RNG And The Role Of Skill in Hearthstone

Lately, there’s been a lot of talk about the impact of the RNG in Hearthstone. Many argue that skill and balance play a significant enough role and that the game is balanced. Their take is pretty simple: sometimes the RNG screws you, suck it up, kid. They have a point in that 80% of the top level players are consistently top level. However, those same top level players are noting that there their skill and deck balance can all be negated by an early or series of bad draws. In fact, there’s a discussion about this on the latest Turn2.Can we mitigate such bad draws? How much of an impact do they really have? What solutions are available? Let’s delve deeper and explore what the current problems are with the RNG and how Blizzard can possibly change that.

Value of Cards

Before we get too deep in this analysis, let’s ask ourselves what a single card means to the game. Cards are choices. They are your ability to exercise skill over chance. If you have 4 cards in your hand, and the other player has 3 cards, that card advantage is significant because you get 33% more option advantage than the other player (however, he has 25% less options than you, which shows the relativity of the matter). While it may seem that three cards or four cards are minor, this really amounts to an entire decision advantage. You could play two cards and break even with him, but if he plays two cards he falls behind you in advantage. A major part of this game is mitigating that card choice disadvantage. Ideally, we’d like out hands to have “an answer to everything,” but that’s difficult without choices. In this way, card advantage is often better than field advantage or mana advantage.

Draws, Mulligans, and Getting Screwed

First turn balance

Blizzard has gone through great lengths to determine what the first turn advantage is for Hearthstone. They have experimented a lot and find that with the current system, going first yields somewhere between a 4% and 5% advantage. This is a fantastic number to be at because it’s really a slim advantage margin. However, it’s important to note that despite the fact this margin is very close to balanced, it does so at the sacrifice of card advantage for the first player. This is normally not a big deal, but you have to ask the question: How does that card disadvantage for the first player screw them?

Mulligans and their odds

The worst case scenario happens: You’re first and you’ve drawn three 5+ cards. What to do, what to do. I guess you have to mulligan (a golf term adapted to CCG which means dump some or all of your cards and pray for better ones). Oh look, another 5+ draw. Life is wonderful. Turn 1 comes. You draw a 4. Turn 2 comes. This is unbelievable; you draw an 8. Turn 3 comes, you draw another 4. How many times has this happened to you?

Daniel Ikuta has posted an amazing chart on this site about just that. It tells you exactly what the odds are… and if you look at it, they’re not really that great for the first player. For instance, if you were to mulligan all three cards, and had a third of your deck as desired cards, you have a 77% chance you’ll get a single card you want. If your opponent does the same thing but with all of his cards, he has an 88% chance of getting a single card he wants, but what’s more important to note is that he has a 50% chance of getting two of those cards. Compare that to your 30% chance of getting two, and you see that playing second really gives an early advantage in options. As we’ve noted, options help skilled players. While it may average out in general play, it is my suspicion that the current system harms skilled players more than it harms average players.

Does best out of three fix this?

In some respects, it mitigates this problem significantly. Best out of three means if you get a bad draw and shuffle, and it happens to ruin your chances of winning, you have two other chances for that not to happen again. Unfortunately, though, it’s not a perfect solution. It is possible that a perfectly well-balanced deck used by a skilled player can encounter this two times in three matches. In fact, it’s quite likely. This is why card advantage from the start of the game is such a major impact on the first player. If the first player fails to draw a 2 or 3 cards early, they’ve essentially wasted two turns and must hope they have a clear to regain some semblance of control.

The Art of Drawing Cards

What is “top decking”?

A common term in CCG is “top decking”. This means you are literally dependent on the top card on your deck to survive. This is an undesirable place to be in because it is tantamount to relying on the grace and good will of Lady Luck. As I will continue to emphasize, choice is the best weapon in this game as it allows a skilled player to make informed decisions and keep the game in his or her favor. If you’re down to using the top card from your deck every single time, where’s the skill? This is something to be avoided at all costs.

What is a “draw engine,” anyway?

Many players builds focus on having at least one draw engine in their decks. A draw engine is a method for drawing more than one card on a given turn or to consistently draw more cards than you use per turn. Actually, to be more accurate, a draw engine is just anything whose intent is to draw cards. This includes Lay on Hands, Arcane Intellect, and the Northshire Cleric. These cards entire intent is to keep you filled with options.

Mana curve?

As most players figure out early, the mana curve of their deck is important. Stack a deck with too many high mana cards and you’re likely to sit around and wait for the first half of the game. Once you can make a move, you’re only using one card per turn, and that’s just awful. Likewise, if you stack your deck with too many low cards, you can find yourself top decking very quickly and be spent by turn 5. So the idea in good deck design is to keep a good solid balance between the mana cost of your cards, mitigating the odds you’ll be heavy fisting or top decking.

