Polarity's Character Ability Statistical Analysis (1/6/15)

Introduction

Ever wanted to know how many cascades are caused by a surgical strike? What about what the probability is for activating Blade’s thirst passive assuming that you avoid red matches for levels 4 and 5? There have been some simple scripts written for calculating the odds of some basic statistics such as the expected number of tiles matched from Loki’s illusion, but up until this point, there hasn’t been a dedicated program that would take more complicated variables such as cascades and board position into account. In order to do this, we basically need to recreate the MPQ game engine from scratch, and well, I’ve had some time on plane rides to and from break to start writing that up. The current version is semi-stable enough that it’s stable enough to produce accurate…ish results, so I’ve decided to publish what I currently have. The simulator isn’t complete enough to fully simulate a game just yet, but I figure that posting these results would hopefully start some discussion and help me debug the program. Specifically, the Loki stats look a little high, but I’m not sure if that’s because of a bug in my code or if the results are actually right: having other peoples data (specifically on how many times it does not result in any matched tiles) would greatly help with this.
(Source Code Here: https://github.com/NorthernPolarity/MPQSimulator)

Current Simulator Status:
Imagine MPQ without any crit tiles or anything pertaining to damage, and thats basically the state of what my simulator can do right now. This means that cascades and match-4s destroying entire rows are all currently supported in the simulator.
Destroy tile and swap tile abilities are currently the only abilities that are supported right now.

Simulation Details:
For each simulation run, I construct a new, valid initial board, and then simulate the ability used on that board. Each simulation is run 200,000 times and averaged out to the numbers that you see here.
Remember that a match-4 destroys an entire row of tiles, which is 8 destroyed tiles.

For destroy tile abilities, these numbers are the tiles destroyed from ensuing cascades and matches, NOT including the tiles destroyed from casting the ability itself.

Devil Dinosaur (Gigantic Reptile) icon_devildino.png

4 Star Rarity (Legendary) Discussion link. Wiki link
At Max Level: HP: 19180 Tile damage: 11/73/9/64/82/10

  • Prehistoric Arms - Purple 3 AP
    Devil Dinosaur waves his foreshortened forearms ferociously, moving one Black tile to the top left of the board.
    Probability of a cascade occurring: 0.09173399999999998
    Average tiles destroyed: 0.458432
    Average Tiles destroyed by color:
    BLACK: 0.09777 tiles destroyed
    RED: 0.059668 tiles destroyed
    BLUE: 0.059498 tiles destroyed
    TEAMUP: 0.06071 tiles destroyed
    YELLOW: 0.059544 tiles destroyed
    GREEN: 0.06112 tiles destroyed
    PURPLE: 0.060122 tiles destroyed

    Level Upgrades

    • Level 2: Also moves one Red tile.
      Probability of a cascade occurring: 0.16137199999999996
      Average tiles destroyed: 0.860412
      Average Tiles destroyed by color:
      BLACK: 0.110118 tiles destroyed
      RED: 0.152672 tiles destroyed
      BLUE: 0.120632 tiles destroyed
      TEAMUP: 0.119456 tiles destroyed
      YELLOW: 0.11764 tiles destroyed
      GREEN: 0.12018 tiles destroyed
      PURPLE: 0.119714 tiles destroyed

      Level 3: Also moves one Green tile.
      Probability of a cascade occurring: 0.22321000000000002
      Average tiles destroyed: 1.237676
      Average Tiles destroyed by color:
      BLACK: 0.158364 tiles destroyed
      RED: 0.163098 tiles destroyed
      BLUE: 0.176912 tiles destroyed
      TEAMUP: 0.177918 tiles destroyed
      YELLOW: 0.177264 tiles destroyed
      GREEN: 0.20775 tiles destroyed
      PURPLE: 0.17637 tiles destroyed

      Level 4: Also moves one Yellow tile.
      Probability of a cascade occurring: 0.278366
      Average tiles destroyed: 1.598566
      Average Tiles destroyed by color:
      BLACK: 0.16814 tiles destroyed
      RED: 0.213838 tiles destroyed
      BLUE: 0.236418 tiles destroyed
      TEAMUP: 0.235758 tiles destroyed
      YELLOW: 0.247566 tiles destroyed
      GREEN: 0.26131 tiles destroyed
      PURPLE: 0.235536 tiles destroyed

      Level 5: Also moves a Purple and a Blue tile.
      Probability of a cascade occurring: 0.347738
      Average tiles destroyed: 2.121538
      Average Tiles destroyed by color:
      BLACK: 0.253218 tiles destroyed
      RED: 0.261364 tiles destroyed
      BLUE: 0.354934 tiles destroyed
      TEAMUP: 0.34608 tiles destroyed
      YELLOW: 0.292494 tiles destroyed
      GREEN: 0.315838 tiles destroyed
      PURPLE: 0.29761 tiles destroyed[/color]
      [/list]

    Daken (Classic) icon_daken.png

    3 Star Rarity (Rare) - Gold Character Discussion link. Wiki link.
    At Max Level: HP: 6800 Tile damage: 11/12/61/70/13/79/4.0

    • **Chemical Reaction - Blue 5 bluetile.png
      **
      Daken springs a trap, but his addiction to “Heat” threatens to push him over the edge. Damages the target for 99, converts two blue tiles to green, and converts up to 2 friendly strike tiles to basic tiles doing 50 damage per strike tile converted.
      Probability of a cascade occurring: 0.16993800000000003
      Average tiles destroyed: 0.998456
      Average Tiles destroyed by color:
      BLUE: 0.045092 tiles destroyed
      GREEN: 0.615916 tiles destroyed
      BLACK: 0.067416 tiles destroyed
      PURPLE: 0.06869 tiles destroyed
      YELLOW: 0.066726 tiles destroyed
      TEAMUP: 0.066914 tiles destroyed
      RED: 0.067702 tiles destroyed
      • Level 2: Increases cleared strike tile damage to 58.
        Level 3: Converts up to 3 Strike tiles (730 Base Damage + 420 per Strike tile * 3 tiles = 1990 damage).
        Level 4: Converts up to 4 Strike tiles (730 Base Damage + 420 per Strike tile * 4 tiles = 2410 damage).
        Level 5: Increases cleared Strike tile damage to 70 (730 Base Damage + 511 per strike tile * 4 tiles = 2774 damage).
        [/color]
        [/list]

        Doctor Doom (Classic)
        3 Star Rarity (Rare) Wiki link.
        At Max Level: HP: 8500 Tile damage: 11/12/79/61/13/70

