Thursday, April 28, 2016

April Arena Challenge Update #3

As mentioned at the end of March, I decided to take on an Arena challenge where you play 10 arena runs and try to achieve a certain number of wins (an overly optimistic 65 total, in my case). Let's check in on how this challenge is progressing.

After the first four runs (Hunter, Paladin, Mage, Warlock), we stand at 15 wins total.

The fifth deck choice was Shaman, which was selected over Paladin, ineligible, and Warrior. Here's what Thrall had to offer:

Results for Run 5 (Shaman)
W vs. Druid (1-0)
L vs. Warlock (1-1)
W vs. Paladin (2-1)
L vs. Paladin (2-2)
W vs. Warrior (3-2)
W vs. Warrior (4-2)
L vs. Mage (4-3)

Total after 5 Arena Runs - 19 wins

Back on the winning side of the ledger with this deck, although some of the card choices offered (3 Bloodlust offered, the epic choice ending up in Mountain Giant was awful, etc.) were not optimal. This deck did have Mage levels of removal, which made for some potent board control and tempo-based victories. I don't know how the prospects look for my upcoming Warrior run given the continued dominance of my decks over that class, but we will cross that bridge when we come to it.

We are substantially averaging 4 wins a run at the halfway mark, which is OK for doing better than breaking even on arena entry fees, but not much more. Opening some final GvG packs awarded on a couple of these runs has been fun, at least!

For round 6 the next selection was between Mage, Shaman, and Priest. The only eligible option is Priest. Here's my sixth deck, which is easily the most late-game oriented of the decks drafted so far in this challenge:

Results for Run 6 (Priest)
W vs. Mage (1-0)
L vs. Hunter (1-1)
W vs. Rogue (2-1)
L vs. Mage (2-2)
L vs. Shaman (2-3)

Total after 6 Arena Runs - 21 wins

Yikes. The first losing record run of this challenge kicks off the second half, with the control-oriented Priest deck getting run over from good draws out of the Hunter and Shaman opponents. When putting together a deck of this strategy, it really needs to have more taunts. Sticky minions are great, but if you are constantly losing the tempo battle anyway, they can't win the game by themselves. Good lesson to learn near the end of the TGT/LOE Arena season.

For round 7 the next selection was between Druid and Rogue and one of the classes already played. I decided to run with the power of Malfurion following my first sub-.500 run in this challenge. Here's my seventh deck, which is easily the most late-game oriented of the decks drafted so far in this challenge:

Results for Run 7 (Druid)
L vs. Paladin (0-1)
W vs. Priest (1-1)
W vs. Warrior (2-1)
L vs. Rogue (2-2)
W vs. Mage (3-2)
L vs. Paladin (3-3)

Total after 7 Arena Runs - 24 wins

After being wrecked by discover cards in the previous run with Priest, I ended up with a metric ton of Scarabs and Spiders in this deck. Although the 3-3 record does not indicate it, this felt like a deck that could've gone above 7 wins with some better draws in the mulligan phase. The discover mechanic is brilliant, bringing even more play skill and decision making to places like Arena. Even with the mediocre result, this deck was a blast to play.

Three runs left to go and we only need 41 wins to reach the target. OK, so clearly that target was flawed. However, with Rogue and Warrior still potentially on the docket for the final runs, at this point just making a better finish will make me happy. We will certainly reset the goal a little lower for next time.

Also on the bright side, the new expansion is releasing in the middle of this challenge, so it will be crazy times seeing everyone adjust to the Old Gods Arena meta. Let's see how high we can reach on the win scale (preferably approaching 40, but I've sailed under the expectation bar pretty well so far).

Monday, April 25, 2016

Bidding Farewell to Naxxramas and GVG - The Effect on Decks

As of today, the patches for the new Hearthstone expansion (Whispers of the Old Gods) and the beginning of the Standard Format have gone live on many devices, which means we are but a few hours away from Naxxramas and Goblins vs. Gnomes rotating out of Standard Format on Tuesday. The Classic/Basic card nerfs are live (R.I.P. Combo Druid), and now we can begin focusing on the new competitive format.

As mentioned in my most recent post, I took a look at all of the 12 or 13 decks currently being played on my account, which also represent a good cross-section of the top ladder meta decks, to see which ones were losing the most from this rotation. Although my conclusion on the Classic/Basic card nerfs was that the impact would be minimal on these top decks, that is not the case with the powerful sets rotating out of Standard Format this week.

