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Unpainted Minis: The Brick

Unpainted Minis: The Brick


There are very few things more frustrating in a game of Shadespire than drawing up a hand of Objectives that you can't score: a "brick".  Recently, friend of the site Tom Denyer asked about the chances of bricking your hand while playing Combination Strike and Opening Gambit.


Prior to the 6-surge restriction, a lot of our decks here were running what we called "Trinity" objective decks: Combination Strike, Victory after Victory, Superior Tactics and 8-9 surge objectives.   Bricking was very rarely a problem at these ratios.  However, now that you're down to 6 surges, it can crop up more often.  Just how often you ask?  Let's find out.

To start with, we'll be using hypergeometric distributions to determine card draw odds, along with some very light combinatorics.  Without going pretty deep into the latter, we won't be able to examine much after the first objective hand draw - but that's the one where bricking really hurts you the worst.


Before we go to far, let's define what we mean by bricking here: a hand where you draw Combo Strike, Opening Gambit, or both; and your other cards aren't surge Objectives.  In this case, you won't score anything during the action phase, and you won't score OG/CS in the end phase.  That's bad.

If you're running both CS and OG, you've still got a 55% chance that you won't draw either one, so you definitely won't Opening-Combo-Brick (OCB) on the first turn there.  Good.  Only 5% of games will see you start with both OG and CS in hand, with the remaining 40% being games where you have one or the other.  To reiterate: 55% of the time you can't OCB.  That's a pretty good start to our analysis.  The remaining calculations on this subject will all relate to this core percentage; what follows will largely be talking about the 45% of games where you draw one or both of CS and/or OG.



The good news is, on those hands where you can OCB, you're not terribly likely to.  In the 5% of games where you'll start with both CS and OG in hand, you've got a 60/40 chance that the other card in hand is a surge Objective, and you've got a chance to roll through and score some stuff.  If you've only drawn one of the two, you've got a 55% chance that you'll have 1 surge objective and a 27% chance that both of your other cards are surges.  So overall, we're looking at something like this:
  • 55% - No OCB possible
  • 22% - Draw OG or CS and 1 surge objective
  • 11% - Draw OG or CS and 2 surge objectives
  • 3% - Draw OG and CS and 1 surge objective
That means you've got a ninety-one percent chance of not getting OCB in the first draw.

 
As a bonus, of the 9% of games where you do OCB, the vast majority (7%) will be games where you OCB by only drawing CS or OG, but not both.  So you can safely use a do-over without losing too much of the surge-steam that powers your deck.  Even when you do brick, it's likely not as bad as it seems!




If you don't  draw either Combo Strike or Opening Gambit in your first hand, you've still got a shot of scoring them in the first round.  In 97% of those games you'll be holding at least 1 surge objective, giving you a chance to draw into one of your point multipliers.  Overall for the 55% of games that you don't draw CS or OG, you're chances of drawing into one look like this (assuming you can score all the surge objectives you have, which you should be able to do):
  • 6% - Have 1 surge, draw into CS or OG
  • 19% - Have 2 surge, draw into CS or OG
  • 1.5% - Have 2 surge, draw into CS and OG
  • 8.5% - Have 3 surge, draw into CS or OG
  • 0.1% - Have 3 surge, draw into CS and OG
So you've got a slightly more than 1/3 chance of picking up Combo Strike or Opening Gambit later on in the round.  The above percentages are actually a little bit low, since they don't account for drawing into more surge objectives, which then draw you into CS/OG, but that gets a bit long in both the probability department and the math-work-we-have-to-do department, so we're going to be satisfied with these.

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