      • Technopathic Strike - Blue 9 AP
        Doctor Doom lashes out with his sinister inventions, swaying the battle in his favor. Transforms 6 basic Blue tiles to Black tiles.
        Probability of a cascade occurring: 0.512268
        Average tiles destroyed: 4.201884
        Average Tiles destroyed by color:
        BLUE: 0.100682 tiles destroyed
        YELLOW: 0.31765 tiles destroyed
        TEAMUP: 0.313732 tiles destroyed
        RED: 0.317342 tiles destroyed
        PURPLE: 0.316376 tiles destroyed
        GREEN: 0.313246 tiles destroyed
        BLACK: 2.522856 tiles destroyed

        • Level 2: Transforms 7 tiles.
          robability of a cascade occurring: 0.575122
          Average tiles destroyed: 5.109416
          Average Tiles destroyed by color:
          BLUE: 0.10473 tiles destroyed
          YELLOW: 0.391226 tiles destroyed
          TEAMUP: 0.391518 tiles destroyed
          RED: 0.390358 tiles destroyed
          PURPLE: 0.386444 tiles destroyed
          GREEN: 0.389048 tiles destroyed
          BLACK: 3.056092 tiles destroyed

                  Level 3: Transforms 8 tiles.
                  Probability of a cascade occurring: 0.624556
                  Average tiles destroyed: 5.984008
                  Average Tiles destroyed by color:
                  BLUE: 0.102096 tiles destroyed
                  YELLOW: 0.462784 tiles destroyed
                  TEAMUP: 0.462774 tiles destroyed
                  RED: 0.464472 tiles destroyed
                  PURPLE: 0.462226 tiles destroyed
                  GREEN: 0.461336 tiles destroyed
                  BLACK: 3.56832 tiles destroyed
          
                  Level 4: Transforms 9 tiles.
                  Probability of a cascade occurring: 0.660236
                  Average tiles destroyed: 6.743458
                  Average Tiles destroyed by color:
                  BLUE: 0.097204 tiles destroyed
                  YELLOW: 0.526532 tiles destroyed
                  TEAMUP: 0.52636 tiles destroyed
                  RED: 0.526658 tiles destroyed
                  PURPLE: 0.526934 tiles destroyed
                  GREEN: 0.529698 tiles destroyed
                  BLACK: 4.010072 tiles destroyed
          
                  Level 5: Transforms all basic Blue tiles.
                  Probability of a cascade occurring: 0.708704
                  Average tiles destroyed: 8.303106
                  Average Tiles destroyed by color:
                  BLUE: 0.072712 tiles destroyed
                  YELLOW: 0.659816 tiles destroyed
                  TEAMUP: 0.659096 tiles destroyed
                  RED: 0.658918 tiles destroyed
                  PURPLE: 0.659422 tiles destroyed
                  GREEN: 0.65993 tiles destroyed
                  BLACK: 4.933212 tiles destroyed
                  [/color]
          [/list]
          
          <span style="font-size: 150px">Human Torch (Classic)</span>  ![icon_humantorch.png|34x34](upload://lVmO1qFlyBS0xkQoRdFeY5FxS9w.png)
          
          *3 Star Rarity (Rare)* [Discussion link](https://forums.d3go.com/discussion/5641). [Wiki link](http://marvelpuzzlequest.wikia.com/wiki/Human_Torch_(Classic)).
          <u>At Max Level:</u> HP: **5950** Tile damage: <span style="color: darkgoldenrod">13</span>/<span style="color: red">79</span>/<span style="color: blue">12</span>/<span style="color: purple">11</span>/<span style="color: green">61</span>/70/3.0
          
        • **Fireball - Red 8 redtile.png
          **
          Johnny hurls a fistful of flame, torching the opponent. Deals 177 damage and blisters the battlefield, destroying 2 red tiles.
          Probability of a cascade occurring: 0.305805
          Average tiles destroyed: 1.860545

          • Level 2: 248 damage.
            Level 3: 319 damage
            Level 4: 389 damage
            Level 5: 460 damage
            Max Level: 3390 damage. [/color]
            [/list]

                  (Some help on verifying these numbers would be greatly appreciated).
                  <span style="font-size: 150px">Loki (Dark Reign)</span>  ![icon_loki.png|34x34](upload://nNxF4NMkhi1vdlMSASLucHMYMey.png)
            
                  *3 Star Rarity (Rare)* [Discussion link](https://forums.d3go.com/discussion/743). [Wiki link](http://marvelpuzzlequest.wikia.com/wiki/http://marvelpuzzlequest.wikia.com/wiki/Loki_(Dark_Reign)).
                  <u>At Max Level:</u> HP: **5023** Tile damage: <span style="color: darkgoldenrod">11</span>/<span style="color: red">10</span>/<span style="color: blue">12</span>/<span style="color: purple">69</span>/<span style="color: green">54</span>/61/3.0
            
          • **Illusions - Purple 5 purpletile.png
            **
            You can’t count on anything when Loki’s around. Changes the location of 14 colored tiles.
            Probability of a cascade occurring: 0.6881280000000001
            Average tiles destroyed: 6.029014
            Average Tiles destroyed by color:
            YELLOW: 0.936542 tiles destroyed
            PURPLE: 0.937994 tiles destroyed
            TEAMUP: 0.409472 tiles destroyed
            BLUE: 0.933416 tiles destroyed
            RED: 0.936088 tiles destroyed
            BLACK: 0.936684 tiles destroyed
            GREEN: 0.938818 tiles destroyed

            • Level 2: Changes the location of 18 colored tiles.
              Probability of a cascade occurring: 0.72986
              Average tiles destroyed: 6.767658
              Average Tiles destroyed by color:
              YELLOW: 1.050648 tiles destroyed
              PURPLE: 1.05467 tiles destroyed
              TEAMUP: 0.464912 tiles destroyed
              BLUE: 1.049222 tiles destroyed
              RED: 1.048222 tiles destroyed
              BLACK: 1.052072 tiles destroyed
              GREEN: 1.047912 tiles destroyed

                                        Level 3: Changes the location of 22 colored tiles.
                                        Probability of a cascade occurring: 0.750724
                                        Average tiles destroyed: 7.2153
                                        Average Tiles destroyed by color:
                                        YELLOW: 1.119284 tiles destroyed
                                        PURPLE: 1.120554 tiles destroyed
                                        TEAMUP: 0.495888 tiles destroyed
                                        BLUE: 1.123598 tiles destroyed
                                        RED: 1.118448 tiles destroyed
                                        BLACK: 1.119518 tiles destroyed
                                        GREEN: 1.11801 tiles destroyed
              