Plus this was a good excuse to take one final look at exactly what superstar cards will not be all over ladder games anymore (except in Wild Format).

Another goal is to see which decks stand as the most likely to continue in close to their present form in the new Standard Format. With a few weeks of experimentation and brewing coming on the ladder, it can be advantageous to play a reliable known deck at times to climb the ladder as well.

Let's take a look first at the numbers, ranked from least to most:
  • Aggressive Shaman - 0 cards from Naxx, 3 cards from GVG (3 total), most notable Crackle
  • Freeze Mage - 2 cards from Naxx, 2 cards from GVG (4 total), most notable Mad Scientist
  • Midrange Druid(*) - 1 cards from Naxx, 3 cards from GVG (4 total), most notable Piloted Shredder
  • Control Warrior - 4 cards from Naxx, 1 card from GVG (5 total), most notable Death's Bite
  • Dragon Hunter - 4 cards from Naxx, 2 cards from GVG (6 total), most notable Glaivezooka
  • Combo Priest - 5 cards from Naxx, 1 cards from GVG (6 total), most notable Deathlord and Zombie Chow
  • Patron Warrior - 5 cards from Naxx, 2 cards from GVG (7 total), most notable Death's Bite and Unstable Ghoul
  • Dragon Priest - 4 cards from Naxx, 3 cards from GVG (7 total), most notable Velen's Chosen and Piloted Shredder
  • Reno Warlock - 3 cards from Naxx, 5 cards from GVG (8 total), most notable Dr. Boom and Healbot
  • Zoo Warlock - 5 cards from Naxx, 4 cards from GVG (9 total), most notable Nerubian Egg and Imp-losion
  • Raptor Rogue - 6 cards from Naxx, 3 cards from GVG (9 total), most notable Nerubian Egg and Piloted Shredder
  • Secret Paladin - 5 cards from Naxx, 9 cards from GVG (14 total), most notable Shielded Minibot and Muster for Battle
  • Midrange Paladin - 4 cards from Naxx, 10 cards from GVG (14 total), most notable Muster for Battle and Sludge Belcher
(*) For Midrange Druid, this was the only deck decimated by the Classic/Basic card nerfs, as it ran 2 Ancient of Lore, 2 Force of Nature, and 2 Keeper of the Grove. This deck does not exist anymore in the Standard Format as it used to be, despite the low Naxx/GVG rotation totals.

There's certainly a wide range of effects, as the Paladin decks will be completely rebuilt from scratch and the Warlock decks will need to slot in new tools for their diverse strategies, while Aggressive Shaman and Freeze Mage basically go through unchanged.  What this means is that while some classes which have dominated ladder like Paladin and Druid will need to be far different to top the Standard Format, there's a baseline of (mostly Tier 2 currently) decks which will continue to be a solid base for the ladder meta.

I strongly recommend keeping Aggressive Shaman (and/or Face Hunter, not listed above) and Freeze Mage in your repertoire moving forward in view of the information above. You should also continue to expect plenty of Warlock decks and Warrior decks as well. Dragon-based decks are also largely unchanged and may actually get better thanks to the rotation and some new cards in Whispers.

At a minimum, we have a starting place for those who don't want to jump in and explore the totally new cards and decks available with Whispers. Although I find such deck brewing to be fun, it's not for everyone.

The other way to look at this information is based on the cards lost. Here's a list of the cards lost from each set that appeared in these decks, including the number of decks out of 13 they appeared in:

  • Sludge Belcher - 6 decks
  • Haunted Creeper - 4 decks
  • Zombie Chow - 4 decks
  • Loatheb - 3 decks
  • Nerubian Egg - 2 decks
  • Death's Bite - 2 decks
  • Deathlord - 1 deck
  • Avenge - 1 deck
  • Mad Scientist - 1 deck
  • Shade of Naxxramas - 1 deck
  • Dark Cultist - 1 deck
  • Unstable Ghoul - 1 deck
  • TOTAL - 12 cards
Goblins vs. Gnomes
  • Dr. Boom - 7 decks
  • Piloted Shredder - 7 decks
  • Antique Healbot - 3 decks
  • Shielded Minibot - 2 decks
  • Muster for Battle - 2 decks
  • Coghammer - 2 decks
  • Darkbomb - 2 decks
  • Imp-losion - 2 decks
  • Shieldmaiden - 1 deck
  • Crackle - 1 deck
  • Whirling Zap-O-Matic - 1 deck
  • Glaivezooka - 1 deck
  • Velen's Chosen - 1 deck
  • Lightbomb - 1 deck
  • Quartermaster - 1 deck
  • TOTAL - 15 cards
Obviously the power level of that first adventure Naxx was off the charts, with 12 out of 30 cards seeing regular play. The top tier of GVG was also pretty thick, although Dr. Boom and Piloted Shredder outpace the rest by a wide margin.

