 150000: Very Difficult
  • From 150000 to 200000: Extremely Difficult
  • From 200000 to 300000: Insanely Difficult
  • From 300000 to 500000: Alien Level
  • Above 500000: Quite Impossible

5. An example of difficulties

The following list indicates the most difficult and the easiest levels according to the above calculation, together with their points. Of course there are some (very few) pieces for which I don't agree with the classification.

TOP 30 MOST DIFFICULT PIECES (to 3 stars):

  1. Star Clock (Adapted by Pi): 279891
  2. Christmas Rhapsody (Adapted by Pi): 264004
  3. Dance Of The Golden Snake 2 (Er Nie): 187034
  4. Crazy pharaoh (Luo Ni): 165588
  5. Champagne Bridge (Adapted by Pi): 162138
  6. Etude Op.740 No.19 (Czerny): 161775
  7. Etude de Virtuosite in E (Moszkowski): 158773
  8. Rondo A Capriccio Op. 129 (Beethoven): 149640
  9. Flight of the Bumblebee (Rimsky-Korsakov): 139205
  10. William Tell Overture (Gioachino Rossini): 137462
  11. Christmas Zoo (Plants): 137349
  12. Hungarian Dance No. 5 (Johannes Brahms): 135962
  13. Fantasie - Impromptu (Chopin): 129176
  14. Sonata Pathetique Mvt. 3 (Beethoven): 124398
  15. Moonlight Sonata Mvt. 3 (Beethoven): 122807
  16. Penguins' game (Unknown): 122294
  17. Etude Op.849 No.21 (Czerny): 115502
  18. First Noel (English Folk Music): 112779
  19. Madding Wind (Clack Chen): 110128
  20. Etude Op.299 No.11 (Czerny): 108821
  21. Etude Op.740 No.42 (Czerny): 107656
  22. Etude Op.10 No.5 (Chopin): 105361
  23. Etude Op.849 No.6 (Czerny): 102942
  24. Carmen Overture (Bizet): 98810
  25. Csikos Post (Hermann Necke), original revision: 98393
  26. The Song of the Robin (George W. Warren): 97663
  27. Dance Of The Hours (Amilcare Ponchielli): 96995
  28. Hungarian Rhapsody No. 6 (Franz Lizst): 96033
  29. Solfeggietto (C. P. E. Bach): 95647
  30. Polonaise Op.53 (Chopin): 95050

TOP 30 EASIEST PIECES (to 3 stars):

  1. Romance De Amor (Narciso Yepes): 710
  2. Forest Of Blocks (Congfei Wei): 1003
  3. Serenade (Schubert): 1028
  4. Berenice (Congfei Wei): 1658
  5. Birthday Song (Adapted by Pi): 1949
  6. Little Star (English Folk Song), 3rd revision: 2467
  7. Jingle Bells (James Lord Pierpont), 2nd revision: 2676
  8. Moonlight Sonata Mvt.2 (Beethoven): 2968
  9. Little Star (English Folk Song), 2nd revision: 2971
  10. Moonlight Sonata Mvt.1 (Beethoven): 2978
  11. Nocturne Op.55 No.1 (Chopin): 2986
  12. Little Star (English Folk Song), 1st revision: 3005
  13. Little Star (English Folk Song), original revision: 3139
  14. Aurora (Confei Wei): 3425
  15. Warblings At Eve (Brinley Richards): 3433
  16. Londonderry Air (Ireland Folk Music): 3565
  17. A Tear (M.P. Mussorgsky): 3800
  18. Prisoners Dream (Kyrene): 3887
  19. Happy New Year (English Folk Music), 1st revision: 3888
  20. Ode An Die Freude (Beethoven): 4069
  21. Solitary Awakening (Kyrene): 4079
  22. Arirang (Korean Folk Music): 4177
  23. Douze Etudes de Salon Op.5 No.11 (Adolf von Henselt): 4256
  24. Two Tigers (French Folk Song), 2nd revision: 4271
  25. Red Berries in Blossom (Dunayevsky): 4367
  26. Love's Dream After the Ball (Alphons Czibulka): 4401
  27. Torna a Surriento (Ernesto De Curtis): 4429
  28. The Steadfast Palm Grass (You Xue-zhi): 4498
  29. Happy New Year (English Folk Music), original revision: 4593
  30. Traumerei Op.15 No.7 (Robert Schumann): 4702

