RNG Series: Un’Goro Edition

EDIT: Thanks to @Old_GuardianHS for reminding me adapt is 3/10 not 3/9. Post fixed.

When I first started this blog in the last quarter of 2015, I wrote a bunch of posts where I tried to quantify RNG in the game, the RNG Series. I guess doing the math became too much work for me, as it appears I have not written one of these in 2016 or 2017. Upon the release of all the Journey to Un’Goro cards yesterday, I felt that this expansion had quite a bit of reduction in randomness. Let’s go in and see look at all the random effect cards, and try to quantify some probabilities.

Hearthstone Screenshot 04-26-16 20.02.29.png
Un’Goro RNG ain’t your Old Gods’ RNG

Adapt

  • Single Adapt (12 cards) = 3/10 = 30%
  • Double Adapt (2 cards) = 1 – (7/10)^2 = 51%
  • Galvadon = 1 – (7/10)^5 = 83%

Single Adapts are easy to calculate, just 3 out of 10 outcomes. For multiple Adapts, the events are independent, meaning each roll will be 3/10. So when Galvadon screws you over by not getting Stealth, that was a 17% chance. It will happen.

Discover

  • Hydrologist = 3/5 = 60%
  • Primalfin Lookout = [3/18, 3/14] = [16.7%, 21.4%]
  • Chittering Tunneler = 3/25 = 12%
  • Tortollan Primalist = [3/32, 3/25] = [9.4%, 12%]
  • Free from Amber = 3/30 = 10%
  • Primordial Glyph = 3/32 = 9.4%
  • Servant of Kalimos = 3/36 = 8.3%
  • Stonehill Defender = [3/56, 3/49] = [5.4%, 6.1%]
  • Curious Glimmerroot = 3/59 = 5.1% + Your Brain
  • Hallucination = 3/59 = 5.1%
  • Explore Un’Goro = 3/366 = 0.8%

Discover cards all have a numerator of 3, since you are selecting 1 of 3 picks. The denominator will vary quite a range. Hydrologist has a fairly low RNG, as there will only be 5 Paladin secrets in Standard. While Curious Glimmerroot has an inherent 5.1% of a card, you will likely know what class card is in the opponent’s deck. Also since Discover picks from the pool of Class + Neutral, some cards will vary like Primalfin Lookout for Murlocs, Tortollan Primalist for Spells and Stonehill Defender for Taunts. Explore Un’Goro draws from a pool of Warrior + Neutral cards, giving a 0.8% chance for each card.

Random Card Advantage + Molten Blade

  • Crystalline Oracle = [1/26, 1/1] = [3.8%, 100%]
  • Megafin = 1/19 = 5.3%
  • Molten Blade = 1/23 = 4.3%
  • Elise the Trailblazer = 5/135 = 3.7%
  • Lyra the Sunshard = 1/31 = 3.2%
  • Shimmering Tempest = 1/32 = 3.1%
  • Stampede / Jeweled Macaw = 1/76 = 1.3%

Crystalline Oracle will vary depending on how many cards are left in the deck, so highly variable, but limited in Constructed with repeated cards. Megafin will give a 5.3% chance for each Murloc, and that probability will increase depending on how many cards you get to draw. Stampede and Jeweled Macaw had the probability for a desired Beast plummet after the heavy insertion of Beasts in the new set.

Draw

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  • Tortollan Forager = Turn 2 – 5 attack minions
  • Arcanologist = Turn 2 – Secret
  • Tol’vir Warden = Turn 5 – 2 1-cost minions
  • Mimic Pod = Turn 3 – Anything

Draw cards always start off with a limited denominator of how many cards are left in a deck. Turn 1 players start with 26 cards, while the Coin player starts with 25 cards in deck. Then you subtract what turn a card can be played on inherent card draw. So, the Tol’vir Warden for example, will likely be drawing cards from the smallest deck pool, on average. Mimic Pod is the most variable of these cards, as there is no limiter on what is drawn, like Thistle Tea. Getting 5-attack guys and Secrets are likely more discriminating than 1-cost minions, but these are all random outcomes of limited probability, given the parameters of 30 card decks.