              
                                        Level 4: Changes the location of 26 colored tiles.
                                        Probability of a cascade occurring: 0.759622
                                        Average tiles destroyed: 7.399498
                                        Average Tiles destroyed by color:
                                        YELLOW: 1.146806 tiles destroyed
                                        PURPLE: 1.150456 tiles destroyed
                                        TEAMUP: 0.510474 tiles destroyed
                                        BLUE: 1.14881 tiles destroyed
                                        RED: 1.149742 tiles destroyed
                                        BLACK: 1.14733 tiles destroyed
                                        GREEN: 1.14588 tiles destroyed
              
                                        Level 5: Changes the location of 32 colored tiles.
                                        Probability of a cascade occurring: 0.759988
                                        Average tiles destroyed: 7.432984
                                        Average Tiles destroyed by color:
                                        YELLOW: 1.160318 tiles destroyed
                                        PURPLE: 1.152388 tiles destroyed
                                        TEAMUP: 0.50907 tiles destroyed
                                        BLUE: 1.15506 tiles destroyed
                                        RED: 1.151638 tiles destroyed
                                        BLACK: 1.152512 tiles destroyed
                                        GREEN: 1.151998 tiles destroyed
                            </span>
              
          • **Illusions Used Right After Polarizing Force- Purple 5 purpletile.png
            **
            You can’t count on anything when Loki’s around. Changes the location of 14 colored tiles.
            Probability of a cascade occurring: 0.79647
            Average tiles destroyed: 8.551478
            Average Tiles destroyed by color:
            BLACK: 1.392442 tiles destroyed
            TEAMUP: 0.194494 tiles destroyed
            RED: 1.392654 tiles destroyed
            GREEN: 1.392828 tiles destroyed
            PURPLE: 1.390598 tiles destroyed
            YELLOW: 1.39293 tiles destroyed
            BLUE: 1.395532 tiles destroyed

            • Level 2: Changes the location of 18 colored tiles.
              Probability of a cascade occurring: 0.8378220000000001
              Average tiles destroyed: 9.740064
              Average Tiles destroyed by color:
              BLACK: 1.585076 tiles destroyed
              TEAMUP: 0.224488 tiles destroyed
              RED: 1.590054 tiles destroyed
              GREEN: 1.58356 tiles destroyed
              PURPLE: 1.587174 tiles destroyed
              YELLOW: 1.583846 tiles destroyed
              BLUE: 1.585866 tiles destroyed

                                        Level 3: Changes the location of 22 colored tiles.
                                        Probability of a cascade occurring: 0.859708
                                        Average tiles destroyed: 10.538032
                                        Average Tiles destroyed by color:
                                        BLACK: 1.713142 tiles destroyed
                                        TEAMUP: 0.24264 tiles destroyed
                                        RED: 1.716022 tiles destroyed
                                        GREEN: 1.713856 tiles destroyed
                                        PURPLE: 1.716996 tiles destroyed
                                        YELLOW: 1.716912 tiles destroyed
                                        BLUE: 1.718464 tiles destroyed
              
                                        Level 4: Changes the location of 26 colored tiles.
                                        Probability of a cascade occurring: 0.8718319999999999
                                        Average tiles destroyed: 10.979988
                                        Average Tiles destroyed by color:
                                        BLACK: 1.784592 tiles destroyed
                                        TEAMUP: 0.254284 tiles destroyed
                                        RED: 1.792782 tiles destroyed
                                        GREEN: 1.7833 tiles destroyed
                                        PURPLE: 1.78927 tiles destroyed
                                        YELLOW: 1.788108 tiles destroyed
                                        BLUE: 1.787652 tiles destroyed
              
                                        Level 5: Changes the location of 32 colored tiles.
                                        Probability of a cascade occurring: 0.877366
                                        Average tiles destroyed: 11.208996
                                        Average Tiles destroyed by color:
                                        BLACK: 1.825024 tiles destroyed
                                        TEAMUP: 0.2625 tiles destroyed
                                        RED: 1.822766 tiles destroyed
                                        GREEN: 1.82243 tiles destroyed
                                        PURPLE: 1.82404 tiles destroyed
                                        YELLOW: 1.822218 tiles destroyed
                                        BLUE: 1.830018 tiles destroyed
                            </span>
              
              
                  <span style="font-size: 150px">Magneto (Classic)</span>  ![icon_magneto.png|34x34](upload://5rBrhWXH2TjgGDbwlHIYyQnVATo.png)
              
                  *3 Star Rarity (Rare)* [Discussion link](https://forums.d3go.com/discussion/603). [Wiki link](http://marvelpuzzlequest.wikia.com/wiki/http://marvelpuzzlequest.wikia.com/wiki/Magneto_(Classic)).
                  <u>At Max Level:</u> HP: **6800** Tile damage: <span style="color: darkgoldenrod">61</span>/<span style="color: red">70</span>/<span style="color: blue">79</span>/<span style="color: purple">11</span>/<span style="color: green">12</span>/13/3.2
              
          • **Polarizing Force - Red 8 redtile.png
            **
            Magneto hurls a massive metal object towards the heart of the enemy team, landing with tremendous force and causing them to scatter. Destroys all Team-Up tiles, dealing 27 damage per tile. Does not generate AP.
            Probability of a cascade occurring: 0.692705
            Average tiles destroyed: 6.470575

            • Level 2: Deals 43 damage per tile.
              Level 3: Deals 49 damage per tile.
              Level 4: Deals 59 damage per tile.
              Level 5: Deals 81 damage per tile.
              Max Level: 261 damage per tile[/color]
              [/list]
            • **Magnetized Projectiles - Blue 10 bluetile.png
              **
              Magneto turns metallic objects into deadly projectiles, causing devastation and chaos. Swaps up to 5 random Blue tiles with Red tiles. Does 93 damage for each swap.
              Probability of a cascade occurring: 0.30454000000000003
              Average tiles destroyed: 1.977335
              • Level 2: Does 126 damage for each swap.
                Level 3: Swaps up to 6 tiles.
                Probability of a cascade occurring: 0.29413500000000004
                Average tiles destroyed: 1.916975

                                                      Level 4: Does 169 damage for each swap.
                                                      Level 5: Swaps up to 7 random tiles and does 224 damage for each swap.
                                                      Probability of a cascade occurring: 0.26805999999999996
                                                      Average tiles destroyed: 1.73974
                
                                                      <u>Max Level: 713 damage per swap. Max damage of 4991.</u>[/color]
                                        [/list]
                
                                        <span style="font-size: 150px">Mystique (Raven Darkholme)</span> 
                
                                        *3 Star Rarity (Rare)* [Interview at Marvel.com](http://marvel.com/news/video_games/23607/piecing_together_marvel_puzzle_quest_mystique). 
                