Adios to all these fun and powerful cards, except in Wild Format where everything lives on forever. I'm looking forward to finding admittedly lesser-powered replacements which hopefully promote good deck building skills and good play when trying to compete at the highest rungs of the ladder.

It's been a blast GVG and Naxx, but it's time for you to go. See you in Arena!

Thursday, April 21, 2016

Hearthstone "Standard" Rebalancing Nerfs Announced: Checking in on the Predictions

In February, when Standard Format was announced by the Blizzard team that makes Hearthstone, the transition to the new format was also announced to involve a rebalancing of several Basic and Classic cards. Based on lead designer Ben Brode's public comments, I predicted 10-12 cards in these sets would end up adjusted in this first of what may be annual passes through the evergreen Standard Format sets.

This week, Blizzard announced one week before the Whispers of the Old Gods expansion release what those rebalancing nerfs would be. Let's check in on my predictions, and then give some brief thoughts about the actual changes and the effect it will have on my preferred decks.

The predictions

Here are links to the series of posts (part 1 here) (part 2 here) (part 3 here) (part 4 here) that discussed many of the Classic and Basic cards, including an analysis of likelihood to be changed and a proposed re-design for the cards most likely to be changed. The list below is the summary from the final article in the series, even though many other cards were discussed:

More Than 50% Likelihood, or Almost Certain

Savage Roar - Druid
Force of Nature - Druid
Divine Favor - Paladin
Doomhammer - Shaman
Battle Rage - Warrior
Leper Gnome - Neutral
Knife Juggler - Neutral
Alexstraza - Neutral

50/50 Likelihood

Sorcerer's Apprentice - Mage
Tirion Fordring - Paladin
Northshire Cleric - Priest
Big Game Hunter - Neutral
Baron Geddon - Neutral

The Actual Rebalancing Nerfs

Ancient of Lore - Option to draw 2 cards now just draws 1 card
Force of Nature - Cost reduced to 5 mana, the three 2/2 treants summoned no longer have charge
Keeper of the Grove - now a 2/2 minion instead of a 2/4
Ironbeak Owl - Cost increased to 3 mana
Big Game Hunter - Cost increased to 5 mana
Hunter's Mark - Cost increased to 1 mana
Blade Flurry - Cost increased to 4 mana, now only deals damage to enemy minions (not opponent)
Knife Juggler - now a 2/2 minion instead of a 3/2
Leper Gnome - now a 1/1 minion instead of a 2/1
Arcane Golem - now a 4/4 minion instead of a 4/2, but no longer has charge
Molten Giant - Cost increased to 25 mana
Master of Disguise - Battlecry changed to give a friendly minion stealth only until your next turn

Prediction Results and My Thoughts

I'll start with the good news: Blizzard adjusted 12 cards overall, which was right on the 10-12 prediction in my series of articles. From there, the results go a bit south.

Only 3 of the 8 cards I identified as high likelihood rebalancing targets actually showed up on the list, and then only 1 of the 5 cards listed as 50/50 chance.  That's 4 correct out of 12, which is not terribly great. So what went wrong?

Clearly one item which Blizzard felt needed adjusting and I did not consider in detail was the silence minions. It is totally understandable that if Ironbeak Owl needed to be changed, then so did one or more of the others (in this case, Keeper of the Grove). Honestly, the change to Keeper feels slightly heavy-handed when comparing that card to Spellbreaker, so maybe Spellbreaker should have also been adjusted upwardly in mana cost.

