The 11th Company BLOG

I was reading a BLOG post today : http://nike40k.blogspot.com/2011/05/theory-luck-vs-skill-vs-your-mom.html ... And it got me thinking.

The part that interested me was the mental exercise of examining what happens when you take a list that is great against most armies but not so great against a few to a tournament. As expressed in this article, common wisdom would tell us that you will do great in tournaments with only a few rounds, but in tournaments with more rounds, your odds of winning the whole thing should go down.

Let me be a little more clear. Let’s take a win/loss tournament as an example. That means that you win the tournament by winning every game you play. Now, let’s say you take some army that you developed that wins 80% of its games versus most armies, but there are just a few match-ups where you only win 20% of your games. The foil (opposite) of this is the balanced army. The concept here is that you have any army where it has a 50% chance of winning every game it plays.

First and foremost, I don’t believe there is such an army that is so well balanced that it has an even chance against every other list in the game given two equally skilled players. Some people do believe this, but I always believe that any given army has some match-ups where it will excel and some where it will perform less admirably. I definitely do not believe there is such a list that wins more than 50% of its games versus every army. That would mean you have the SUPER list, the best list possible. Why? Logic tells us that if your list performs at above 50% than ALL OTHER LISTS, there is no other list that can be better than it! Gotta love it!

Okay, back on track. Here are the questions I want to examine:

• First, is it better to take a list that performs well against most match-ups but suffers against a few, specific match-ups to a tournament and gamble that you don’t run into your bad match-up?
• Second, is it actually better to take a balanced list that has a 50% chance against any other list and rely on your luck and player skill to carry the day?
• Third, does the answer to the first two questions change depending on how many rounds are in our win/loss tournament?

Now, you know, people don’t publish papers to simply express boring results. I wouldn’t even be writing this if I didn’t think there was something surprising about to happen. Common wisdom tells us that “balanced lists are the way to go!”, but are they really?

Let’s set up a scenario to examine.

First, let’s pretend that I have a list that wins 80% of its games versus 75% of all the lists out there. However, it only wins 20% of its games versus 25% of the remaining lists. This means that if I take this list to a tournament and only run into the 75% of the lists I’m good against, I should rock this thing. However, if I run into one of the 25% of the other lists that kick my butt, I’m in trouble!

Now, let’s pretend that my buddy built a list that functions at a 50/50 versus 100% of all lists.

WHO IS MORE LIKELY TO WIN A 4 ROUND WIN/LOSS TOURNAMENT?

My Buddy has: 0.5 * 0.5 * 0.5 * 0.5 = 6.25% chance to win the whole thing. Assuming all things are equal meaning player skill, luck, etc. Not very good is it? He only has a 50% chance to win each game. And we all know that rolling a 4+ 4 times in a row without failing is pretty darn difficult to do!

Now, let’s look at my list!

First, I have a 32% chance that all 4 of my opponents will have a list that my list kicks butt against. How? Because 0.75 is my chance to get an opponent I’m good against and 0.75 * 0.75 * 0.75 * 0.75 = 0.32 (approximately).

My overall odds of winning the tournament if I get all 4 of my opponents being favorable match-ups is: 41% WOAH! That’s WAY better than my buddy who only had a 6.25% chance! The problem is, I’ve only got a 32% chance of this occurring… a little confusing but follow along!

Carrying on, I have a 42% chance of EXACTLY ONE of my opponents being a bad match-up for me. That’s not good! 42% is more likely than my 32% chance to get all 4 of my opponents being favorable. Surely, if this scenario happens, I’ll have a worse chance of winning the tournament than my buddy?

Actually, your odds of winning this event are: 10%.

SAY WHAT? Even with a bad match-up, I’m still more likely to win the tournament than my buddy with the evenly balanced match-ups. So 32% + 42% or 74% !!!!! of the time, I have better odds of winning than my buddy does.

Okay, what about the dreaded scenario of running into 2 bad match-up? 21% chance of that happening. Turns out, I only have a 2.5% chance of winning. Now, my buddy was better off with his list than I was with mine. However, 74% of the time, or the amount of times you roll hits with a Twin-Linked Lascannon on a Vendetta, I would be better off with my list.

There’s more analysis to take place. For starters, we haven’t answered question #3 yet. I also want to discuss how things change when the numbers change.

Stay tuned for the next article.