TaKtiX: Warlord CCG guest column

Guest and occasional columnists for the Warlord CCG

Wednesday, May 17, 2006

Lady Luck is a Moody Wench

I am known, in some circles, as a devilishly "lucky" player. While I have witnessed friends ritualistically bless their dice with their own blood in order to bring the luck factor under control, a few basic insights into the way that probability works might suggest more practical ways of coping (and give my opponents some insights into why I seem to be so damn lucky all the time).

Let us begin with a simple idea: Lady Luck is highly susceptible to mood swings. Aside from tasteless stereotyping, what exactly do I mean by that?

Well, say you flip a coin six times. Of the three possible outcomes below, which is more probable?

  1. H T H T H T
  2. T T T T T T
  3. H H H T T T

If you answered "1," you're wrong. If you answered "2," you're also wrong. And "3"? Nope, that's not the correct answer, either.

All outcomes are equally likely.

To see why, let's simplify things a bit. Say you flip a coin twice. There are four possible outcomes:

  1. H T
  2. T H
  3. H H
  4. T T

Each of the four outcomes is equally likely. You'll note that two of them contain one heads and one tails. You've got a better chance of getting a mix of heads and tails than straight heads or straight tails. But no specific sequence of flips is more likely than any other.

I won't waste your time writing out all 64 possible unique combinations of the six flips we started with. But note that there are only two possible outcomes of those 64 that contain strictly alternating heads and tails:

  1. H T H T H T
  2. T H T H T H

All the rest of the combinations contain at least two heads or two tails in a row. Lots of them contain more than that. This means that, most of the time, when you go to flip a coin, you'll see runs of heads or tails.

If we replace "heads" with "a roll of 11 or better" and "tails" with "a roll of 10 or less," you begin to see that you should expect runs of "good" rolls or "bad" rolls over the course of any Warlord game. Unfortunately, since any particular sequence of rolls is just as likely as any other, it's impossible to predict how long the runs will be or when they will occur.

What this means is that you're going to have to build a deck that can deal with runs of bad luck. I don't mean that you should have a contingency plan for the occasional statistical anomaly. I mean that you have to realize that, while you might get about an even number of bad and good rolls over the course of the tourney, they're going to come in fits and starts and runs, and your deck is going to have to be able to suck it up and win anyway, even if you have those first turns where you can't hit anything, and your opponent makes every strike.

In other words, don't plan for the "ideal" situation -- where you're expecting a neat little row of alternating good and bad rolls. I see a lot of people make this mistake; their decks generally fall apart come tourney time. Instead, prepare for the more likely situation, which is that you're sometimes going to roll 3 20s in a row, and other times not be able to roll above a 4 to save you life.

You already know some of the ways to cope: big bonuses to the roll, making as many strikes as possible, using cards to fix the roll to a pre-determined result.

More import than that is to keep in the fore of your mind the knowledge that this is how probability works . Don't get flustered by it. I see far too many players psych themselves out and lose a game because of a few bad rolls.

If you just rolled the 3rd 4 in a row, realize that the Good Lady is just a bit grumpy at the moment. Instead of throwing dice, cards, and/or sharp objects, keep a cool head and play through it. Her mood could change at any moment, and you need to have the presence of mind to see it and take advantage of it when the rolls start going your way again.

~ PeteVG
Rogue Elf


At 6:41 pm, Anonymous Marius Lemm (Dwarven Srike Force) said...

Not trying to be a douchebag, seriously not^^, but getting three heads (H) with six throws (and not caring for a certain order) is a lot more probable than getting 6 H / 6 T. It is truly not about a strict alternation, but a general balance of die rolls. And this balance does occur, specific orders of results are normally ignored in statistics and should be to (practically) in Warlord. It doesn't matter which of your four strikes kills the opponent if he can't stop you from attacking anyway.

That being said, I still agree to what you basically said. Often players tend to get worked up too much about bad die rolls that they make mistakes when their chance comes back. Nice writing style!

At 9:40 pm, Anonymous Rod(Puzzlehunter) said...

I'v tried ot get this across to many people, but never have I seen it said so eloquently. This is a great article that any warlord player should read.

@marius, he never said anythign against balance and there is no guarantee of balance just you will "probably" have more balanced results the more dice you roll if you measure balanced by an equal number of high and low rolls.

You will also have more extreme patterns the more dice you roll. Since the unusual has a better chance of occurring.


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