                                        <u>At Max Level:</u> HP: **5950** Tile damage: <span style="color: darkgoldenrod">12</span>/<span style="color: red">13</span>/<span style="color: blue">70</span>/<span style="color: purple">79</span>/<span style="color: green">11</span>/61/3.0
                
              • **Infiltration - Blue 9 bluetile.png
                **
                Blue brings us Infiltration, which works to power her other two abilities. This ability acts much like Doctor Doom’s Technopathic Strike in that it converts tiles from one color to another. In this case, Raven changes a certain number of basic Red, Green, and Yellow tiles to Purple and Black ones. Higher levels of the ability increase the number of tiles affected. With this, Mystique can better control the incoming damage the opponents are able to put out, since those colors she converts are the ones most often used in directly damaging abilities. Transforms 5 tiles
                Probability of a cascade occurring: 0.40357
                Average tiles destroyed: 2.79847
                Average Tiles destroyed by color:
                GREEN: 0.144645 tiles destroyed
                PURPLE: 0.988965 tiles destroyed
                BLUE: 0.197105 tiles destroyed
                YELLOW: 0.14456 tiles destroyed
                TEAMUP: 0.196405 tiles destroyed
                BLACK: 0.98514 tiles destroyed
                RED: 0.14165 tiles destroyed

                • Level 2: Transforms 6 Tiles
                  Probability of a cascade occurring: 0.47714999999999996
                  Average tiles destroyed: 3.534995
                  Average Tiles destroyed by color:
                  GREEN: 0.174155 tiles destroyed
                  PURPLE: 1.25528 tiles destroyed
                  BLUE: 0.249835 tiles destroyed
                  YELLOW: 0.17296 tiles destroyed
                  TEAMUP: 0.25289 tiles destroyed
                  BLACK: 1.256795 tiles destroyed
                  RED: 0.17308 tiles destroyed

                                                                      Level 3: Transforms 7 Tiles
                                                                      Probability of a cascade occurring: 0.546075
                                                                      Average tiles destroyed: 4.356165
                                                                      Average Tiles destroyed by color:
                                                                      GREEN: 0.20703 tiles destroyed
                                                                      PURPLE: 1.55399 tiles destroyed
                                                                      BLUE: 0.31593 tiles destroyed
                                                                      YELLOW: 0.205615 tiles destroyed
                                                                      TEAMUP: 0.31733 tiles destroyed
                                                                      BLACK: 1.55187 tiles destroyed
                                                                      RED: 0.2044 tiles destroyed
                  
                                                                      Level 4: Transforms 8 tiles.
                                                                      Probability of a cascade occurring: 0.6090249999999999
                                                                      Average tiles destroyed: 5.24024
                                                                      Average Tiles destroyed by color:
                                                                      GREEN: 0.23634 tiles destroyed
                                                                      PURPLE: 1.87576 tiles destroyed
                                                                      BLUE: 0.388435 tiles destroyed
                                                                      YELLOW: 0.239535 tiles destroyed
                                                                      TEAMUP: 0.38246 tiles destroyed
                                                                      BLACK: 1.88098 tiles destroyed
                                                                      RED: 0.23673 tiles destroyed
                  
                                                                      Level 5: Transforms 10 tiles.
                                                                      Probability of a cascade occurring: 0.71912
                                                                      Average tiles destroyed: 7.28177
                                                                      Average Tiles destroyed by color:
                                                                      GREEN: 0.3083 tiles destroyed
                                                                      PURPLE: 2.619425 tiles destroyed
                                                                      BLUE: 0.55659 tiles destroyed
                                                                      YELLOW: 0.310495 tiles destroyed
                                                                      TEAMUP: 0.556525 tiles destroyed
                                                                      BLACK: 2.623495 tiles destroyed
                                                                      RED: 0.30694 tiles destroyed
                                                                      <u>Max Level: </u>[/color]
                                                      [/list]
                  
                                                      <span style="font-size: 150px">The Punisher (Dark Reign)</span>  ![icon_punisher.png|34x34](upload://1G0eFai74NAiO3oENeoh6uhp1ly.png)
                  
                                                      *3 Star Rarity (Rare)* [Discussion link](https://forums.d3go.com/discussion/1123). [Wiki link](http://marvelpuzzlequest.wikia.com/wiki/The_Punisher_(Dark_Reign)).
                                                      <u>At Max Level:</u> HP: **6800** Tile damage: <span style="color: darkgoldenrod">11</span>/<span style="color: red">61</span>/<span style="color: blue">12</span>/<span style="color: purple">13</span>/<span style="color: green">70</span>/79/4.0
                  
                • **Judgement - Green 8 greentile.png
                  **
                  The Punisher unloads his arsenal. Destroys a 3x3 group of tiles, doing damage but not generating AP. Chaos creates an opening, converting a basic color tile to a strength 12 Strike tile.
                  Probability of a cascade occurring: 0.37356
                  Average tiles destroyed: 2.358616
                  Average Tiles destroyed by color:
                  YELLOW: 0.338282 tiles destroyed
                  TEAMUP: 0.33645 tiles destroyed
                  GREEN: 0.336656 tiles destroyed
                  BLACK: 0.336926 tiles destroyed
                  RED: 0.33823 tiles destroyed
                  BLUE: 0.337034 tiles destroyed
                  PURPLE: 0.335038 tiles destroyed

                  • Level 2: Increases Strike tile strength to 14.
                    Level 3: Creates 2 Strike tiles.
                    Level 4: Increases Strike tile strength to 17.
                    Level 5: Creates 3 Strike tiles.
                    Max Level: Damage increased by 122 per Strike tile

                                                      <span style="font-size: 150px">Storm (Mohawk)</span>  ![icon_storm.png|34x34](upload://pVf9AJZnvZn83N5aad3w8BH9Nrc.png)
                    
                                                      *3 Star Rarity (Rare) - (Gold Character)* [Discussion link](https://forums.d3go.com/discussion/6628)
                                                      <u>At Max Level:</u> HP: **5100** Tile damage: <span style="color: darkgoldenrod">70</span>/<span style="color: red">12</span>/<span style="color: blue">11</span>/<span style="color: purple">13</span>/<span style="color: green">79</span>/61/3.5
                    
                • **Lightning Strike - Green 10 greentile.png
                  **
                  Storm calls a blinding bolt of electricity from the heavens, shattering 8 tiles, doing damage and earning AP for each.
                  Probability of a cascade occurring: 0.585045
                  Average tiles destroyed: 4.444835

                  • Level 2: Shatters 9 tiles.
                    Probability of a cascade occurring: 0.6075550000000001
                    Average tiles destroyed: 4.706675

                                                                                        Level 3: Shatters 10 tiles.
                                                                                        Probability of a cascade occurring: 0.62503
                                                                                        Average tiles destroyed: 4.953605
                    