Damage

636265805068200603

  • Volatile Elemental = [1/7, 1/1] = [14.3%, 100%]
  • Sulfuras = [1/8, 1/1] = [12.5%, 100%]
  • Volcano
    • Chance of getting hit with no minions = 99.9%
    • Chance of not getting hit with 14 minions on board = 38%

Back in GvG, random damage appeared to be the main mechanic. Surprisingly, there are only 3 cards like this in the expansion. Volatile Elemental will range from 1/1 to 1/7, so that can obviously be modified. The Ragnaros hero power from Sulfuras will include the hero, so that bumps an extra character. Volcano, obviously is highly variable, depending on it’s own randomness and how much stuff is on the board. With an empty board, the chance of a hero dodging 15 shots is 0.0031%, so nary impossible. On a full board of 14 minions and 2 heroes, the chance of something not getting hit once is 38%. Of course, there are more complicated calculations depending on how much health everything has, as a minion with 1 health dying off will increase the odds of everyone else getting hit. Too complicated.

Summon

636265786513309245

  • Giant Anaconda = [1/10, 1/1] = [10%, 100%]
  • Cruel Dinomancer = varies

Again, we’re not in GvG, when Piloted Shredder dropped off anything. Giant Anaconda at the least has a 10% chance, and this is the highly unlikely scenario of having a hand of 10 5-attack guys. Cruel Dinomancer can be controlled by how much discard you are running. If Clutchmother Zavas was thrown away a lot, she will likely be the most likely outcome of summon, as a 2/2.

The upshot

It’s safe to say that Team 5 took the feedback that bad RNG is bad for the game and competitive Hearthstone. Most of the RNG in Un’Goro is Discover and Adapt, outcomes which have a skill requirement to it. Cards with really wacky RNG outcomes likely won’t be all that good in this set. A card like Stampede is likely a card advantage engine, where you’ll just be looking to get “A Beast” rather than “OP Beasts.”

I think that state of the RNG discussion will focus on the Discover cards, since there will always be variation in a pool of 59 or so cards. Adapt is pretty safe as a mechanic, with the 30% probability floor (not to mention multiple good Adapts).

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Occasionally Huffer?

Hearthstone is over 2 years old, and players have been duking it out Wizard Poker style well before that in the beta stages. It’s safe to say that some cards are more well-known than others, owing to either effectiveness in the meta, being nerfed, or just being well-known for some inexorable reason. Take Annoy-o-Tron for example.

Annoy-o-Tron had utility when Mech Mages roamed the earth, but they weren’t typically a staple card. It’s still pretty good in the Arena, at all phases of a game. But Annoy-o-Tron became a factotum of Hearthstone because of it’s effective absurdity. The card fit as being good, but wacky and a butt monkey of GvG. These qualities allowed Annoy-o-Tron to have it’s own Tavern Brawl and have it featured in Hearthstone commercials.

Hearthstone Screenshot 09-30-15 13.22.25.png
OP pls nerf.

As such, another really well-known card amongst the Hearthstone community is Animal Companion. And of course, Huffer. Just plug in “always Huffer” into Google, and you’ll find 276,000 results.

Context

“Always Huffer” refers to Animal Companion always getting Huffer. Typically, this applies to your opponent playing Animal Companion, and having a 4-attack charge for insta-reach, and allowing cards like Kill Command to hit face. In a recent and spectacular Hearthstone cartoon, “always Huffer” was cleverly invoked with the Random Animal Generator (R.A.G.).

r.a.g..PNG

Animal companions

If you bootstrap it enough times, each Animal Companion should come out 33% of the time. And really, all of the Animal Companions are great value plays for 3 mana. Huffer is a +1/+1 over Wolfrider. Misha is a +1/+1 over Ironfur Grizzly. Leokk is a 0/+2 over Raid Leader. All have their respective uses and are appreciated.

Small sample results

Last night, I had my first successful Arena in a few days, taking a Hunter to 8 wins. And the deck had 3 Animal Companions. Through the run, I realized it wasn’t always Huffer. In fact, it was infrequently Huffer! I went back and looked at my Animal Companion summons over the 11-game Arena run.

  • Total Animal Companions played: 13
  • Huffer: 3/13
  • Leokk: 3/13
  • Misha: 7/13

Conclusion

In my Arena, I got Misha over half the time. And I can’t argue with the results, given we are in the “taunt meta” in the Arena, where taunts are just really good. Anyways, I’ve come to some conclusions about “always Huffer.”

