The Intersection of Meta and ‘Winning’

 

The Warmachine and Hordes meta-game is a living breathing entity.  Players try to out-think, out-plan and out-bamboozle one another by creating lists designed to fair best in their current Meta.  This article is going to give you a description of one piece, its probability of effect and how that probability interacts with your view on the current local Meta.

The piece in question is Anastasia Di Bray and the power is Intelligence.  Intelligence gives you +1 to your starting roll to determine the order of deployment and play.  There are a few other ways to increase your starting roll including multiple theme forces.  For brevity’s sake, I’m talking about those too.  In a game where jam lists are rushing to occupy zones the term “roll to win” has been coined more often then I can count.  Let’s take a look at what the actual probability of “winning” initiative (a la Charlie Sheen) is.

Player 1 (w/ Anastasia Di Bray) rolls one die with outcomes 2-7.  Player 2 (w/o Anastasia Di Bray) rolls a die with outcomes 1-6.  There are 36 combinations of rolls between the two players with the following results.  Player 1 will win 58.3%, Tie 13.9% and Lose 27.8% of the time.  The tie will lead to a re-roll with the same statistics.  If you chase this pattern to its end, the net result of having the benefit of Anastasia over your opponent means that you’ll win the initiative roll 67.7% of the time.  For players that REALLY want the edge, the additional 17.7% can make a difference.

Now, don’t go putting Anastasia into all of your lists at once.  As a reminder, if your opponent ALSO has Anastasia in their list the odds of winning the initiative roll are back to 50/50.  Fortunately, there are a few factors mitigating this effect.  First off, she’s a character and can be restricted.  Secondly, she only works for Cygnar and Protectorate.  Those two factors alone will reduce your chance of seeing her pretty significantly.  Neither of these comments hold true when you’re talking about theme lists, but their appearance in competitive play is touch and go as well.

I’m not one to leave you hanging with half of an answer so I’ll show you how to balance what you know about Anastasia (17.7% incremental benefit) with your perception on the Meta.  You’re going to have to calculate a few intersection probabilities.  Let’s take a look at this nice little probability tree.

 

Figuring out your total win rate lies in calculating what happens in each of the states of the world and then totaling the ones in which you win.  Here there are four potential outcomes.  One in which your opponent ALSO has Anastasia in which you win (#1) or lose (#2) and one in which your opponent DOES NOT have Anastasia in which you win (#3) or lose (#4).  The total win rate is the added percentages of #1 and #3.

 

Now let’s run the numbers.  Let’s say you live with a Meta that values this +1 to start roll INTENSELY.  You think that roughly 30% of the lists you’ll face have her in it.  The probability of you winning the initiative roll with Anastasia is STILL 62%!  Even while encountering her (or something like her) in 3 of every 10 lists you’re still getting a 12% benefit on your initiative roll.

 

Anastasia is a great model and having +1 to roll is a phenomenal choice depending on your list strategy.  From here on out you’ll be able to balance this power with your perception on your local Meta to get a more accurate picture of what it will do for you.  Viewing the scenario this way gets easier over time and this same algorithm can be applied when weighing similar choices during list creation and in-game assassination planning.  To make things even easier I calculated a few other sample perception/effect combos.  Enjoy!

 

Odds Opponent Odds of
Will Also Have Winning
+1 Effect Roll
0% 67.7%
5% 66.9%
10% 66.0%
30% 62.4%
50% 58.9%
60% 57.1%
80% 53.5%
100% 50.0%

 

Author: Tmage

I'm a gaming and math enthusiast. I find games that balance strategic interaction with economic principles (delayed option, resource control, etc.) are some of the most rewarding for me as a player. I concentrated in Finance, Analytic Consulting, Decision Sciences and Management Strategy while getting my MBA at Kellogg (Northwestern University) and majored in Chemical Engineering during my undergrad at University of Illinois. I view gaming through this lens and share my perspective via periodic articles. Thanks for reading!

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