Checks and Balances: The Math of Universus
By Richard Bernard
Howdy gamers and Happy Fourth of July! I’ve been told by my locals on numerous occasion that the way I look at the math of Universus strays from the norm and thought it would be a good topic to talk about!
I’m going to try and explain my thought process behind the math of Universus in a couple key points. This article is going to focus on a topic I’ll call: Check Chance!
You’ve heard it from almost everyone: “Oh man, I checked a 3!” “I would’ve won if I had just checked a 5!” Something so very fundamental to this card game we love that a lot of people chalk it up to pure, random chance. However, once you start paying attention to where your bad checks are, and start to memorize what is actually in your deck, you’ll find you start having better “luck” and stop winning and losing games to random chance.
Deck Construction
Let’s start off with deck construction. On average a deck consists of approximately an even third of attacks, i.e. 20 attacks in a 60 card list, 25 in a 75, etc. This means without thinking further into it, you’ll have a 33.33 (repeating, of course) chance to check an attack. This is way too generic of an expectation as when you draw your very first hand of the game, that goes entirely out the window and the math gets more complicated. For the remainder of the article, we can assume we are working with a 60 card list with 20 attacks as a 6-hand size character (with 3 control attacks and 5 control foundations).
Your First Hand
Your first build turn can determine how a game is going to go. Try to check a 4 out of the gate and end up checking a 3? I’ve seen it happen too many times. The ideal build turn is almost always 2 or 3 difficulty foundation, followed by another 2 diff, a 1 diff, and then a 0 diff. Some people may dare to go further and try to play another foundation, however. What does that look like in terms of probably to check? Assuming you draw a hand full of foundations, you would have then ripped a 6 of your good checks out of your deck to pass checks later on, this is usually ideal on your first turn, however the odds change based on your first turn checks. I’ve created this small spreadsheet below to give you a run down.
Granted, the chart is quite generic and assumes that you will only check one type of card throughout your build turn. This is unrealistic and won’t be very common in your games, but can and will happen! There are also turns where our build hand is undesirable and forces us to play foundations that need a 4 check or more. Below is a spreadsheet that explains the likelihood of checking an attack assuming you checked straight foundations prior to it:
The math shows us that we have a 38% chance to fail a 2 diff foundation if we played it with 2 progressive difficulty. That is a HUGE chance. You, as the player, will then have to weigh the risk of playing that non-guaranteed 2 difficulty foundation, or play a guaranteed 0 diff and then attempt to play your 2 difficulty foundation on a 5 check. The choice is ultimately yours to make based on numerous other factors that are involved in our game. The math is only part of the process.
Attack Strings
This is the big one. It’s how you win the game! (Well…. Most of the time anyway.) Let’s lay the scene. You had a grip full of attacks and you’re trying to find lethal. Let’s assume that you have 5 attacks in hand, 7 attacks in the deck with 20 cards total left in it, and the rest of your attacks are accounted for and won’t get in your way of sweet victory. Here is another spreadsheet (yes, another one) that will express your likelihood to check an attack during your attack turn, assuming you check straight foundations prior to that pesky 3 check.
However, as per usual, the likelihood of the above is slim to none. One of my teammates somehow manages to prove this time and time again. Shout out to you, Jordan!
To have a more realistic representation of an attack turn. Here is yet ANOTHER spreadsheet (the last one, I promise) showing the likelihood of checking an attack on each individual attack if you checked well prior to it:
As you can see, the chance of checking an attack grows quite quickly once you slimmed down the deck by going through some of your remaining foundations. This is why whenever I play an attack, I always try to do the math and gauge the likelihood I will check an attack. From there, I think about “What happens if I DO end up checking an attack on my first attack? My second? My third? My fourth??” What is my game plan from there if I do?” Weighing risk and reward is a constant tug-of-war in Universus.
Keeping track of where your bad checks are and how plentiful they are, is a key part of improving as a Universus player. As I said earlier, checking poorly is an inevitability in Universus and WILL happen to you. That is why you need to find ways to mitigate this, and plan for the inevitability to the best of your ability! (You can’t spell Inevitability without Ability!) Once you’ve mastered this skill, you will keep your being taken aback from checking a 3 to the bare minimum and not have them totally ruin your game plan.
Thanks for reading and as always, Keep Coping!