What We Can Learn from Games with Variance and Hidden Information

ยท 1608 words ยท 8 minute read

A discussion about the primary similarities between two of my favorite games (Magic: The Gathering and poker), those being variance and hidden information. Discusses the effects they have on the game, why these effects are important, and takeaways that can be applicable outside of the games.

Contents ๐Ÿ”—

  • Background
  • Hidden information
  • Stakes
  • Variance, process, and results
  • Emotional responses
  • Closing words

Background ๐Ÿ”—

Since the pandemic, I’ve made games a part of my lifestyle. I started playing Magic: The Gathering competitively in 2019, it being one of my primary sources of motivation until 2022, when at some point I shifted more focus towards school. In 2023, I started playing poker (Texas hold-em) with some friends weekly with low stakes, which has persisted to the time of writing this post.

Hidden information ๐Ÿ”—

Hidden information is a core component of both Magic and poker. In poker, a significant part of one’s mental process is devoted to determining what may be in other people’s hands based on their previous patterns of play and how they have played the current hand. This is also a core component of Magic, although it is far less emphasized until a certain level of play.

In a game of Magic, what is unknown often exceeds what is known significantly. The first aspect of this is the opponent’s deck. Oftentimes a player can limit the amount of uncertainty on this axis via thorough preparation for the given event. This can look like learning each card that the player could possibly play against or learning what cards certain deck archetypes tend to play. While some events naturally soften this source of uncertainty by revealing decklists to players’ opponents before the match, players still have a sideboard of up to 15 cards, from which they can ‘bench’ cards in their deck and ‘start’ cards from their sideboard between games.

The other aspect is what is in the opponent’s hand. Similar to poker, information can be gleaned from how the opponent has played, although there are far more variables in Magic (player’s deck, opponent’s deck, large domain of board states). This effect can make it hard to know what to look for in a game, and has often led me to giving up on gaining such edges and instead focusing more on concrete ideas or relying on heuristics to make decisions (which I often do in poker as well if I want to do less thinking).

Where am I going with this? Hidden information adds layers of complexity to games that cannot be accessed in other ways. There is practically no limit to how much thought and effort people can put into using the information they have to attempt to make predictions about the unknown information. Being able to play the game from the opponent’s perspective is a particularly beneficial skill, which itself requires you to know the opponent’s patterns of play, and in Magic, also requires an understanding of the opponent’s deck. But to answer my question, I’m not really sure where I’m going with this. I just think it’s cool mostly.

Stakes ๐Ÿ”—

Adding stakes to games is a scalable in magnitude and effective way to control and add seriousness to a game. Introducing or increasing stakes will likely increase how much time and energy players put into various decisions, such as figuring out a player’s range of possible cards in their hand. Some players may not need external influences such as stakes to lock in, but for others (such as myself), stakes are a form of discipline, as they are a much more effective way to get me to focus on a game and take my decisions seriously than merely telling myself to do so.

The main downside with stakes is that there is often negative utility associated with putting money on a game you play. That is, the benefit you get when you win is smaller than the emotional damage from losing the equivalent amount (citation needed). Gambling addictions can also occur under the right circumstances. I’ve generally found a beneficial practice to be only gambling with what I’m willing to lose with minimal negative life and emotional impacts. I aim to create a situation for myself in which I still ultimately have a fruitful and beneficial time even in the event that things do not go my way and I lose everything I put in.

Another way to think about gambling is as a variably cost-effective way of spending money recreationally. There are many ways to spend money for emotional and social benefits, and unlike other recreational activities, you sometimes get your money back. This is a very generous framing but I believe there may be some truth to it, although one ultimately needs to sufficiently enjoy the act of playing games with stakes for it to be accurate.

Variance, process, and results ๐Ÿ”—

Variance is an inherent characteristic of games with hidden information. There are plenty of games with minimal variance, most notably to me being chess, but chess even has some variance at all levels, since each player is more prepared for some lines of play than others, but even so, it has about as low variance as any multiplayer competitive game or sport could have. I nonetheless love chess and think it is an extremely cool game, but my most fun experiences with games have been in those with hidden information, and accordingly with variance.

When I play games with variance, I hold the mindset that the variable elements will eventually come close to balancing out, and that over a long period, how much I win is proportional to how well I am playing. However, we can have stretches of positive and negative variance that seem statistically extremely unlikely and last longer than we may expect, and it is important to be aware of these and not draw irrational conclusions from them, which brings me to my next point.

An extremely critical skill not only in games, but life in general, is avoiding results-oriented thinking and being able to separate the process from the results. In general, results are a product of process and variance, and being able to decouple those two inputs is how we draw productive and actionable conclusions while remaining emotionally level. This skill comes with experience, but the first step of setting as a goal and being aware of it goes a long way. People may have a tendency of overly attributing losses to variance and overly attributing wins to strong play, while other people may have overcorrected on this and not know when to give themselves credit (I believe I am in this second camp).

Although results-oriented thinking should be avoided, results can still be helpful for evaluating processes; they just shouldn’t be the sole measure of success. Under situations with noteworthy results, we can examine the process that led to the result and perhaps single out a single or a few pivotal decisions. Knowing the actual result gives us knowledge of one of the possibilities, but we should think about the other possibilities and their likelihoods and evaluate the decision after the fact. Sometimes the actual result will shed new light on a decision and change how you evaluate it, but other times the result may not be likely or impactful enough to change the correctness of the decision. There are situations where a correct decision led solely to a negative outcome, and an incorrect decision led solely to a positive outcome, so we should be aware of those possibilities and be able to identify them as they occur.

Emotional responses ๐Ÿ”—

This is the section that I probably have the least knowledge and comfort with, but I’ll try my best to share what I know. Games with variance are prone to result in negative emotional responses, and stakes can amplify these. As we increase our experience with games with variance and stakes, these emotional responses will likely decrease over time, and while this has plenty of benefits, these responses still have some importance.

Tilt is, as defined by me, the state in which negative emotions cause you to make worse plays due to compromised decision-making processes. This can be combatted by either lowering the magnitude of the emotional response or improving separation between emotions and decision-making processes. Both of these come with experience, but the second way is more beneficial in the long-term since even if we could, we shouldn’t completely suppress the emotions that occur when playing games, and they are bound to occur at some points.

Emotional responses are a key aspect of competitive activities and serve as a strong source of motivation. Some people react negatively to noticing that they made a poor play after the fact, while others react negatively to losing; both of these motivate these people to play better in the long run, and as discussed earlier, both are amplified by stakes, especially the latter. As such, it is important to not become numb to losing, which is pretty common with minimal stakes, but with high stakes, this requires extensive gambling with poor mindsets. Overall, while negative emotions are generally considered a bad thing, they are one of the strongest motivators for good play.

Closing words ๐Ÿ”—

If you’ve made it this far, thank you. This is the first piece I’ve written with the primary goal of sharing my ideas with other people, and while I am by no means an expert on any of this, I’ve tried my best to provide complete and informed arguments based on my experiences that are applicable to people with and without experience with the discussed games. Feel free to contact me if you have any questions or comments.