Warhammer Underworlds - Analysis Series - Objective Card Draw
Objective Card Draw Analysis in Warhammer Underworlds
Probability, Mulligans and Opening Hands
In Warhammer Underworlds, games are won by scoring glory. Some of this comes from Bounty, gained by taking enemy fighters out of action, however the majority typically comes from Objective cards.
Objective cards come in two forms: Surges and End Phase cards.
Surge cards can be scored immediately at various points throughout the game, depending on the condition and scoring window described on the card. Importantly, these can be scored outside of the End Phase, allowing for more immediate scoring, which helps to get the glory train rolling during a round. Early glory, then allows you to start upgrading fighters, which helps with scoring more glory, leading to a snowballing effect. Scoring surges early helps you make a Strong Start.
End Phase cards, as the name suggests, can only be scored during the End Phase.
Therefore, having access to surges early is important, to allow for rapid scoring and a strong start to the game. You ideally want at least two surges, if not three, in your opening hand of three Objective cards.
The Probability Problem
I was recently shown a probability puzzle involving a ball hidden under one of three cups. You pick a cup, and then the person running the game reveals one of the other cups that definitely does not contain the ball. You are then given the option to switch your choice.
The correct play is to always switch.
This is the classic Monty Hall problem. While it feels counterintuitive at first, the reasoning is fairly straightforward. Your initial choice has a 1 in 3 chance of being correct (~33%), while the other two cups together have a 2 in 3 chance. When one of those losing cups is removed, that probability effectively transfers to the remaining cup, providing you with a 50% chance of being correct.
It got me thinking about whether this idea applies to Warhammer Underworlds, particularly when it comes to drawing an opening hand and deciding whether to mulligan; leading me write this article.
The Baseline: 12 Cards
In Warhammer Underworlds, the minimum Objective deck size is twelve cards made up of a maximum of six surges and, therefore, at least six End Phase cards. At the start of the game, you draw your opening hand of three cards, the aim is to have at least one, if not two surges.
Here are the assumptions:
- Objective deck: 12 cards
- 6 surges, 6 end phase
- Opening hand: 3 cards
- Goal: at least 2 surges
- Mulligan: discard all 3 and draw 3 new cards (without reshuffling)
On the initial draw, the chance of finding at least 2 surges is 50%.
This probability initially feels wrong but hang on a minute. In a twelve-card deck, with 6 surges and 6 End Phase cards you are as equally likely to draw a surge as an End phase card because the deck is stack 50:50 (6:6).
The Mulligan Decision
Once you’ve seen your opening hand, the basic decision is straightforward:
- 2 or 3 surges → keep
- 0 or 1 surge → mulligan
Of course, this simplified decision does not take into account the individual scoring conditions of the cards you have in hand. As such, you need to make a choice on whether you want to mulligan or not. Here, I am just looking at the maths, and the mulligan is particularly strong in this setup.
- If your initial hand has 0 surges, you are removing three end phase cards, making the remaining deck heavily weighted toward surges. Your redraw is ~77% likely to have two or more surges.
- If your initial hand has 1 surge, the deck becomes slightly surge-favoured. Your redraw is ~60% likely to have two or more surges.
In both cases, the mulligan improves your odds of reaching the two plus surge target.
A Further Consideration
If your opening hand, either before or after the mulligan, contains 2 or more surges, those cards are likely to be scored early and replaced by new cards from your Objective deck.
As a result, you are removing surges from your deck at the start of the game. This, effectively, stacks your deck with End phase cards, as you approach the End phase, helping to improve the flow of your deck. Early surge scoring can lead to more reliable End Phase scoring.
Example:
If I start the game with twelve cards, six surges and six end phase cards. I draw three cards, either initially or through the mulligan, and end up with two surges and one End phase in hand. I then score one of the surges, what is the chance the next card drawn is an End phase card?
The Objective deck is now made up of nine cards, five of which are End phase cards, therefore, the chance the next card is an End phase is 5/9 = ~56%
If I then draw an End phase card, upon scoring the next surge in my hand, the chance the next card drawn is an End phase is drawn drops to 50% = 4/8.
If I then pull another End Phase card, the next card is more likely to be a surge, just in time to head into the second round of the game.
What does this mean?
By aiming to increase the number of surges in your opening hand, you are increasing the probability of drawing Objective cards in their correct scoring windows.
Expanding to 13 Cards
For many months, if not years, I often take thirteen cards in my Objective decks, as I am trying to raise the Glory ceiling. How does this change the probability of the draw and is this the correct idea?
If you increase the deck size to 13 cards:
- 6 surges, 7 end phase
Your chance of drawing 2 or more surges on the first draw drops to around 44%, because the initial deck is no longer equally split between surge and End Phase cards.
The mulligan still helps:
- From a 1 surge hand, your redraw becomes a 50% chance of drawing two of more surges, as the deck is once again split 50:50 between surge and End phase cards.
