Cognitive Biases in Hearthstone – Gambler’s Fallacy (#1)

The human brain is a wonderful thing. Sometimes, when presented with two choices, which are the same, just worded differently, it will assume that one option is better than the other. Other times, when you don’t have enough information, it will fill the gaps itself (often incorrectly). It looks for correlations, even if there aren’t any. Or leads you to situations in which something just FEELS right, even though it’s really not.

Believe it or not, but cognitive biases aren’t something rare. To put it simply, they’re common flaws in logic. Person’s own, subjective interpretation of reality. Of course, after you really start thinking about them, you realize that they make no sense. But what’s important is that they affect everyone – like you and me – in our daily lives.

In this series, I will cover some of the common cognitive biases that can affect Hearthstone players in particular. How do they work? Why do they happen? Are there any situations in which they actually make sense? Identifying them and realizing what they are is a big step in terms of becoming a better player. Plus some of them are just interesting to read about.

In the first part, I will talk about probably the most common fallacy tied to randomness – gambler’s fallacy. When playing Hearthstone, or any other card game, a fair bit of chance is involved, and understanding gambler’s fallacy can make you look very differently at every random roll. I will also give some examples of situations in which gambler’s fallacy… actually works.

What is a Gambler’s Fallacy?

It’s actually very simple. When a series of independent, random events happen, people tend to look at them and think that they’re somehow connected – if one thing happens more often now, it means that it will happen less often in the future (or vice versa). The easiest way to explain it is by looking at the series of coin flips. The perfect coin flip is, obviously, always a 50/50. You flipped it 4 times and got tails four times in a row. What has the higher chance of coming up next? Heads or tails?

The obvious answer is “heads”. After all, tails came up four times in a row already. But randomness doesn’t work like that. Each flip is an independent random event, and it’s always 50/50. Which means that even if you somehow get tails 20 times in a row, the chance to get heads will still be 50% in the 21st flip.

Yes, if we look at the entire series of random rolls, the chance to get tails 5 times in a row is only 1/32 (~3%), which means that there is a 31/32 (~97%) chance that at least one of those flips will be heads. And that’s exactly how gambler’s fallacy works. If you showed someone any of the individual flips, their answer would be “the chances are equal”, but if you show them a whole series, they will try to judge the next flips based on the previous outcomes.

The fallacy’s name is also very telling. It most commonly affects gamblers playing random games, such as slot machines. If you lost 10 times in a row, it FEELS like your chance to win will be higher now, which obviously is not true.

When Gambler’s Fallacy Actually Works

Funnily enough, there are situations in which everything I’ve just said doesn’t apply. For gambler’s fallacy to be an actual fallacy, the randomness must be truly… random. I know how weird it sounds, but bear with me. Instead of trying to fight against that bias, some people accepted it as a part of human nature and… made it real. Those people are game designers.

You see, here is the thing. Games are meant to be fun. And in order to be fun, they must FEEL correct, not necessarily BE correct. And, because of that, game designers have embraced gambler’s fallacy (as well as many other cognitive biases, but that’s material for another article) and turned it into in-game mechanics. There are two basic upsides of making gambler’s fallacy work in games. The first one is decreasing the frustration that comes with streaks of bad RNG, and the second one is making the game subjectively feel right – even though objectively it isn’t.

One great example of a working gambler’s fallacy in games is the hit chance system in XCOM: Enemy Unknown. For those of you who haven’t heard of it, it’s a turn-based tactical strategy game – I really recommend it if you’re into that sort of games. It will be a gross oversimplification, but the game is basically about shooting aliens. If you aim at one of them, the game shows you how likely you are to hit your target. However, when playing on easy or normal difficulty setting, if you have a 50% or higher chance to hit the shot, and you miss, your next shot will have +15% chance to hit (or +10%, depending on the source), even though the extra chance won’t be displayed. And so, if you take two 50% shots in a row, and miss the first one, the second one will still show as a 50%, but will instead have a 65% chance to hit. If you miss again, it will add another 15%, and so on until you finally hit. It makes long streaks of misses less likely, and thus making the game more fun to play. The mechanic also works the other way around – each time an alien hits one of your soldiers, the next one will have a 10% lower chance to hit, until it misses. Because, once again, getting hit a few times in a row is frustrating and doesn’t feel fair (even though it WOULD actually be more fair). The game is rigged in the player’s favor, and pretty much no one notices, because gambler’s fallacy makes people think that it actually SHOULD work that way.

If you think that XCOM is an exception, you would be very wrong. Sid Meier talked about this fallacy (as well as many others) in his lecture about psychology in video game design – he confirmed that they’ve employed this sort of mechanic in the Civilization series, at least the latest installments. It’s pretty common in single player video games in general, for good reason. Everyone understands that getting unlucky is a part of gaming, but the majority of players wouldn’t actually want to be on the receiving end of bad RNG all the time. We simply don’t notice those mechanics, because they aren’t very blatant. They’re subtle enough that our gambler’s fallacy masks it, and devs aren’t really rushing to inform players about them. Why? Because knowing that the game is “rigged” in your favor might feel even worse than getting a bad streak of randomness. Players want to think that they beat the enemy fair and square – not that the game “cheated” for them.

To go even further, a working gambler’s fallacy seems like something that is harder to apply to video games. However, some games still introduce similar systems to decrease the streaks of bad RNG. They make random rolls feel more “fair”, even though they throw true randomness out of the window. One example would be League of Legends and its critical chance mechanic. Let’s say that you have a 10% chance to critically hit with a normal attack, it means that you would expect 10 critical hits in 100 attacks. If it was truly random, the number could as well be 20 or 2 – that’s how randomness works. However, the game tries to dynamically adjust the critical chance in order to hit the right mark (so 10 crits in 100 hits in this case). Each hit that wasn’t critical increases the chance of the next one being critical. I’m actually not sure if the system works the other way around – if lucky streaks of crits are eliminated too. It would seem best from the balance perspective, because lucky streaks of crits might seem as unfair as unlucky ones – if you’re the one getting hit, that is.