                                                                                        Level 4: Shatters 12 tiles.
                                                                                        Probability of a cascade occurring: 0.6579699999999999
                                                                                        Average tiles destroyed: 5.41383
                    
                                                                                        Level 5: Shatters 14 tiles.
                                                                                        Probability of a cascade occurring: 0.68544
                                                                                        Average tiles destroyed: 5.83543
                                                                      </span>
                    
                • **Mistress of the Elements - Yellow 9 yellowtile.png
                  **
                  Clouds darken the battlefield and lightning streaks across the sky as Storm’s awesome power inspires her teammates and assaults her foes. Destroys up to 5 Team-Up tiles, generating Team-Up AP and dealing 38 damage per tile.
                  Probability of a cascade occurring: 0.52984
                  Average tiles destroyed: 3.923435

                  • Level 2: Deals 46 damage for each tile shattered
                    Level 3: Deals 53 damage for each tile shattered
                    Level 4: Deals 68 damage for each tile shattered
                    Level 5: Destroys 7 Team-Up tiles

                                                                                        Probability of a cascade occurring: 0.6119049999999999
                                                                                        Average tiles destroyed: 5.010295
                                                                                        <u>Max Level: 220 damage per tile (1540 total) </u>
                                                                      </span>
                    
                    
                                                      <span style="font-size: 150px">Thor (Modern)</span>  ![icon_thor.png|34x34](upload://4ekeHqDZIFhzZwz6PpytrcOZjww.png)
                    
                                                      *3 Star Rarity (Rare) - (Gold Character)* [Discussion link](https://forums.d3go.com/discussion/4281). [Wiki link](http://marvelpuzzlequest.wikia.com/wiki/Thor_(Modern)).
                                                      <u>At Max Level:</u> HP: **10200** Tile damage: <span style="color: darkgoldenrod">70</span>/<span style="color: red">79</span>/<span style="color: blue">12</span>/<span style="color: purple">11</span>/<span style="color: green">61</span>/13/3.5
                    
                • **Mjolnir’s Might - Red 8 redtile.png
                  **
                  Thor brings his hammer down on the enemy, dealing 44 damage. The magical energies of his hammer begin to charge his next strike, adding 3 Yellow tiles to the board.
                  Probability of a cascade occurring: 0.26688
                  Average tiles destroyed: 1.674645
                  Average Tiles destroyed by color:
                  GREEN: 0.10305 tiles destroyed
                  TEAMUP: 0.11666 tiles destroyed
                  BLUE: 0.104855 tiles destroyed
                  YELLOW: 1.03711 tiles destroyed
                  PURPLE: 0.10463 tiles destroyed
                  BLACK: 0.10498 tiles destroyed
                  RED: 0.10336 tiles destroyed

                  • Level 2: 135 damage.
                    Level 3: 187 damage. (Max: 1370)
                    Level 4: 239 damage.
                    Level 5: 291 damage.
                    Max Level: 2132 damage[/color]
                    [/list]
                  • **Thunder Strike - Yellow 12 yellowtile.png
                    **
                    A lightning bolt pierces the sky and rips into the target, dealing 154 damage. A storm is brewing; 4 Green tiles are added to the board.
                    Probability of a cascade occurring: 0.362105
                    Average tiles destroyed: 2.460635
                    Average Tiles destroyed by color:
                    YELLOW: 0.15433 tiles destroyed
                    TEAMUP: 0.173805 tiles destroyed
                    BLACK: 0.15225 tiles destroyed
                    PURPLE: 0.1547 tiles destroyed
                    GREEN: 1.5233 tiles destroyed
                    BLUE: 0.1514 tiles destroyed
                    RED: 0.15085 tiles destroyed
                    • Level 2: Converts 5 tiles. 200 damage.
                      Probability of a cascade occurring: 0.45879000000000003
                      Average tiles destroyed: 3.404655
                      Average Tiles destroyed by color:
                      YELLOW: 0.208055 tiles destroyed
                      TEAMUP: 0.25313 tiles destroyed
                      BLACK: 0.208625 tiles destroyed
                      PURPLE: 0.209495 tiles destroyed
                      GREEN: 2.10045 tiles destroyed
                      BLUE: 0.21319 tiles destroyed
                      RED: 0.21171 tiles destroyed

                                                                                                            Level 3: Converts 6 tiles. 246 damage.
                                                                                                            Probability of a cascade occurring: 0.55051
                                                                                                            Average tiles destroyed: 4.494845
                                                                                                            Average Tiles destroyed by color:
                                                                                                            YELLOW: 0.27996 tiles destroyed
                                                                                                            TEAMUP: 0.34022 tiles destroyed
                                                                                                            BLACK: 0.277645 tiles destroyed
                                                                                                            PURPLE: 0.279625 tiles destroyed
                                                                                                            GREEN: 2.756725 tiles destroyed
                                                                                                            BLUE: 0.28058 tiles destroyed
                                                                                                            RED: 0.28009 tiles destroyed
                      
                                                                                                            Level 4: Converts 7 tiles. 293 damage.
                                                                                                            Probability of a cascade occurring: 0.636285
                                                                                                            Average tiles destroyed: 5.747725
                                                                                                            Average Tiles destroyed by color:
                                                                                                            YELLOW: 0.354215 tiles destroyed
                                                                                                            TEAMUP: 0.452115 tiles destroyed
                                                                                                            BLACK: 0.35486 tiles destroyed
                                                                                                            PURPLE: 0.355335 tiles destroyed
                                                                                                            GREEN: 3.519175 tiles destroyed
                                                                                                            BLUE: 0.357065 tiles destroyed
                                                                                                            RED: 0.35496 tiles destroyed
                      
                                                                                                            Level 5: Converts 9 tiles. 339 damage.
                                                                                                            Probability of a cascade occurring: 0.780725
                                                                                                            Average tiles destroyed: 8.72598
                                                                                                            Average Tiles destroyed by color:
                                                                                                            YELLOW: 0.53998 tiles destroyed
                                                                                                            TEAMUP: 0.720015 tiles destroyed
                                                                                                            BLACK: 0.539935 tiles destroyed
                                                                                                            PURPLE: 0.537825 tiles destroyed
                                                                                                            GREEN: 5.311655 tiles destroyed
                                                                                                            BLUE: 0.53791 tiles destroyed
                                                                                                            RED: 0.53866 tiles destroyed
                      
                                                                                                            <u>Max Level: Deals 2486 damage and Converts 9 tiles to green.</u>[/color]
                                                                                        [/list]
                      