TOP 30 MOST DIFFICULT PIECES (to 3 crowns):

  1. Christmas Rhapsody (Adapted by Pi): 1753737
  2. Star Clock (Adapted by Pi): 961121
  3. Etude de Virtuosite in E (Moszkowski): 707522
  4. Dance Of The Golden Snake 2 (Er Nie): 667867
  5. Etude Op.740 No.19 (Czerny): 648830
  6. Crazy pharaoh (Luo Ni): 640727
  7. Flight of the Bumblebee (Rimsky-Korsakov): 604388
  8. Christmas Zoo (Plants): 565003
  9. William Tell Overture (Gioachino Rossini): 564694
  10. Fantasie - Impromptu (Chopin): 555225
  11. Rondo A Capriccio Op. 129 (Beethoven): 554562
  12. Champagne Bridge (Adapted by Pi): 554409
  13. Sonata Pathetique Mvt. 3 (Beethoven): 539349
  14. Moonlight Sonata Mvt. 3 (Beethoven): 519621
  15. Etude Op.299 No.11 (Czerny): 480582
  16. Etude Op.849 No.21 (Czerny): 462527
  17. Polonaise Op.53 (Chopin): 452344
  18. Etude Op.740 No.42 (Czerny): 446364
  19. Hungarian Rhapsody No. 6 (Franz Lizst): 442847
  20. First Noel (English Folk Music): 440287
  21. Penguins' game (Unknown): 436646
  22. Paganini Caprice No. 9 (Robert Schumann), original revision: 428515
  23. Etude Op.10 No.5 (Chopin): 427213
  24. Hungarian Dance No. 5 (Johannes Brahms): 425819
  25. Etude Op.849 No.6 (Czerny): 422750
  26. Solfeggietto (C. P. E. Bach): 416795
  27. Csardas (Vittorio Monti): 416189
  28. Appassionata Mvt. 3 (Beethoven): 408560
  29. Sonata in C Major K279 (Mozart): 408430
  30. Madding Wind (Clack Chen): 380557

TOP 30 EASIEST PIECES (to 3 crowns):

  1. Romance De Amor (Narciso Yepes): 4847
  2. Serenade (Schubert): 9226
  3. Forest Of Blocks (Congfei Wei): 9741
  4. Birthday Song (Adapted by Pi): 11209
  5. Berenice (Congfei Wei): 13959
  6. Jingle Bells (James Lord Pierpont), 2nd revision: 16497
  7. Moonlight Sonata Mvt.2 (Beethoven): 18555
  8. Little Star (English Folk Song), 3rd revision: 19642
  9. Happy New Year (English Folk Music), 1st revision: 19789
  10. Two Tigers (French Folk Song), 2nd revision: 20838
  11. Nocturne Op.55 No.1 (Chopin): 21411
  12. Little Star (English Folk Song), 2nd revision: 22095
  13. Little Star (English Folk Song), 1st revision: 22456
  14. Warblings At Eve (Brinley Richards): 22992
  15. Aurora (Confei Wei): 23696
  16. Little Star (English Folk Song), original revision: 23738
  17. Moonlight Sonata Mvt.1 (Beethoven): 23767
  18. Happy New Year (English Folk Music), original revision: 24923
  19. Happy Birthday to You (American Folk Music), 1st revision: 24924
  20. Londonderry Air (Ireland Folk Music): 26295
  21. Prisoners Dream (Kyrene): 26527
  22. Solitary Awakening (Kyrene): 26908
  23. The Steadfast Palm Grass (You Xue-zhi): 27457
  24. Canon (Johann Pachelbel), 1st revision: 28393
  25. A Tear (M.P. Mussorgsky): 28627
  26. Jasmine (Chinese Folk Song), 1st revision: 28724
  27. Douze Etudes de Salon Op.5 No.11 (Adolf von Henselt): 29302
  28. Nocturne Op. 9 No. 2 (Chopin), 1st revision: 29507
  29. Torna a Surriento (Ernesto De Curtis): 29979
  30. Red Berries in Blossom (Dunayevsky): 30192