  • It is a byproduct of “salt.” Huffer doesn’t come out 90% of the time, probably.
  • Hate for Aggro Hunter has always been a thing, and Huffer represents all that is bad with that playstyle.
  • Misha and Leokk deserve some love too!
Hearthstone Screenshot 05-07-16 23.40.59.png
Where the F is Huffer?

 

Elements of Hearthstone RNG: Pings

I made a pact... to clear big taunts for lethal
I made a pact… to clear big taunts for lethal
The most common type of RNG in Hearthstone comes in the form of a card having an ability that will cause damage or destroy other characters, without actually attacking on it’s own. Unlike a Mage Fireblast, these “pings” go random places and cannot be targeted.
  • Battlecries and other one-time effects have less RNG than continuous effects or triggered effects, by virtue of the effect happening once.
  • Abilities that hit minions only have less RNG than those that can hit face.
One time effect, limited minions affected
Stampeding Kodo – The kodo is the least random card in the ping/attack class. It has a one-time effect to kill something that has 0, 1, or 2 attack. The effect is most effective (and has zero randomness) when there is only 1 opposing minion that has 0-2 attack on the board. It is clearly ineffective when the opponent has stacked 7 small creatures on the board (14% for each minion). Against 3+ attack minions, the kodo is just a bad tempo 3/5.
One time effect, one random minion
Bomb Lobber/Flamecannon – Bomb Lobber and Flamecannon have the same exact effect of dealing 4 damage to a random minion. Like the Kodo, it works best when there is one minion on the board with 4 or less health.
Deadly Shot/Sabotage – Same effect, except with a much bigger swing, as it completely destroys a minion. These random hard removals work best against one big thing on the board. The 4 cards above have probabilities to hit minions from 100% to 14%.
 Void Crusher – The Void Crusher is unique and doesn’t technically have a one-time effect. However, the potential to destroy itself upon inspiring really limits how long it will stay on the board. Also the amount of RNG is potentially doubled depending on how many minions are on each side. A board with 2 minions on each side will result in 4 possible outcomes, for a 25% chance. A board with 7 minions on each side will result in 49 possible outcomes, for a 2% chance. The chance of destroying a particular minion on each side remains at 14%.
One time effect, 2 minions hit
Forked Lightning/Multi-Shot/Dark Bargain – Like above, the fewer minions on the opposing side, the better the chances, however there is a minimum of 2 minions. Using these spells on a stacked board of 7 minions can result in 27 possible outcomes, for a small 3.7% chance. However, the chance of hitting a particular minion on a stacked side is about 28.5%.
One time effect, one character hit
Flame Juggler /Fist of Jaraxxus – The Flame Juggler is considered one of the better 2-drops in the arena, as it has the chance to snipe an annoying 1 health minion, like Worgen Infiltrator. Well, unless it hits the face. Any pings that open up heroes to attack are automatically more random than those that just target minions, as an extra target is provided. Though these pings are more dangerous (closer to lethal), their reliability of clearing a minion (what you typically want) is reduced by a big margin.
One time effect, 2 characters hit
Misdirection – Misdirection is unique, though it fits the one time effect being a secret, but causes 2 characters to run into each other. The RNG hurts the side with more minions, causing the possibility of 2 minions killing each other off. The only way this card has 0 RNG is if your opponent has 1 minion on the board while you don’t have any. This will cause a 100% probability of your opponent hero getting hit with their minion. Same goes will opponent hero attacking their own minion instead.
Two time effect, one character hit
Dr. Boom – Dr. Boom is unique in that he has Shaman RNG (damage range) and is the only card that will specifically allow for 2 independent instances of one character being hit. Each Boom Bot that is destroyed will have a chance to hit any one character on your opponent’s side.
Turn-based effect, one character hit
Ragnaros the Firelord – Pretty much the same probabilities as the above class, except the ping occurring each turn will help increase the number of instances occurring. The concept of flooding the board to prevent Rag from getting a lethal shot demonstrates the basic understanding of probability. Flood the board and he has a 12.5% chance to go face and end things.
Demolisher – These two cards have the same effect, except that the Demolisher has slightly more RNG than Ragnaros. Because Ragnaros will hit after your turn, it means you can actively help reduce the number of minions on the board, in order to increase the probability of something getting hit. Demolisher hits at the start of your turn, which means, your opponent has a chance to set up a board to reduce the probability of something getting hit.
One time effect, multiple missiles
