Marvelous Math #1: Using Probability to Win More Games!

Published 4 months ago by Cqrbon Article Views 2748 Estimated Reading Time 6 minutes

Introduction

Hello hello! My name is Cqrbon, and this is the first article in a new series called Marvelous Math! In these articles, we will go over different ways to harness the power of data, probability, and statistics to optimize your Marvel Snap deckbuilding and gameplay. The goal of these articles is to help you gain a better understanding of core aspects of the game, which will allow you to gain a competitive edge over your opponents!

About Me

I am a big fan of video games, but I especially love card games! I have quite a bit of previous experience with online card games, including Hearthstone and Legends of Runeterra. I am very competitive, and I love to theorycraft and come up with new ideas to give myself an advantage! I have been greatly enjoying the Marvel Snap closed beta, and I look forward to bringing you quality content to help you build better decks and win more games!

What is Probability?

We'll start off by answering an easy question. What is probability? Probability is defined as the likelihood of an event occurring. In mathematics, the probability of an event occurring can range from 0 to 1, where 0 means that an event will never occur, and 1 means an event will always occur. There are an infinite number of probabilities in between 0 and 1. Probability is written in one of two ways. It can either be written in decimal form (0.42) or as a percent (42%). Both of these values convey to us that the given event will happen approximately 42 out of 100 times.

Let's take a look at a simple example of how you can use probability in Marvel Snap.

The White Tiger Scenario

Imagine the following scenario. It is the sixth and final turn of a game. You are confidently winning the middle location with 3 high-power cards, but you aren't doing so well on the left location, only having 2 low-power cards there. The location on the right is Knowhere (161), which is very challenging to access. If you try to play a card here, it will get destroyed immediately. Your opponent is winning Knowhere by 2 power, as they were able to move a Nightcrawler (91) into that location.

 

 

 

 

 

 

 

 

 

 

 

 

You currently have a White Tiger (141) in hand. White Tiger summons a 7 power Tiger at a different location on reveal. You don't think you will be able to win the left location, so you want to try and put the Tiger into Knowhere, as it will easily beat your opponent's Nightcrawler.

In this situation, you can either play White Tiger at the middle location or the left location in order to try and get the Tiger into Knowhere. Regardless of if you pick to play White Tiger in the center or on the left,1 out of 2 events are going to occur:

1: The White Tiger summons a Tiger in Knowhere.
2: The White Tiger does not summon a Tiger in Knowhere.

This results in a 50% chance for White Tiger to potentially win you the game. However, what if we also had another 1 energy card in hand, like Ant-Man (7)? In this scenario, you could first play Ant-Man into the central location as your fourth card to fill up the center. Now, you can play White Tiger at the left location, and 1 out of 1 event is going to occur:

1: The White Tiger summons a Tiger in Knowhere.

This results in a 100% chance for the Tiger to go to the location you want it to go to, which more than likely will win you the game. While this is obviously a very simple and straightforward example, it is important to recognize that the smallest decisions can have a big impact on the outcome of a game. Whenever possible, you should try to maximize the probability of you winning the game.

Let's take a look at a slightly more complicated example of probability.

The Ironheart Scenario

Ironheart (64) is a very interesting card. While 3/0 is not a very good statline, she provides +2 power buffs to 3 cards at random on the field. The random aspect of the card definitely poses some probability questions. What's the best way to get the most value out of the card?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Suppose it is Turn 3 of a game. One of the locations was Central Park (285), which puts a 1 power Squirrel at each location. You also have an additional 1 energy card played at each location, for a total of 2 cards at each location and 6 cards in play total. What a great board for Ironheart! However, you want to maximize the number of Ironheart buffs you get at the left location because you believe you have a good chance of winning that location if you can land a few buffs.

There are a few important things about how Ironheart works that we need to understand in order to do the math correctly.

1: Ironheart cannot buff herself.
2: Ironheart cannot buff the same unit twice (unless you are retriggering her reveal effect). If you only have 2 other cards on the board, you will lose 1 of the 3 buffs.

With this in mind, let's take a look at the math! First, we need to know the chance that a specific unit receives a buff. 1 divided by 6 is roughly 0.1667. This means that any of the 6 given units on the board has a 16.67% chance to receive a buff. To find the chances that one of your 2 units on the left gets a buff, we can multiply that by 2.

0.1667 * 2 = 0.3333

This means that you have a 33.33% chance to buff 1 of the 2 units at the left location.

This is a decent chance, but it definitely could be better. If you really want to maximize your power at the left location, you need to increase the odds that you will get that buff.

An in-game example of this might be playing a different card to the left on Turn 3 and then playing Ironheart on Turn 4. With 3 units on the left, you have improved your chances to get a buff from 33.33% to 42.86%. That is much better! 

Here's another example: it's turn 5, and you have 2 cards at each location. You want to play Ironheart as well as another 2 energy card. You want to play the 2 energy card to the right, but you want to try and get at least 1 buff at the left location.

The ordering of cards becomes very important here. Ironheart won't buff cards that haven't been revealed yet. If you play Ironheart first, you will have a 33.33% chance to hit a buff on the left side. If you play the 2 cost card first, then Ironheart second, your chances for a buff on the left go down to 28.57%. While that is not a huge difference, it could potentially cause you to lose or win the game. The order you play cards helps to maximize your odds of landing Ironheart's buffs where you need them.

Conclusion

While the above two examples were not very complicated, they showcase the importance of using the tools at your disposal to give you the best possible chance to win. Both the positioning of your cards on the board and the order in which you play them can help you achieve your goal more consistently. Maximizing probability is important in any card game, but especially so in Marvel Snap, as there are fewer cards played and fewer turns taken in a given game. 

There is an abundance of scenarios in card games where probability can be used. How often will I draw this specific card by this turn? How often will Ironheart buff two cards in the same location? How often will I see this location in my games? Understanding the fundamentals of probability makes it easier to answer more complex questions like the ones above. We will look at these questions and more in future articles! Thanks for reading!


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