Another area where I missed the boat was cards which mainly only enable OTK game-ending combinations (other than Force-Roar, which we all knew was being adjusted).  The reasoning for adjusting cards like Arcane Golem and Blade Flurry make sense, but I didn't see either as a real problem since the use cases were pretty narrow in my experience.

That leaves the small outliers like Hunter's Mark and Master of Disguise (the latter had been rumored to be needing adjustment as well, even though it did not see any play currently), which are harder to predict, and two cards I considered but did not pull the trigger on, Ancient of Lore and Molten Giant. With all the potential focus on Druid, I thought if Blizzard would adjust any card drawing engine cards, it would more likely be from other classes (plus I think Battle Rage and Divine Favor are just better cards overall). I analyzed Sea Giant instead of Molten Giant, but the key difference there is that Blizzard does not like the ability to drop free Giants and swing a late game in somewhat of an OTK fashion, which Molten Giant did better than Sea Giant.  I'm not surprised a Giant was adjusted, but I was not willing to pull the trigger on Sea Giant, which turned out to be correct.

Other than the card drawing engines in my prediction list, the only real miss I see in the actual nerfs is some change to Freeze Mage, or mages in general. The Mage cards revealed for Whispers appear to be very strong, which means those decks (and Freeze Mage in particular) might become the new Patron Warrior or Secret Paladin. It makes me wonder if Sorcerer's Apprentice should not have also been reduced to a 2/2 or something similar, as that seems like a change consistent with the likes of other minions changed in this pass. Plus Alexstraza helps enable OTK combos often, so that card seems like a natural inclusion when knocking out items like Blade Flurry and Arcane Golem. There's always next year, but regardless, I will enjoy continuing to play these cards!

As for the changes themselves, I think Blizzard did a nice job of not nerfing most of these into totally unplayable cards (only a couple exceptions like Arcane Golem). Sure, it may be that many of them will end up not being selected in most decks, but they still are competitive with other cards in their mana slots and will deserve potential selection in future deck choices. Plus they are still useful in Arena as well. 

Those types of changes, unlike the ones we've seen to cards like Warsong Commander, are much better for the player base invested in these cards (while also achieving the goals of Blizzard.  So despite my poor prediction record and my penchant for more drastic changes in my prediction pieces, I applaud the changes in the manner they were actually made.

Plus, only a few more days until Standard Format and new cards...HYPE!

Don't forget to disenchant many of these cards when the patch drops next week, as you can always re-craft the ones you need to use for the same price later. For free-to-play players, this is a great opportunity for increased dust value at a critical time heading into a new expansion.

Effect on My Current Stable of Decks

With Standard Format on the horizon, I also took a look this week at the 12 decks in my rotation of constructed decks to see how many cards each would be losing (or having nerfed in the list above) next week.  I'll save the overall totals for the next post since this one is already very long, but I do want to share the total number of the nerfed cards I was using, to illustrate a quick point.

For reference, the decks I am using include: control warrior, secret paladin, freeze mage, agro shaman, dragon hunter, zoo warlock, midrange combo druid, dragon priest, patron warrior, Reno warlock, combo priest, and midrange paladin. Here's the summary:

Knife Juggler, Ironbeak Owl, and Big Game Hunter show up in 3 of these 12 decks.
Leper Gnome shows up in 2 of the 12 decks.
Arcane Golem is a 1-of in Reno Warlock.
Ancient of Lore, Force of Nature, and Keeper of the Grove are all in Midrange Combo Druid.

So while 8 of the 12 cards adjusted do show up somewhere, and 2 more are in Rogue which I don't currently play, the impact is fairly minimal across the board. The aggressive decks will adjust to the neutral minion changes, and the "tech" cards like Owl and BGH likely still will be run in the changed form.  In other words, other than Midrange Combo Druid, these rebalancing nerfs will not significantly alter the decks or play styles I currently choose to enjoy. So at the end of the day, there's no huge reason to complain about the changes!

Stay tuned for the next post, when I elaborate on this further and look at total numbers of cards lost in these archtypes, which represent many of the top decks on constructed ladder meta reports heading into Standard Format.

Tuesday, April 19, 2016

April Arena Challenge Update #2

As mentioned at the end of March, I decided to take on an Arena challenge where you play 10 arena runs and try to achieve a certain number of wins (65 total, in my case). Let's check in on how this challenge is progressing.

After the first two runs (Hunter, Paladin), we stand at 8 wins total.

