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

NorthernPolarity

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.

[anchor=devildino4]Devil Dinosaur (Gigantic Reptile)[/anchor]
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

[anchor=daken3]Daken (Classic)[/anchor]
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
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).

[anchor=doctordoom3]Doctor Doom (Classic)[/anchor]
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

[anchor=humantorch3]Human Torch (Classic)[/anchor]
3 Star Rarity (Rare) Discussion link. Wiki link.
At Max Level: HP: 5950 Tile damage: 13/79/12/11/61/70/3.0

Fireball - Red 8
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.

(Some help on verifying these numbers would be greatly appreciated).
[anchor=loki3]Loki (Dark Reign)[/anchor]
3 Star Rarity (Rare) Discussion link. Wiki link.
At Max Level: HP: 5023 Tile damage: 11/10/12/69/54/61/3.0

Illusions - Purple 5
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

Illusions Used Right After Polarizing Force- Purple 5
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

[anchor=magneto3]Magneto (Classic)[/anchor]
3 Star Rarity (Rare) Discussion link. Wiki link.
At Max Level: HP: 6800 Tile damage: 61/70/79/11/12/13/3.2

Polarizing Force - Red 8
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

Magnetized Projectiles - Blue 10
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

Max Level: 713 damage per swap. Max damage of 4991.

Mystique (Raven Darkholme)

3 Star Rarity (Rare) Interview at Marvel.com.

At Max Level: HP: 5950 Tile damage: 12/13/70/79/11/61/3.0

Infiltration - Blue 9
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

Max Level:

[anchor=thepunisher3]The Punisher (Dark Reign)[/anchor]
3 Star Rarity (Rare) Discussion link. Wiki link.
At Max Level: HP: 6800 Tile damage: 11/61/12/13/70/79/4.0

Judgement - Green 8
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

[anchor=storm3]Storm (Mohawk)[/anchor]
3 Star Rarity (Rare) - (Gold Character) Discussion link
At Max Level: HP: 5100 Tile damage: 70/12/11/13/79/61/3.5

Lightning Strike - Green 10
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

Mistress of the Elements - Yellow 9
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

Max Level: 220 damage per tile (1540 total)

[anchor=thor3]Thor (Modern)[/anchor]
3 Star Rarity (Rare) - (Gold Character) Discussion link. Wiki link.
At Max Level: HP: 10200 Tile damage: 70/79/12/11/61/13/3.5

Mjolnir’s Might - Red 8
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

Thunder Strike - Yellow 12
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

Max Level: Deals 2486 damage and Converts 9 tiles to green.

[anchor=juggernaut1]Juggernaut (Classic)[/anchor]
1 Star Rarity (Common) Discussion link
At Max Level: HP: 3520 Tile damage: 7/22/6/7/25/9

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.

Single, Green Colored CD Tile Being Destroyed
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.

Contributors

HUGE thanks to eeeeeee, who has done a ton of refactoring on the code and implementing of new features.

NorthernPolarity

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

zeeke

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

atomzed

Thanks NP for all the effort! It looks impressive!

NorthernPolarity

zeeke wrote:

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

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.

vudu3

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

NorthernPolarity

vudu3 wrote:

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.

CrookedKnight

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.

NorthernPolarity

CrookedKnight wrote:

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.

Unknown

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.

Unknown

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

NorthernPolarity

Red Panda wrote:

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.

daibar wrote:

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.

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.

vudu3

NorthernPolarity wrote:

Red Panda wrote:

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.

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.

mischiefmaker

vudu3 wrote:

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.

atomzed

mischiefmaker wrote:

vudu3 wrote:

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.

Unknown

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

NorthernPolarity

Disembiggen wrote:

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.

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.

Unknown

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?

NorthernPolarity

ark123 wrote:

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.

Unknown

NorthernPolarity wrote:

Disembiggen wrote:

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.

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.

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.

Unknown

Just out of curiosity, does the simulation account for any particular color biases when considering the moves used? For example, if I gathered 10 green AP for Mohawk's green, the board will almost certainly have notably less green than other colors.

Either way, this is amazing. Really, really cool stuff, and thanks for making this. You rock!