This, still, is susceptible to Lady Luck, as even with a balanced deck, you could be drawing deep mana cards for the first five turns. The only option in ths scenario is work out a board clear plan, possibly with some health or armor recovery. You can also have too many low value cards in your early turns, expending your resources. The only choice in this scenario is restraint. Do enough to make an impact, but not so much that you run out of options in the late game and top deck. These are all ways to mitigate by skill, but they’re not fool proof. Either way, plan your mana curve so that it’s balanced, but also plan your cards so that you have enough outs given both of these scenarios.

The 90/10 Goal

80/20?

The number being tossed around, one which I cannot support but agree with being a good heuristic guess, is that this game is 80% skill and 20% luck. People seem satisfied with this, but I am not. I believe that the more skill you have, the more benefit you should see. In a best out of three scenario, you should be able to win a tournament with a high focus on skill… but let’s look at the chart below.

Role of skill and luck in 128 participant tournament.

1. This chart below is a rough estimation of the role of luck in a best out of three tournament with 7 rounds.
2. It’s not gospel or even entirely sound reasoning, just an approximation of reality. Consider it a heuristic.
3. Formula used: (1 - ((LUCK^3 + 3*( SKILL*(LUCK)^2)))^7 … ex: (1 - ((0.2)^3 + 3*( 0.8*(0.2)^2)))^7
4. %Skill - Ideal skill odds weight. Factors in deck and play.
5. %Luck - Ideal luck odds weight. Factors in draw luck and opponent luck.
6. Skill’s Role - Ideal role skill plays in winning the tournament. These are the odds that all rounds are won by skill alone.

%Skill	%Luck	Skill’s Role
90	10	81.9%
80	20	46.3%
70	30	18.2%
60	40	4.7%
50	50	0.7%
40	60	0.0006%

Of course, the more a game focuses on skill, the better. The question you have to ask yourself is how much of a role you think skill plays in Hearthstone. If you feel that it’s 80/20 then you’re accepting that your skill isn’t likely to get you all the way through the tournament.

Proposed Solutions

Obviously, luck will always play a role in this game. The general consensus I get on IRC is that the game is 80% skill or less. So obviously our goal is to make the game 90% skill or more. With this goal in mind, here are some proposed solutions that may or may not work.

Solution 1 - Nyhx’s proposal

On Turn2 Ep9, Nyhx proposed a solution to this very problem which focuses strongly on early draw chance. His proposal is to increase the initial draws to six and have the player pick three. Both first and second pick the same number of cards. There’s been a few variants of this I’ve heard myself, too. First draws 5, second draws 6, both pick 3. Or first draws 6, second draws 7, both pick 3. Or even first and second draw 6, first picks 3, second picks 4. All of these variants are related.

The positive impact of this is pretty obvious: it helps improve the first 4 rounds of the game tremendously. It decreases the odds of a bad draw. It increases the power of initial decisions. It improves early choice.

The negative impact of this isn’t so negative as it’s just a reality. It has the same problem as before, just less frequent. Does this bring us to the 90/10 goal? Hard to say, but I hope Blizzard considers this as one of their options as the beta continues.

Solution 2 - Draw effects

Another option is to just increase the number or quality of draw effects in the early game. Maybe this could be accomplished by giving every player a low card draw engine like the Northshire Cleric. Maybe you can just increase the number of bail out draws on cards like the Novice Engineer. It’s hard to say, what this could look like, but it’s worth a look.

The positive impact of this is that recovery from bad draws is more of an option. It also increases the initial hand size, which, choice impacts skill, so that’s not bad. Either way, it would help things…but…

The negative impact of this is that you’ll go through cards MUCH faster. This may mean your deck needs to be 35 cards now, and that’s just a huge impact on the game balance already. Otherwise, fatigue management is going to be a more common problem. In addition, now a player has to worry more about overdraws, which also is a bad thing. It’s difficult to say, but I think this is not an option.

Solution 3 - A radical (and unlikely) proposal

What if… just what if… instead of one deck of 30, a player was to design two decks of 15? How would that impact the game? The idea is that one deck would only draw on odd rounds and the other deck would only draw on even rounds. Could this possibly be a solution to the 90/10 problem?

The positive impact of this is massive and sweeping. A player could choose to put control cards in one deck and aggressive cards in another, giving them a more balanced aggression/control option. Or they could stack one deck with AE’s and the other with minions, making them more assured that in what their next turn would yield. Or, they could balance their cards between odd and even mana, thereby allowing them to engineer better mana usage in games. It would really change the way people build their characters and could add a LOT of variance to the game. Variance I believe is going to be MUCH NEEDED as the game is played more after release.

However, the coding challenges behind such a radical new approach is why I think this proposal will not happen. The learning curve would also increase as the game has now become more complex. There’s also potential balance issues with KNOWING that your next card will fall on an odd or even turn. That said, I wish this solution was easy to test on Blizzard’s end, because I think it warrants a looksee.

So there you have it…

…that’s randomness and luck in a nutshell. It makes sense to strive for a balance that is closer to 90/10, but maybe this isn’t even possible. I think if it is, though, it needs to be implemented immediately. It is very disheartening for a skilled player to not even have a chance due to terrible, terrible draws. If anything, the initial “early draw” problem might need some attention, and it is my hope that Blizzard takes a look into it.