The third deck choice turns out to be Mage, which was selected over Warlock and Rogue. Trying to get this challenge back closer to on track, and this is the deck offered up in the draft:

Results for Run 3 (Mage)
W vs. Mage (1-0)
W vs. Warlock (2-0)
L vs. Paladin (2-1)
W vs. Mage (3-1)
W vs. Rogue (4-1)
L vs. Shaman (4-2)
L vs. Warlock (4-3)

Total after 3 Arena Runs - 12 wins

Maybe we should've set the bar at 40 or 50 wins! Regardless, at least the early struggles give me a high bar to try and hurdle over as we continue. Two of the three losses with this Mage deck were aggressive rundowns where it would've been difficult to come back even with a good draw, and those losses (while frustrating) are somewhat understandable. Just unusual for me to pick up two of those type of losses before reaching 6 or 7 wins. On the bright side, this deck felt like it was approaching the groove once again, as it's clear my rust from playing so much constructed is showing off.

For round 4 the next selection was between Shaman, Hunter, and Warlock. Having already run hunter, the choice was simple...go with Warlock and hope for the best. Here's my fourth deck, which turned out to be well on the aggressive side:

Results for Run 4 (Warlock)
W vs. Hunter (1-0)
L vs. Druid (1-1)
L vs. Paladin (1-2)
W vs. Shaman (2-2)
W vs. Druid (3-2)
L vs. Rogue (3-3)

Total after 4 Arena Runs - 15 wins

The first two losses with this deck were agonizing close losses, particularly against the Druid where my taunt minions stabilized my health at 1 life for about 10 turns before the Druid finished the job (both decks largely in topdeck mode, and Warlock with only one card a turn is at a disadvantage generally). Another 3-3 record shows that the road to 65 is going to take some serious climbing, and perhaps the goal for the next challenge should be adjusted. However, we will continue on with this experiment and see whether we have any more luck with more late-game oriented Arena drafts.  Aggressive decks are fun but not always that consistent, as was the case here.

Four runs in and we've got some serious work left on the agenda.  It's not mathematically impossible to reach the 65 win goal, but we will see what happens with some lesser used classes like Priest and Warrior, which are bound to come up soon.

Thursday, April 14, 2016

A Hearthstone Brain-Bender (and why I enjoy the puzzle that is Aggro Shaman)

One of the strengths of Hearthstone and other top card games is the depth of strategy one can find in different major archtypes of constructed decks.  Although I personally enjoy making a combo deck work or using control decks, there's also beauty in some of the aggressive decks in the current "Wild" format.

Plus, it just feels terribly powerful to always be dictating the pace by making the questions and threats which all need to be answered for a slower deck to survive and possibly defeat you. Zoo is a shining example of this phenomenon performing well on the Hearthstone ladder, and aggressive Paladin strategies also do well.

But the deck I find to be really fun to pilot is aggressive Shaman, thanks in large part to the puzzle-like quality that comes from playing cards with the overload mechanic. Unlike many turns with a deck like Face Hunter (which also has decisions, don't get me wrong), a good Shaman player must look ahead and plan for the unknown when dealing with the high power and big drawback of overload spells and minions.

I finally came across a perfect example of the fun complexities at the end of a thrilling game I played today with aggro Shaman against a Paladin.

Fair warning, this is a bit of a brain bender with math involved, but I think we all can learn from analyzing such situations. We all must yearn to play better if we want to be successful, after all, and that takes hard math and metrics sometimes.


The situation plays out like this: the opposing Paladin uses his board of minions to clear three minions from my board on his 8th turn and then swings with a Truesilver to go to 14 life, and he clearly has lethal damage for his next turn. None of these minions have taunt.

So the goal will be to deal 14 damage.

I only have a Doomhammer with some charges left in play. My hand going into the 8th turn is Crackle, Lava Burst, Earth Shock (which would've been handy if a taunt was played). I have 6 total mana available because two overload applies from the previous turn. I start the turn by drawing a second Crackle.

What do you do?

Seriously, look over that situation and figure out how you would spend the six mana available. There's certainly going to be some RNG randomness determining whether you can win from this position, but the second Crackle opens up a series of potential lines of play, each having a different Estimated Value (EV) of winning. Can you, in 70 seconds, evaluate what maximizes the EV here and then execute the play before time runs out?