                                                                                        <span style="font-size: 150px">Juggernaut (Classic)</span>
                                                                                        *1 Star Rarity (Common)* [Discussion link](https://forums.d3go.com/discussion/820)
                                                                                        <u>At Max Level:</u> HP: **3520** Tile damage: <span style="color: darkgoldenrod">7</span>/<span style="color: red">22</span>/<span style="color: blue">6</span>/<span style="color: purple">7</span>/<span style="color: green">25</span>/9
                      
                    • Unstoppable Crash - Green 10 AP
                      Juggernaut’s momentum sends him barreling through the battlefield, destroying 16 random tiles. Does not generate AP.
                      Probability of a cascade occurring: 0.704602
                      Average tiles destroyed: 6.195122
                      Average Tiles destroyed by color:
                      GREEN: 0.882762 tiles destroyed
                      TEAMUP: 0.886968 tiles destroyed
                      PURPLE: 0.881424 tiles destroyed
                      YELLOW: 0.887794 tiles destroyed
                      RED: 0.885588 tiles destroyed
                      BLACK: 0.885824 tiles destroyed
                      BLUE: 0.884762 tiles destroyed

                      • Level 2: Costs 1 AP less.
                        Level 3: Costs 1 AP less.
                        Level 4: Costs 1 AP less.
                        Level 5: Costs 1 AP less.[/color]
                        [/list]

                                                                                                            <span style="font-size: 150px"> Single, Green Colored CD Tile Being Destroyed </span>
                                                                                                            Probability of a cascade occurring: 0.17865799999999998
                                                                                                            Average tiles destroyed: 1.002972
                                                                                                            Average Tiles destroyed by color:
                                                                                                            BLACK: 0.150524 tiles destroyed
                                                                                                            TEAMUP: 0.150732 tiles destroyed
                                                                                                            YELLOW: 0.150504 tiles destroyed
                                                                                                            BLUE: 0.150536 tiles destroyed
                                                                                                            PURPLE: 0.15124 tiles destroyed
                                                                                                            RED: 0.15094 tiles destroyed
                                                                                                            GREEN: 0.098496 tiles destroyed
                        
                                                                                                            **"Immediate" Goals**:
                                                                                                            Finishing adding all abilities that are currently supported (destroy random colored tiles, swap tiles, change tile colors).
                                                                                                            Adding support for abilities that destroy tiles in a particular pattern at random (X-Force). 
                                                                                                            Implementing crit tiles.
                        
                        
                                                                                                            **The Distant Future Goals**:
                                                                                                            Accounting for match 5 potential after cascades (the idea being that after you use an ability, if the resulting board has a match-5 available, then that should be counted as part of the cascade since the player can just perform the match-5 and continue cascading). 
                                                                                                            Programming an AI so we can simulate full matches. 
                                                                                                            Simulating damage dealt and taken.
                                                                                                            Simulating more accurate board states (average board a player sees probably has a higher density of TU tiles since we tend to not match TU tiles).
                                                                                                            Support for board tile types (attack, defense, etc)
                                                                                                            Super crazy idea - you take a picture of your game just before you want to use say GSBW and send it to MPQSimulator, who will then tell you exactly where to place the tiles to optimize tiles destroyed / cascade potential.
                        
                                                                                                            **<span style="font-size: 150px">Contributors</span>**
                        
                                                                                                            **HUGE** thanks to eeeeeee, who has done a ton of refactoring on the code and implementing of new features.</span>
                                                                                        </span>
                                                                      </span>
                                                      </span>
                                        </span>
                            </span>
                        

Changed formatting to be much more readable. (Thanks Nonce for letting me use his templates!) Added stats for Thor and Mystique.

Wow Northern, just wow.

On Loki’s power its doesn’t change place on 32 tiles, it swaps up to 32 pairs of colored tiles. Maybe that is what’s bugging because those numbers actually look quite high as you say.

/z

Thanks NP for all the effort! It looks impressive!

Yeah, I currently have it coded as 32 pairs of tiles. The numbers were even higher before, but locked pointed out that I was swapping TU tiles as well: the current ones look sort of right? Keep in mind that these tests are performed on boards with a roughly uniform distribution of tiles on average. I could see a case where the actual average board has a higher density of TU tiles than normal since players tend to match colored tiles and ignore TU tiles, which would lead to less cascades overall. The simulator unfortunately doesn’t have the capability to account for this… yet, so I’m content with those numbers for now.

What’s the definition of a cascade? Does a single match-3 count as a cascade?

A cascade means that using the ability resulted in at least one-match 3 (or more) being generated afterwards.

So for example, you use Storm’s green. That destroys 14 tiles or whatever at level 5. After the tiles have been destroyed and the board shifts accordingly from the initial tile destruction, there is a 68% chance that the new board will immediately contain 3 adjacent horizontal/vertical tiles which are matched away immediately in a “cascade”, which further changes the board. The simulator right now accounts for all of the cascades that occur, including the ones caused by cascades themselves. What the simulator doesn’t cover though, is tiles that are spawned in a position that aren’t matched away immediately, but can be matched by the player in a match 5 formation to get an extra turn, which I think should be counted as a “cascade” → a later update, I suppose.

The part where the odds of a cascade actually drop slightly when you level up Magneto’s blue from 1 to 3 (and then go back up from 3 to 5) kind of blows my mind.

It actually drops from 3->5 as well, which blew my mind when I first saw it too. It makes when you think about it: if there were 7 red/blue tiles and you swapped all of them, then that would lead to 0 cascades. The only time a cascade is caused is if you’re only swapping some of the tiles so that a swapped red tile can be swapped into 2 adjacent, unswapped red tiles. This means that the less tiles you swap, the more cascades are caused, which is pretty crazy.

Can you do a simulation of one coloured tile being destroyed? This would fit in with goons and many countdown abilities. I’m sure after the last heroic, people would be interested in Unstoppable Crash results.

Do you have any results on devil Dino that would lead to recommending 3, 4 or 5 purple covers? Mine is currently 3/5/5 but I have some covers expiring in a couple days

Done.

And done.

Let me know if there are any abilities that you guys are dying to know specifically. I’m going to add all of them eventually, but priorities could be helpful. Just note that X-Force and abilities that destroy patterns isn’t really implemented yet, and is gonna take some time.

3 purple - 22.3% chance of cascade
4 purple - 27.8% chance of cascade
5 purple - 34.8% chance of cascade

As expected, doesn’t seem like going with 5 in purple is worth nerfing one–or both–of his other abilities.