Gambler’s Fallacy in Hearthstone

So, since you already understand this fallacy, let’s talk about Hearthstone. First things first – let me assure you that unlike in League of Legends, Hearthstone has no such “odds-manipulation” system in place (at least not in the actual game, more about that later). A streak of bad rolls doesn’t make your next roll better. And that’s the main point. Below, I will present a few examples of common applications of this bias in game.

A few bad RNG rolls won’t make your next RNG roll have a higher chance of being good. It was actually pretty common thinking back in the day when Ragnaros the Firelord was all over the ladder. 50/50 flips were common. You often wanted to hit that big minion, but it hit your opponent’s face instead. Or vice versa – your opponent was at 8 health and you missed a few 50/50’s in a row. It also worked the other way round – if your opponent did win a few 50/50’s (or any other rolls) in a row, it didn’t mean that his next outcome will be worse. You need to remember that the randomness doesn’t work like that. Look at each of the random rolls individually. Thinking that “I was unlucky, so I HAVE to get lucky this time” is just wrong. Assuming that your chance to succeed is higher than it really is might lead to suboptimal plays.

Card drawing. This is still very common, and a terrible way to think about drawing cards. Let’s say that you’re looking for one, specific card. Duskbreaker, for example. You’re in a dire need of AoE and you were digging for it for the last few turns, trying to stall the game as long as you could. You didn’t draw it when you had 14 cards left in your deck, you didn’t draw it when you had 13, 12 or 11 cards left in the deck. Since you didn’t get it so many times in a row, the chances to finally draw it should be pretty high, right? Well, wrong. If you have 10 cards left in your deck, the chances to draw it will always be 1 in 10. It doesn’t matter that you didn’t draw it for a few turns in a row. So, why might it matter? Since you were so unlucky for the last few turns, you just HAVE to get it now. And you might try to go for a desperate card draw. But the truth is that 1 in 10 is still a low chance, if you put all your bets on it being the next card, you would lose that game 9 out of 10 times. Instead, you might do some other play that would have a higher chance to win. Of course, if the situation is absolutely desperate and you have no other way to win, you will still take a 1 in 10 chance – just don’t think that it will be any higher because you were unlucky.

Matchups. Matchup RNG is huge, but people often miss it when talking about randomness in Hearthstone. This is something I hear very often from my friends playing the game. The fact that you play against a certain deck a few times in a row DOES NOT mean that the next time you queue, you will have a lower chance of facing it. If there are 30% Even Paladins between Rank 5 and Rank 1, it means that if you queue into one 5 times in a row, you will have exactly the same chance of facing it again 6th time. So thinking that “since I faced the same deck X times in a row, I can’t possibly face it again” is wrong. But, what is even worse is the exact opposite. Let’s say that you queue a Cube Warlock counter, and you don’t face any Cube Warlocks for 10 games in a row. It might mean that the meta has changed a bit, maybe today people don’t feel like playing Cube, maybe there just aren’t enough Cube Warlocks on the ladder to justify you playing the counter deck. Or maybe you just got unlucky. But not facing Cube Warlock X times does NOT mean that you will suddenly have a higher chance to face it when you queue X+1th time.

Of course, those are just a few examples. Gambler’s Fallacy can occur any time you face a series of individual random rolls. In order to improve, you need to understand that each roll is independent and they aren’t connected in any way. Make your decisions based on your CURRENT chances instead looking at how lucky or unlucky you were during the previous rolls.

But, there is one more thing I want to talk about. Remember that XCOM or League of Legends examples I gave earlier? Even though Hearthstone has no such system in the actual game, or matchmaking, it actually adapted gambler’s fallacy as a part of the pack opening. The Pity Timer works exactly like that. In general, you should see one Legendary in 20 packs, which means that you have a roughly 5% chance to open it per pack. However, that number is only an AVERAGE. The actual number depends on how far you’re into your pity timer.

Ignoring the guaranteed Legendary in the first 10 packs (let’s say that you got it already), your first pack from a certain expansion won’t have a 5% chance to contain a Legendary – the chance will be lower, calculated at around 3%. The more packs (from the same expansion) you open without getting a Legendary, the higher your chance to open one will get. The chance ramps up heavily after 30 packs without a Legendary, reaching 100% at 40th pack. It means that if you haven’t opened a Legendary in 39 packs, 40th will have a guaranteed Legendary. Here is an older study on that matter with exact numbers, if you’re interested.

The reason for this system is simple – to eliminate some extremely unlucky streaks that would eventually happen. Reaching pity timer already feels terrible. Now imagine buying 100 packs from a new expansion and not opening a single Legendary. If there was a flat 5% chance per pack to open a Legendary, and no pity timer, it would happen roughly 0.6% of time, so more than 1 in 200 players would end up with no Legendaries from a HUNDRED packs. That would surely be bad for business.

Closing

That’s all folks. At least when it comes to the first part of the series. If you liked it, let me know and I will write more – there are many more cognitive biases to cover, but I don’t know if you enjoy this kind of content.

If you have any questions, or want to add some more examples, be sure to leave a comment below.

Also, please keep in mind that I’m no psychologist or sociologist, so I’m mostly basing my definitions on well-known online sources, such as wikipedia. If I made a mistake somewhere, was wrong about something etc. please let me know.

Good luck on the ladder and until next time!