Sunday, April 14, 2013

Updated: Doing the Math

That is why you fail. - Yoda

Prior to the premier of the midseason return of Doctor Who, we broke out a game of Star Wars miniatures. I'd never played the game before and it looks a bit like Warhammer 30k. There is board for the game, just use any flat surface as the cold emptiness of space and then your ships fly around using various move guides (aka rulers).As a pretty standard combat system you have attack dice and defense dice, each side rolls, and then the result is attacks - defense. The pilots have skills like "focus," "target lock," and "dodge" that allow you to do various things with your roll. As my Darth Vader was zooming in on the Millenium Falcon I asked the obvious question, "is it better for Vader to focus or target lock to maximize damage." The owner of the game replied, "I feel like I've had better luck with focus." Not the answer I was looking for. "It's a simple probability analysis. One will be statistically better. Have you done the math?" "I have not." Wait. What?!? Isn't this how you play strategy war games? You do the math about attack, defense and causality rates. That's how you judge what to do.So when the game was over, while we were watching Doctor Who, I did the math!The idea with focus is if the "focus" comes up on the roll, you can convert it to a hit or a to a miss. If you choose to Target Lock or to Dodge, you can re-roll any of the dice you want. If you choose dodge you get one dodge for free.

Sides of the Attack Die: 2 Misses, 2 Focus, 3 Hit, 1 Critical Hit

  • Normal Unmodified Hit: 4/8 = 50%
  • Normal Unmodified Critical: 1/8 = 12.5%
  • Focused Hit: 4/8 + 2/8 = 75%
  • Focused Critical: 1/8 = 12.5%
  • Target Lock Hit: 4/8 + (4/8 * 4/8) = 75%
  • Target Lock Critical: 1/8 + (4/8 * 1/8) = 18.75%

Attack Conclusion: Focus and Target Lock give the precisely the same change of damage. Doing a target lock slightly increases the chances you can score a critical.

Sides of the Defense Die: 3 Misses, 2 Focus, 3 Dodge

  • Normal Defense: 3/8 = 37.5%
  • Focused Defense: 3/8 + 2/8 = 62.5%
  • Dodge Defense: 3/8 + (5/8 * 3/8) = 60.9375%

Dodge Conclusion: Focus gives an advantage over Dodge. If you have Focus available, you should always focus.

I misunderstood the rules of dodge. Need to redo the math. What dodge actually does is give you an extra dodge. The math is a little trickier.

  • d Dice - Normal Defense: 3/8 x d
  • d Dice - Focused Defense: (3/8 + 2/8) x d
  • d Dice - Dodge Defense: 3/8 x d + 1

So the question is - how many dice before it makes sense to focus instead of dodge? When will: (3/8 + 2/8) x d > 3/8 x d + 1? The answer? When d > 4.

Roll Type1 Die2 Dice3 Dice4 Dice5 Dice
Normal Defense0.350.751.1251.51.875
Focused Defense0.6251.251.8752.53.125
Dodge Defense1.3751.752.1252.52.125

Updated Dodge Conclusion: If you have fewer than four defense dice, dodging does giving an advantage over focus. Focus doesn't give you an advantage until you are rolling over four defense dice.

Strategic Conclusion: Always Focus. I suppose under rare occasion the addition 6.25% of critical hit might be enough you want to Target Lock - but it really seems like Focus is the way to go. Because after you attack, you can choose not to use focus and save it for your dodge. So if you roll a good attack, save your focus for defense.

Focus seems to be an obvious choice over target lock. But from a dodge perspective it does make sense to dodge over focus. So play on and may the Force be with you.

That is how you play Star Wars Minatures.