It's precisely the type of challenge, whether in a single turn or over multiple turns, that I love about aggro Shaman and other more puzzle-style decks like Patron Warrior. Because we have the benefit of more than 70 seconds now, let's figure out what the correct line of play would have been.

We can simplify the circumstance a bit by swinging for 4 damage with two hits of the Doomhammer, leaving the Paladin at 10 life. With 6 mana, the likely options with that hand boil down to:
  • Play Lava Burst, Crackle (this would've been the only play if Earth Shock were needed to clear a path for the Doomhammer hits, but I digress)
  • Play double Crackle with a potential Shaman Totem hero power summon as well
So what do you do first? Play Lava Burst, a first Crackle, or do the hero power? Each ends up with a different potential EV of winning!

Option 1 - Lead with Lava Burst

Let's start with the simple. If you lead with Lava Burst, it will bring the Paladin to 5 life. But the 3 mana left will allow for only one normal Crackle. With a 25% chance on each outcome (3/4/5/6 damage), that means the chances of winning are exactly 50% (EV=50%).

Not bad, but can we do better?

Option 2 - Lead with Hero Power

Let's instead say you lead with the hero power, which will leave you with 4 mana and commit you to the double Crackle plan. You might be very tempted to do this because the swing in potential win percentage is obviously dramatic when a spellpower totem is rolled from the hero power.

More specifically, the math plays out like this. There are 16 potential results from playing two normal Crackles (3/4/5/6 and 3/4/5/6, paired together have 16 total outcomes ranging from 6 damage to 12 damage). Of those 16, only 6 deal 10+ damage. That means a 37.5% win chance if the two Crackles are not powered up. This will happen 75% of the time using the Shaman hero power, but let's come back to that number in a moment.

However, in the 25% chance a spellpower boosting totem is the result of the Shaman hero power, the expected chances of winning jump all the way up to an astounding 81.25%! That is because when firing off the 16 possible outcomes of double powered-up Crackle (4/5/6/7 plus 4/5/6/7), 13 of the 16 potential outcomes will lead to 10+ damage. Winning over 80% of the time sounds like a great bet, if the fates favor you in the hero power.

So adding it all together, there's a 75% chance of a 37.5% EV and a 25% chance of increasing that to a 81.25% EV based on the result of the Shaman hero power. Doing the math...the total win percentage chance of using hero power first comes out to (.75*37.5% + .25*81.25%) = 48.4% (EV=48.4%).

So despite the allure of maybe getting lucky on that hero power and having an 80+% chance to claim the victory, the actual EV of such a line of play is LESS than that of just leading with Lava Burst. Surprised?

A quick side note: the math would obviously change if there were already another totem left on the board by the opponent. Indeed, just having one other totem increases the chance of getting the spellpower totem to 33% instead of 25%, and that scenario would raise the EV of this line of play to about the details matter, a lot!

Option 3 - Lead with the Crackle

This turns out to be another math-intensive of the options thanks to the RNG associated with the first Crackle (3/4/5/6). There are really three different outcomes of note after the first Crackle to consider.

First, if the Crackle hits for 5 or 6 (50% chance of this), Shaman will win automatically by playing the Lava Burst to finish off the remaining 4 or 5 health on the Paladin. In other words, in 50% of the Crackle outcome, the Shaman wins 100% of those games.

Second, if the Crackle hits for 3 (25% chance of this), there's going to be 7 life left on the Paladin. There's only one way to have that happen, which is use two of the four remaining mana to hero power, hoping for the spellpower totem, and then the final two mana on the other Crackle (hoping to hit for 7 damage as buffed up). There's a 25% chance of the spellpower totem, multiplied by a 25% chance the second Crackle then maximizes damage at 7 on the (4/5/6/7) choice. In other words, for this 25% of the time, the Shaman will only win (.25*.25) = 6.25% of the time.

Third, if the Crackle hits for 4 (25% chance of this), the Paladin will be at 6 health which is out of range for Lava Burst. The best available option is to then hero power to try and buff up the chances that the second Crackle using the final two mana will provide 6 or more damage. There's a 25% chance the spellpower totem arrives, which would result in a 50% chance of the second Crackle hitting for 6 or 7 to win the game...and in the 75% chance of another totem, the Shaman still might RNG 6 damage from a normal Crackle for a 25% win chance. Totaling this math: (.25*50% + .75*25%) = 31.25% chance of winning in this circumstance, which again happens 25% of the time based on the first Crackle result.

