This Karazhan card was mostly conceived as underwhelming at first glance. After it has seen play and considering late-game oriented deck strategies, the card becomes more appealing. Yet, what are the real numbers behind that chess piece and is it really worth paying 6 mana for? These are the questions this article is intended to clarify. Please remember that even with thorough calculation, not all variables can or may be included. There is the problem of calculating the value of flexibility of a card as well as the worth of combining multiple effects into one card. Nevertheless, the average outcome can be expressed by numbers which approximate the real-life outcome to a satisfactory degree.
Note: Evaluations and calculations are made for Standard play mode only with competitive tournament or ladder decks in mind. Some assumptions made may be subjective in nature but were nevertheless made with the most objective approach intended.
Minion Body
It is rather easy to calculate how much mana is a minion worth if we look at vanilla minions. They can be calculated with an easy formula: attack + health = mana cost*2 + 1; e.g. Chillwind Yeti: 4+5 = 4*2+1=9. Of course it can be argued that vanilla minions are not played in competitive play and are therefore undercosted but it is assumed that this downside is at least outweighed by the flexibility and the combinations of effects Ivory Knight offers. Using this formula, the 4/4 body translates into roughly 3.5 to 3.6 mana, depending of what vanilla card you base calculations on. Another formula proposed by the_patman is: cost = 0.41 * attack + 0.48 * health. This translates into 3.56 mana for Ivory Knight.
Conclusion: the 4/4 body equals 3.55 mana.
Healing
Calculating healing is the simplest to calculate. Besides priest, which is the “healing expert” among all classes and has therefore a discount on healing effects, each point of healing is worth about 0.33 mana. Examples are Healing Touch (3 / 8 = 0.38) or Holy Light (2 / 6 = 0.33). For simplicity, the calculations were made using the lower value of 0.33.
Conclusion: Each point healing equals 0.33 mana.
Discover
Mana-wise, discovering a card is almost the same in value as drawing a card. According to the game plan / deck design (compare fatigue vs. combo), the difference is huge but regarding mana cost, we can assume similar costs. A slight penalty for the discover mechanic may be justified as it normally weaker than card draw from the deck because you may get card choices that are totally useless in discover whereas cards drawn from your deck are usually in line with your overall strategy. This calculation though assumes no difference.
Based on Arcane Intellect, Nourish, Sprint and minions like Gnomish Engineer or Gnomish Inventor, the assumed mana cost for drawing a card is 1.5 to 1.75. It is here it is assumed 1.65 mana.
Conclusion: discovering one card equals 1.65 mana.
Figure 1: Spell distribution of Paladin spells
This is the question that has to be answered. According to the previous calculations, the equation that answers the question is as follows:
value body + value discover + points of healing/3 ≥ 6.
Transformed, the final formula we get is:
x ≥ 6 -5.2 or x ≥ 0.8.
Tab. 1: Spell distribution, probability to discover and value calculation.
Ivory Knight will always provide body without variation as well as the discover effect. Those two together are worth 3.55 + 1.65 = 5.2 mana. In order to being at least the same value of a vanilla minion, we need equal or more than 2.42 points of healing. Therefore, beginning with 3-mana spells, Ivory Knight is mathematically worth playing according to the above mentioned formula (compare tab. 1). When calculating the probability of receiving 3 points of healing (or more), the result is 86.3% (87.6% before Gadgetzan) despite the fact that there are a lot of cheap spells in paladin (compare figure 2). In the table above, you can find all the numbers for each mana slot.
Figure 2: Probabilities to discover at least one card of x-mana or higher; e.g. the chance to discover a 4-mana or higher costed spell is 77.0%.
As already mentioned, the key to the value of Ivory Knight lies not in its body but rather in the flexibility and the combinations of effects it provides. It is already kind of proven that exactly this flexibility makes it worth playing the card. One of the strengths of the Druid class, which we all see every day on ladder, is the “Choose One” mechanic, which provides a reasonably comparable amount of choice as discover.
It’s the liberty of choosing the right path depending on the situation. You can either weight the importance of the card discovered higher in comparison to the healing received, or vice versa. As an example, on the one hand, even though the net value of the card would result in less than 6-mana, by discovering a 2-mana spell like Equality, that draw can enable massive swing plays not otherwise possible. On the other hand, discovering a useless Anyfin Can Happen may result in surviving the next turn and winning the game. The advantage of Ivory Knight is the possibility to adapt the play according to your needs. For better understanding, imagine the following situation:
Turn 11. You are at 8 health and you have lethal on board for next turn. Your opponent, a warrior, has a 16/16 C’Thun and two cards in hand. One Silver Hand Recruit is still able to attack on your side. You play Ivory Knight as your last card and the discover options are: Noble Sacrifice, Consecration and Lay on Hands. Which one would you choose? The Healing from LoH won’t prevent lethal, neither can the 16/16 minion be cleared by Consecration. The rather absurdly best choice in the described circumstances is Noble Sacrifice despite the providing only one point of healing.
Imagine the same scenario as described above. Discover reveals the choice of an Equality in the place of above mentioned Consecration. Taking Equality over Noble Sacrifice is in that case a viable option, enabling the removal of the opponent’s C’Thun with the Silver Hand Recruit. This play does also prevent lethal but opens the board up to a Ravaging Ghoul killing all minions while on the other hand a charge minion would ruin the effect of Noble Sacrifice in the first scenario.
That much is sure; there are a multitude of similar situations in which the way to victory is not the mathematically best option.
Conclusion
Ivory Knight is 86.3 % mathematically worth playing but numbers aren’t everything.
Flexibility is an incalculable and invaluable factor.
RNGesus is sometimes on your side, and sometimes not.
Author: Martin ‘OtakuMZ’
Hearthstone enthusiast, content creator for the Good Gaming team and Hearthstone site manager for BlizzPro. Martin is best known for infographics which focus on single Hearthstone cards or game mechanics.
Twitter: https://twitter.com/OtakuMZ1978
BlizzPro: http://hearthstone.blizzpro.com/author/otakumz
Citations
All card images and symbols are the property of Blizzard Entertainment: http://us.battle.net/hearthstone/en/
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