Arcane Missiles/Goblin Blastmage/Avenging Wrath – With more pings comes more RNG. The health of opposing minions matters more than ever with these. If a board with all 1-health minions is hit by Avenging Wrath, each dead minion will increase  the probability of the other minions are getting hit. A minion that is hit and dead will not get overkilled, and thus increase the probability of another getting hit. Another example, let’s say it’s turn 4, you have a Target Dummy and your opponent summons an Evil Heckler (5/4). You drop Blastmage. Because each ping has a 50% chance to hit the Heckler, the chance of the Blastmage killing the Heckler is a little over 6%. Let’s say same scenario, but instead of an Evil Heckler, your opponent plays Mini-Mage (4/1). The Blastmage still has 50% chance of hitting the minion, but there is an almost 94% chance the Mini-Mage will get killed.
Triggered effect, one character hit
Ship’s Cannon/Eydis Darkbane – Triggered ping minions are interesting because they can provide a good deal of RNG or none at all. Their effects are typically more useful in decks built around them, meaning they can do more damage in constructed. Ship’s Cannon and Eydis Darkbane can be picked in the arena, and due to the lack of synergy or an incompatible class, never have their effects activated at all. The Knife Juggler will always have it’s effect activated (as you’ll always have minions), while the Shadowboxer will always have it’s effect activated (so long as a Priest can spend mana to heal.) These cards have a little more RNG than the one-time effect minions, as there are more chances for their effects to hit. Ship’s Cannon and Eydis Darkbane cannot throw multiple shots in one turn, and instead have an independent event for each trigger.
Knife Juggler/Shadowboxer – While these 2 minions have the weaker ping effects, they are hybrids of one character hit and multiple missiles types. Knife Juggler will throw multiple knives in one instance if 2 minions are summoned at once, or if a card like Unleash the Hounds is played. Shadowboxer will throw multiple punches in one instance if Holy Nova is used, and multiple characters are healed. As described above, the health of opposing minions matters more in affecting the randomness for multiple missile cards.
Triggered effect, multiple missiles
Flamewaker – The Flamewaker is unique on the RNG list in that it is the only true trigger multiple ping. Cast a spell, and 2 pings will be sent at opposing characters. While the RNG of each trigger is lower than a Goblin Blastmage, the ability to cast multiple instances of pings will help increase the RNG.
Turn-based effect, one minion hit, either side, most minions effected
Fel Cannon – Fel Cannon finally brings about the concept of friendly fire. This essentially doubles the amount of RNG, as the amount of minions is potentially doubled. On a board state with 7 minions on either side, Fel Cannon has a 7.7% chance to ping any particular minion. Because Fel Cannon can’t hit itself, the probability of your minion getting hit (46%) is lower than that of your opponent’s getting hit (54%). The rub is that Fel Cannon will not hit any mechs, so if your opponent plays mechs, the Fel Cannon can backstab your own board.
Warrior RNG
Brawl – Oh hey, the Warrior is a roulette player sometimes. Brawl RNG is pretty simple, as the side that has more minions is more likely to have a minion live. Any opposing boards with the same number of minions on each side will be a 50% coin flip for who wins the brawl. Brawl is funny, as The Warrior typically doesn’t care if he wins the Brawl. Brawl is typically played as a board clear (who cares who dies, as long as there is one minion left) or to kill one big threat.
Bouncing Blade – The same concept with Brawl, except the cumulative health points of minions will help determine the probability here. A side with 2 Yetis (4/5) has a 67% chance to win a Bouncing Blade foray over a side with 1 Yeti. While cumulative health totals are important here, the appearance of a low-health minion is even more important, as Bouncing Blade ends once a minion dies. So, the side with a one health minion is a the greatest disadvantage of that minion dying. There is no real way to calculate the probability of this card, as every situation is different. Much situational RNG.
One-time effect, multiple missiles, any character hit
Mad Bomber/Madder Bomber – These goblins are used in promotional work for Hearthstone and happen to be the most RNG cards in the game. Sticks of dynamite are thrown haphazardly 3 or 6 times, at any character on the board. While they are typically used to clear a board, enraging your own minions can serve some utility as well. Let’s go through a specific case, ADWCTA’s Gahz’rilla Dream.
I do not own this. It was stolen off ADWCTA's YouTube. Source: https://www.youtube.com/watch?v=5tgyOg795Dg
I do not own this. It was stolen off ADWCTA’s YouTube. Source: https://www.youtube.com/watch?v=5tgyOg795Dg

The premise here is that Gahz’rilla needed to be hit by 2 out of 6 Madder Bomber pings to grow to 24 attack and win the game. There are 8 characters on the board (Uther, Mad Bomber, 2 Silver Hands, Faerie Dragon, Youthful Brewmaster, Gazh’rilla, Rexxar).