Level 3 average tiles destroyed: 1.237676
Level 4 average tiles destroyed: 1.598566
Level 5 average tiles destroyed: 2.121538

I’m not so sure I agree. L3 to L5 purple makes getting any match at all over 50% more likely, and it gives you nearly 1 more AP on average, which is a pretty big deal for an ability you’ll cast 2-4 times on offense and maybe twice that on defense. Also consider opportunity cost – purple is getting better, with Mystique and Blade in the mix, but in general you’d rather cast almost any green, and usually you’ll have a better red, too.

Sure, the damage difference for even L4 to L5 green/red is big (about 1k), so it’s definitely not cut-and-dried, but I’m running mine 4/4/5 and have no plans to respec him (already tossed a green cover, in fact). I feel like Dino’s main utility is defensive scarecrow, and if you’re looking to get defensive wins, I think your best bet is to increase the chance the AI gets a lucky cascade or four.

I tend to agree with mischiefmaker on this. Considering that the best value of dino is in defence. I had played against max dino, and man, the games were long bec he was using purple very often. As such, you really want to increase the % of the cascades, and having 5 purple helps.

Since a cascade has to destroy at least 3 tiles, I’m assuming that the “average tiles destroyed” is the average number of tiles destroyed in all simulations. However, I think it might also be helpful for people to see the average number of tiles destroyed in only the situations where a cascade occurs. Based on the simulation results you posted, I believe these are those numbers. Please correct me if I’m wrong.

  • Devil Dino - Prehistoric Arms:

    • Level 1
      • Total Tiles Destroyed: 4.997405542
        BLACK Tiles Destroyed: 1.06579894
        RED Tiles Destroyed: 0.6504458543
        BLUE Tiles Destroyed: 0.6485926701
        TEAMUP Tiles Destroyed: 0.6618047834
        YELLOW Tiles Destroyed: 0.64909412
        GREEN Tiles Destroyed: 0.6662742277
        PURPLE Tiles Destroyed: 0.6553949463

        Level 2

      • Total Tiles Destroyed: 5.331854349
        BLACK Tiles Destroyed: 0.6823860397
        RED Tiles Destroyed: 0.9460873014
        BLUE Tiles Destroyed: 0.7475398458
        TEAMUP Tiles Destroyed: 0.7402523362
        YELLOW Tiles Destroyed: 0.728998835
        GREEN Tiles Destroyed: 0.7447388642
        PURPLE Tiles Destroyed: 0.7418511266

        Level 3

      • Total Tiles Destroyed: 5.544894942
        BLACK Tiles Destroyed: 0.7094843421
        RED Tiles Destroyed: 0.7306930693
        BLUE Tiles Destroyed: 0.7925809776
        TEAMUP Tiles Destroyed: 0.7970879441
        YELLOW Tiles Destroyed: 0.7941579678
        GREEN Tiles Destroyed: 0.9307378702
        PURPLE Tiles Destroyed: 0.7901527709

        Level 4

      • Total Tiles Destroyed: 5.742676907
        BLACK Tiles Destroyed: 0.6040249168
        RED Tiles Destroyed: 0.7681900807
        BLUE Tiles Destroyed: 0.849306309
        TEAMUP Tiles Destroyed: 0.8469353297
        YELLOW Tiles Destroyed: 0.8893543033
        GREEN Tiles Destroyed: 0.9387281493
        PURPLE Tiles Destroyed: 0.8461378186

        Level 5

      • Total Tiles Destroyed: 6.10096682
        BLACK Tiles Destroyed: 0.7281861631
        RED Tiles Destroyed: 0.7516118457
        BLUE Tiles Destroyed: 1.020693741
        TEAMUP Tiles Destroyed: 0.9952320425
        YELLOW Tiles Destroyed: 0.841133267
        GREEN Tiles Destroyed: 0.9082642679
        PURPLE Tiles Destroyed: 0.8558454929

    Daken (Classic) - Chemical Reaction

    • All Levels
      • Total Tiles Destroyed: 5.875413386
        BLUE Tiles Destroyed: 0.2653438313
        GREEN Tiles Destroyed: 3.624357118
        BLACK Tiles Destroyed: 0.3967093881
        PURPLE Tiles Destroyed: 0.4042062399
        YELLOW Tiles Destroyed: 0.3926490838
        TEAMUP Tiles Destroyed: 0.3937553696
        RED Tiles Destroyed: 0.3983923549

    Human Torch (Classic) - Fireball

    • All Levels
      • Total Tiles Destroyed: 6.084089534

    Loki - Illusions

    • Level 1
      • Total Tiles Destroyed: 8.725941711

        Level 2

      • Total Tiles Destroyed: 9.302827555

        Level 3

      • Total Tiles Destroyed: 9.558460412

        Level 4

      • Total Tiles Destroyed: 9.760169246

        Level 5

      • Total Tiles Destroyed: 9.803495658

    Magneto (Classic) - Polarizing Force

    • All Levels
      • Total Tiles Destroyed: 9.3410254

    Magneto (Classic) - Magnetized Projectiles

    • Levels 1-2
      • Total Tiles Destroyed: 6.492858081

        Levels 3-4

      • Total Tiles Destroyed: 6.517330478

        Level 5

      • Total Tiles Destroyed: 6.490114154

    Mystique - Infiltration

    • Level 1
      • Total Tiles Destroyed: 6.934286493
        GREEN Tiles Destroyed: 0.3584136581
        PURPLE Tiles Destroyed: 2.450541418
        BLUE Tiles Destroyed: 0.4884034988
        YELLOW Tiles Destroyed: 0.3582030379
        TEAMUP Tiles Destroyed: 0.4866689794
        BLACK Tiles Destroyed: 2.441063508
        RED Tiles Destroyed: 0.3509923929

        Level 2

      • Total Tiles Destroyed: 7.408561249
        GREEN Tiles Destroyed: 0.3649900451
        PURPLE Tiles Destroyed: 2.630786964
        BLUE Tiles Destroyed: 0.5235984491
        YELLOW Tiles Destroyed: 0.3624855915
        TEAMUP Tiles Destroyed: 0.5300010479
        BLACK Tiles Destroyed: 2.633962066
        RED Tiles Destroyed: 0.3627370848

        Level 3

      • Total Tiles Destroyed: 7.977228403
        GREEN Tiles Destroyed: 0.3791237467
        PURPLE Tiles Destroyed: 2.845744632
        BLUE Tiles Destroyed: 0.5785469029
        YELLOW Tiles Destroyed: 0.3765325276
        TEAMUP Tiles Destroyed: 0.5811106533
        BLACK Tiles Destroyed: 2.841862382
        RED Tiles Destroyed: 0.3743075585

        Level 4

      • Total Tiles Destroyed: 8.604310168
        GREEN Tiles Destroyed: 0.3880628874
        PURPLE Tiles Destroyed: 3.079939247
        BLUE Tiles Destroyed: 0.6377981199
        YELLOW Tiles Destroyed: 0.3933089775
        TEAMUP Tiles Destroyed: 0.6279873568
        BLACK Tiles Destroyed: 3.088510324
        RED Tiles Destroyed: 0.3887032552

