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

636265784240330987

  • 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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