Bomb 1 – Rexxar
Bomb 2 – Gahz’rilla
Bomb 3 – Mad Bomber
Bomb 4 – Faerie Dragon
Bomb 5 – Rexxar
Bomb 6 – Gahz’rilla
Gahz’rilla got hit 2 times. What were the chances of that happening?

(Disclaimer: This math could be very wrong)

8 characters, 6 flips of dynamite

8^6 = 262144 possible independent events

2 Gahz = GahzA, GahzB

_ _ _ _ _ _

GahzA = 6 spots; GahzB = 5 spots

_ _

Gahz A = 2 spots; GahzB = 1 spot

# of possible outcomes = (6 x 5) / (2 x 1) = 15 possible outcomes where Gahz is hit exactly 2 times

Probability = 15 / 262144 = 0.0000572%

The math is not completely correct, as if one of the opponent minions died, the chances of hitting Gahz increase for each minion death.

As seen the bombers make for extreme RNG, as there are so many different combinations/permutations to consider. But they also make for some great moments now and then.


 Upshot
  • This is the most common form of RNG in Hearthstone as of now.
  • Ping RNG is typically countered by playing more minions on the board to reduce the chances of particular minions getting hit.
  • Conversely, to make the RNG work in your favor, reduce the number of minions on the board to have a better chance of hitting the desired target.
  • Health of minions matters more for some types of this RNG.
  • Minions with trigger pings or turn-based pings allow for more events to occur.
  • Don’t try to do the math for Madder Bomber probability. It literally took me a whole day, and I’m not sure I got it right.

The Elements of RNG: An Introduction

If you’ve ever browsed a forum, blog, or website about gaming, there’s a good chance you have encountered the phrase “RNG.” The acronym itself stands for “random number generator” and typically refers to any random element in a game, or anything subject to probability/chance. As it stands, RNG remains a major issue for Hearthstone.

Typically, RNG is invoked as a complaint by more experienced players losing a game to lesser experienced players, and it does provide a fudge factor in reducing the gap between skill levels. The level of RNG in Hearthstone has often been used by blowhards as the prime reason why they have quit the game. At other times, the RNG in Hearthstone is said to be a good thing, or something that made the game unique. Often, an instance of extreme RNG serves as an amazing highlight reel shot.

So how much RNG is there in Hearthstone? I sought to find out.

What this is

  • I pored over every collectible card in Hearthstone released so far. I was able to bin every card containing a random element into a type of RNG. I was able to discern 14 types of RNG.
  • Some cards have so much randomness, they fall into multiple bins!
  • I try to rank the amount of randomness of each card in each bin.
  • I try to talk about how people lessen the randomness and increase their odds of success.

What this is not

  • I don’t compare Hearthstone RNG to that of other games.
  • I’m not taking a side about whether RNG is bad or good for Hearthstone. I am objectively talking about each type of RNG.

Truth about card games

  • Here’s the inconvenient truth. Every card game has RNG. As long as cards are drawn from a deck, there is an element of probability of what card you get.
  • There is a 30 card requirement in a Hearthstone deck. That means there is a 3.33% of drawing a single card. In constructed, the randomness of drawing cards is reduced by including 2 copies of a card. This means there is a 6.67% chance of drawing it.
  • Cards like Varian Wrynn and Far Sight and Call Pet aren’t really RNG. Cards that have randomness depending on card draw are just at the mercy of being in a card game.
  • The same goes for topdecking. Sure it’s luck you drew the card you needed for lethal, but it’s just the nature of randomness in a card game.

The remaining posts of the RNG series will discuss in depth each of the 14 bins I identified as a source of RNG in Hearthstone.

Stay tuned!