How Much Damage can Puzzle Box of Yogg-Saron Do

hearthstone 10 - How Much Damage can Puzzle Box of Yogg-Saron Do

This post aims to answer a seemingly simple question, what is the max possible damage that could be done when casting one >. For this question, I'll be assuming that the board is completely empty, RNG is always perfect, no help from either players hand or deck, and no fatigue.

The answer to this might initially seem like 100 damage- 10 pyroblasts to enemy face- but it can actually get to the tens of thousands.

The First Box: The goal of the first box is to fill the board with 3 >s, 3 >s and a >. In order to do this, the box will play > into > which summons 1 Vargoth, 3 Velens, and a two cost legendary minion such as Khadgar. Next it plays > 5 times on the Vargoth, > twice on the Vargoth, then > on the two cost legendary into Drakkari Enchanter. At this point I have 3 Vargoths on the board, spell damage +15, and a Drakkari enchanter which means there are 60 more spells to play with.

The Other 60 Spells: The remaining 60 spells will be split between > because they effectively get a 3x boost from spell damage and more Velen's Chosens. To find out how many of each spell to cast, I can use the equation:

Total Damage = (3 * (3 + (8 * (Velen's Chosens + 15)))) * (60 - Velen's Chosens) 

The first 3 represents the 3 missiles, the next 3 represents the base damage of the missiles, the 8 represents the multiplier from the Velens, and the 15 is the existing spell damage. I multiply that by 60 – (the amount of Velen's Chosens played) which would be the amount of Greater Arcane Missiles played.

The only thing left to do is put that function into Desmos and find the max value. Doing this finds 22.313 as the ideal amount, however since you can't cast .313 of a spell I compared 22 and 23 Velen's Chosens and found that 22 resulted in more damage. Finally, by plugging in 22 Velen's Chosens into the initial equation, you get 34,086 damage as the final answer.

TL;DR: The boxes summon 3 Velen's and Vargoths and a Drakkari Enchanter, casts 22 Velen's Chosens then 38 Greater Arcane Missiles at the end of the turn dealing a total of 34,086 damage, a long way from 10 pyroblasts.

Note: I know that you could do more damage by summoning a charge minion then doubling it's attack with >s but that felt to cheap so I chose to ignore it. If I missed something or it can do more damage then I though, let me know

Edit: I just realized that by doing it with 4 velens and somehow using whirlwind plus the card that summons copies of damaged minions to duplicate the Velens you could potentially get more damage. I may reupload after doing the math on that

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