Once again, we have to sum the probabilities. That math for the three scenarios calculated above results in (.50*100% + .25*6.25% + .25*31.25%) = 59.37% chance of winning (EV=59.37%).


Thus, the best option by far is to lead with the first Crackle. Could you figure this out by approximation in the few seconds you have to make a decision? 

For that matter, did I?

That latter answer is NO! I ended up greedy and rolled the hero power first, which actually had the least chance of success (48.4%), a staggering 11% worse than the best line of play. While my luck was poor on the hero power with no spellpower totem, the luck turned around on both Crackles as I rolled a 6 and then a 5 to finish the Paladin off with 15 total damage on the turn (adding the 4 from the Doomhammer).

However, the play was nuanced enough that I wanted to know if I made the right decision, regardless of the positive outcome. And as it turns out, I could not have been more wrong in the line of play.

Lesson to learn: you can always find better lines of play somewhere in a game or deck, especially with complex puzzles like those presented by decks like aggro Shaman.

Furthermore, when faced with a closed world problem like this one, the correct way to think it through quickly would have been to realize that Lava Burst, then Crackle obviously provides 50% chance to win (the simple scenario above), but if you lead with the Crackle you have that same 50% chance plus whatever other small additional chance to win is provided by the second line of play available with 4 mana left (hero power then second Crackle instead of Lava Burst). That inherently is going to be better than 50%, which means you could quickly determine this line of play at least was not the WORST option (AKA, what I ended up on).

I don't know that a regular person could think through the "hero power first" math (which is not as clear on its face) and leave enough time to then implement the plays of the turn before the timer runs out. So while it was enticing to me and could have been better, the normal player facing this scenario for the first time likely should've gone with the sure bet of Crackle first, which as it turns out, is a way better EV to win anyway.

Hopefully you enjoyed this hypothetical brain-bender and even if you dislike playing decks like aggro Shaman, you might be able to respect the complexity and depth of this archtype and the Hearthstone game as a whole in view of this example.

Until next time, keep finding those better lines of play and never just rely on luck.

Monday, April 11, 2016

April Arena Challenge Update #1

As mentioned at the end of March, I decided to take on an Arena challenge where you play 10 arena runs and try to achieve a certain number of wins (65 total, in my case). Let's check in on how this challenge is progressing.

My first deck choice was between Warlock, Hunter, and Warrior. Nothing like starting off with that type of choice. Regardless, we move on with Alleria leading this challenge and the following deck:

Results for Run 1 (Hunter)
W vs. Paladin (1-0)
L vs. Paladin (1-1)
W vs. Shaman (2-1)
L vs. Paladin (2-2)
W vs. Mage (3-2)
L vs. Paladin (3-3)

Total after 1 Arena Run - 3 wins

Not exactly the start you would hope for when shooting for 65 wins in 10 arena runs. Two of the three Paladin decks that I lost to were very high quality, and this particular Hunter deck was really weak in the midgame. Plus, when Chromaggus is the best legendary offered as a first pick, it's not exactly a great set of cards overall. Moving on...

For round 2, the next selection was between Shaman, Paladin, and Warlock. If you can't beat them as in the last run, join them! Paladin it is. Here's deck 2 (cries at no Truesilver or Murloc Knight):

Results for Run 2 (Paladin)
W vs. Warrior (1-0)
L vs. Druid (1-1)
W vs. Druid (2-1)
W vs. Paladin (3-1)
L vs. Priest (3-2)
W vs. Druid (4-2)
W vs. Mage (5-2)
L vs. Mage (5-3)

Total after 2 Arena Runs - 8 wins

Certainly an improvement from the first run, but still not a perfect result when shooting for a 6.5 win average, as Paladin is one of the better options in Arena if not THE best, at the moment. As noted above, there were some notable Paladin staples missing, but the deck still worked well enough. The late-game cards did not pack quite enough punch to finish off the opponents I lost to, as most games did play out with the opponent dropping below 10 health before the game was over.

But regardless, we must move on. Next up will be a Mage run, which is probably more my favorite Arena class than even Paladin. Check back next time to see if we can get this challenge back on track.