The winner of HCT Summer Championship 2017 turned out to be Surrender. As I picked Surrender as my champion, I cannot be happier. It is my very first time to receive more than one pack from the “Choose Your Champion” events. SO LUCKY!
In the finals, Surrender got to play against Orange. It was quite intense and went all the way to the fifth game, the Priest-Priest mirror match-up. From the clip(1:12:55), you can see that Orange decides to mill 6 of Surrender’s cards by Spirit Lash–Circle of Healing–(Hero Power)–Binding Heal combo. With Gadgetzan Auctioneer in his hand, Orange might have drawn a ton of cards using those cheap spells. Now knowing that Surrender’s Raza the Chained was at the bottom of the deck, Orange should have won if he didn’t waste his spells so much.
It was quite entertaining to read the Youtube comments as meaningful discussions were taking place there. Some argued that it was clearly a misplay. Others said that Orange was just taking risks. Some of them even tried to do the math and came up with the chances of Raza or Velen burning. In my humble opinion, I think they have missed some minor details. In this post, I will try to delve into the calculation deeper.
To make things simple, I will assume that burning one of the three key cards(Raza the Chained, Prophet Velen, and Shadowreaper Anduin) can compensate the possible loss that occurs from wasting the cards. Then the critical question becomes: Was it rational for Orange to hope that at least one of the three key cards burns? By rational hope I mean the chances are greater than fifty-fifty.
Orange knows that the following cards are not in Surrender’s deck.
- Turn 1:
- Turn 2: Played Loot Hoarder
- Turn 3:
- Turn 4: Played Gnomish Inventor
- Turn 5: Played Northshire Cleric, Shadow Visions, and Silence
- Turn 6: Played Curious Glimmerroot
At the mulligan stage, Surrender keeps his second card. This means that it is either one of the three combo cards(Raza the Chained, Prophet Velen, and Shadowreaper Anduin, a.k.a. the DK) or one of the useful early game cards like Potion of Madness, Power Word: Shield, Dirty Rat, Novice Engineer, or Loot Hoarder.
At turn six, Surrender draws a card by healing Orange’s (silenced) doomsayer. From this Orange can infer that Raza is currently in Surrender’s deck. There is no reason for Surrender not to play Raza first and then use his zero mana hero power to draw. So Raza is guaranteed to be one of the last eighteen cards of Surrender’s deck. Also, Surrender did not play his second card until now. So it would probably be a key combo card. With Raza out of the list, the only two possible cases are Velen and the DK.
So the setting is as follows.
- 24 unknown cards
- one half-known card, i.e., it is either Velen or the DK
- Raza is one of the last 18 cards
- Orange can burn six cards
Orange can hope to mill Raza, Velen or DK(Orange does not know which one was Surrender’s second card), or both. Let us do the math.
- Only Raza burns: 6/18 * 17/22
- Only Velen/DK burns: 12/18 * 6/22
- Both burn: 6/18 * 5/22
The sum of the three probabilities is 204/396, which is about 51.5%. Slightly over fifty-fifty. It seems that Orange’s decision was justifiable, but I am not sure if it was worth risking the other 49%.