- From 0 surges, your redraw becomes a ~67% (two-thirds) or drawing two or more surges.
However, compared to the 12-card version, both your initial deck consistency and the 'strength' of your mulligan are slightly reduced, which can result in the deck flowing less smoothly. Here you have to consider if the increased Glory ceiling is worth potentially disrupting your Objective decks flow.
Why This Isn’t the Monty Hall Problem
Although this initially feels similar to the Monty Hall problem, it behaves quite differently once you look more closely at what is actually happening.
In the Monty Hall problem, the key detail is that the person running the game knows where the winning option is and deliberately removes a losing choice. That is what causes the probability to shift. You begin with a one in three chance of being correct, while the other two options together account for two thirds of the probability. When one of those losing options is removed, that full two thirds effectively transfers to the remaining choice. This is why switching is always the correct decision.
In Warhammer Underworlds, nothing like that is taking place. When you draw your opening hand, you are not being shown a safe outcome or guided away from a bad one. You are simply drawing cards at random. When you choose to mulligan, you are not acting on carefully revealed information, but instead discarding three random cards and drawing again from what remains.
That difference matters. In the Monty Hall problem, the information you are given is meaningful and changes the probabilities in a very specific way. In Underworlds, the information you gain is partial and entirely random. You learn something about your deck, but not in a way that guarantees a better outcome.
A better way to think about the mulligan is as sampling without replacement. Your first hand gives you some indication of what is left in the deck. If you draw poorly, you have likely removed some of the less useful cards, which improves your chances slightly on the redraw. However, this improvement depends entirely on what you happened to draw in the first place.
This is why there is no equivalent to “always mulligan” here. The correct decision depends on the hand you have in front of you. If you already have what you need, there is no reason to change it. If you do not, the mulligan gives you another chance, but it is still just that, a chance, not a certainty.
Searching for Specific Cards
Another way of looking at the opening draw is not in terms of surges vs end phase cards, but in terms of finding a specific card.
Recently, I played a tournament using a deck pairing built around Countdown to Cataclysm. In those games, I found that I really wanted to see Wreckers in my opening hand.
This raises a slightly different question. If I don’t draw that card in my initial three, what are my chances of finding it on the mulligan?
One Specific Card
What is the maths behind find a particular card in a deck:
12-card deck
-
Chance of drawing it in your opening 3:
3/12 = 25% - If you miss, there are 9 cards left, and the card is still in the deck
-
Chance of drawing it in the mulligan:
3/9 = 33%
13-card deck
-
Chance of drawing it in your opening 3:
3/13 ≈ 23% - If you miss, there are 10 cards left
-
Chance of drawing it in the mulligan:
3/10 = 30%
So, in both cases, if you fail to find the card initially, your chances actually improve slightly on the mulligan. However, the chance of finding a particular card is low, and not something you should be relying upon in a tournament this will make your deck unreliable.
Two Target Cards
If instead you are looking for one of two cards (for example Wreckers or Collateral Damage), the numbers improve further.
12-card deck
-
Chance of finding at least one in your opening hand:
About 45% - If you miss both, there are still 2 targets in 9 cards
-
Chance of finding at least one in the mulligan is ~ 58%
13-card deck
-
Chance of finding at least one in your opening hand:
About 42% - If you miss both, there are 2 targets in 10 cards
-
Chance of finding at least one in the mulligan ~ 53%
Closing Thoughts
Looking at the mulligan from both angles, drawing the right type of card and finding a specific card, the same principle keeps coming up. If your opening hand doesn’t give you what you need, the mulligan improves your chances of getting there. It’s not perfect, and it’s certainly not guaranteed, but it consistently nudges the odds in your favour.
This becomes even more relevant when you think about deck construction. Even when searching for one of two key cards, the probability of finding them early is still relatively low. That naturally pushes you towards building decks where most cards are useful at most points in the game. The more flexible your objectives are, the less likely your deck is to stall. By contrast, decks that rely on drawing a specific card at a specific time carry a real risk of “bricking,” stopping your glory train before it ever really gets going.
Starting from the minimum 12-card deck makes these interactions clearer. You have a clean 50:50 chance of hitting your target, and the mulligan meaningfully improves your position when you miss. Expanding to 13 cards lowers that consistency slightly, but the overall approach remains the same. You are trading a bit of reliability for a higher potential ceiling.
What all of this really highlights is that Warhammer Underworlds is full of small probability edges. The decision to mulligan, the balance of Surges and End Phase cards, and the way your deck evolves as you score early objectives all contribute to how smoothly your game plays out.
None of this guarantees success. But over the course of a game, or a tournament, these small advantages add up. More often than not, small advantages turn a good deck into a reliable one.
I’d love to hear what you think. Does this match your experience on the table? D you use 12 or 13 Objective Cards? What do you think should be my next topic of analysis?
Checkout my Warhammer Underworlds for more articles.
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