        Level 5

      • Total Tiles Destroyed: 10.1259456
        GREEN Tiles Destroyed: 0.4287184336
        PURPLE Tiles Destroyed: 3.642542274
        BLUE Tiles Destroyed: 0.7739876516
        YELLOW Tiles Destroyed: 0.4317707754
        TEAMUP Tiles Destroyed: 0.7738972633
        BLACK Tiles Destroyed: 3.648201969
        RED Tiles Destroyed: 0.4268272333

    Storm (Mohawk) - Lightning Strike

    • Level 1
      • Total Tiles Destroyed: 7.59742413

        Level 2

      • Total Tiles Destroyed: 7.746911802

        Level 3

      • Total Tiles Destroyed: 7.925387581

        Level 4

      • Total Tiles Destroyed: 8.228080308

        Level 5

      • Total Tiles Destroyed: 8.513407446

    Storm (Mohawk) - Mistress of the Elements

    • Levels 1-4
      • Total Tiles Destroyed: 7.404943002

        Level 5

      • Total Tiles Destroyed: 8.188027553

    Thor (Modern) - Mjolnir’s Might

    • All Levels
      • Total Tiles Destroyed: 6.274898831
        GREEN Tiles Destroyed: 0.3861285971
        TEAMUP Tiles Destroyed: 0.4371252998
        BLUE Tiles Destroyed: 0.3928919365
        YELLOW Tiles Destroyed: 3.886053657
        PURPLE Tiles Destroyed: 0.3920488609
        BLACK Tiles Destroyed: 0.3933603118
        RED Tiles Destroyed: 0.3872901679

    Thor (Modern) - Thunder Strike

    • Level 1
      • Total Tiles Destroyed: 6.795363223
        YELLOW Tiles Destroyed: 0.4262023446
        TEAMUP Tiles Destroyed: 0.4799850872
        BLACK Tiles Destroyed: 0.4204581544
        PURPLE Tiles Destroyed: 0.4272241477
        GREEN Tiles Destroyed: 4.206790848
        BLUE Tiles Destroyed: 0.418110769
        RED Tiles Destroyed: 0.4165918725

        Level 2

      • Total Tiles Destroyed: 7.420944223
        YELLOW Tiles Destroyed: 0.4534863445
        TEAMUP Tiles Destroyed: 0.5517339088
        BLACK Tiles Destroyed: 0.454728743
        PURPLE Tiles Destroyed: 0.4566250354
        GREEN Tiles Destroyed: 4.57823841
        BLUE Tiles Destroyed: 0.4646788291
        RED Tiles Destroyed: 0.4614529523

        Level 3

      • Total Tiles Destroyed: 8.164874389
        YELLOW Tiles Destroyed: 0.5085466204
        TEAMUP Tiles Destroyed: 0.6180087555
        BLACK Tiles Destroyed: 0.5043414289
        PURPLE Tiles Destroyed: 0.5079380938
        GREEN Tiles Destroyed: 5.007583877
        BLUE Tiles Destroyed: 0.5096728488
        RED Tiles Destroyed: 0.5087827651

        Level 4

      • Total Tiles Destroyed: 9.033255538
        YELLOW Tiles Destroyed: 0.5566923627
        TEAMUP Tiles Destroyed: 0.7105542328
        BLACK Tiles Destroyed: 0.5577060594
        PURPLE Tiles Destroyed: 0.5584525802
        GREEN Tiles Destroyed: 5.530815594
        BLUE Tiles Destroyed: 0.5611714876
        RED Tiles Destroyed: 0.5578632217

        Level 5

      • Total Tiles Destroyed: 11.17676519
        YELLOW Tiles Destroyed: 0.6916391815
        TEAMUP Tiles Destroyed: 0.9222389446
        BLACK Tiles Destroyed: 0.6915815428
        PURPLE Tiles Destroyed: 0.6888789266
        GREEN Tiles Destroyed: 6.803490346
        BLUE Tiles Destroyed: 0.6889877998
        RED Tiles Destroyed: 0.6899484454

    Juggernaut - Unstoppable Crash

    • All Levels
      • Total Tiles Destroyed: 8.792370728
        GREEN Tiles Destroyed: 1.252851965
        TEAMUP Tiles Destroyed: 1.258821292
        PURPLE Tiles Destroyed: 1.25095302
        YELLOW Tiles Destroyed: 1.259993585
        RED Tiles Destroyed: 1.25686274
        BLACK Tiles Destroyed: 1.25719768
        BLUE Tiles Destroyed: 1.255690447

Your assumption is correct, but your numbers make me think that something is wrong with the simulation… (mjolnirs destroying 6 tiles on average when it actually does things? whaaa?) After programming in the rest of the current batch of characters I’m working on, I think I’ll stop programming new abilities and start writing tests to make sure that what I’m doing is correct.

Would it be possible to do this like:

% chance of destroying 3 tiles
% chance of destroying 6 tiles

etc? Because the magic behind cmags red and xforce’s black is that they cause multi-level cascades. I mean obviously the first match after the skill is used is already very useful but I’d love to see something like that.
Maybe a google docs spreadsheet if it becomes too long?

The averages that you currently see ALREADY account for multi-level cascades. That might explain why they’re so high actually, but yeah, I was planning on having more detailed distributions as one of the next steps for the simulator. I’m kind of burnt out on programming this though, so don’t expect any very major updates at a constant pace.

Of all the simulations you’ve run, only Prehistoric Arms, Chemical Reaction, and Fireball have a lower average tiles destroyed in cascades then Mjolnir’s Might. And no one thinks of those as being cascade starters, so it’s not like Mjolnir’s Might is in rarefied air or anything.

Thinking about it, though, a cascade has to have a minimum of 3 tiles destroyed. However, there really doesn’t have to be an upper limit to how many tiles are destroyed. Something like Mjolnir’s Might is rarely going to cause a 10+ tile cascade, but it will happen enough when you run 200,000 simulations. I think the averages work out all right for all simulations because for an ability with a low probability for cascade, the 0’s will drag down the average to where it should be. However, when you take the average of only the cascades, it is probably being pulled too high by a group of outliers. The most common result for Mjolnir’s Might is probably something between 4 and 5. But with a set minimum of 3 and no real maximum, large cascades can skew the average. It’s possible that for low probability abilities, or maybe all abilities in general, instead of using a mean average for the the tiles destroyed when a cascade occurs, the median would be a better indicator of how many tiles are typically being destroyed.