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 Features
Statistically Speaking, It's Probably a Good Game, Part 1: Probability for Game Designers
 Quiz Show Redux
If you’ve read this far, then we’re both exhausted. Hopefully, though, we have also developed a nice golden-brown brain tan. So let’s revisit the questions from the beginning of this article.
Q1) Orc Nostril Hair Drop Rates
It’s too early to panic. Never panic unless you are sure you should panic. If you are sure you should panic, then panic, and panic well.
In this case, both testers’ results are certainly within the realm of probability. If there is a base 10% chance of finding the Orc Nostril Hair (ONH) on each monster-slaying, then the chances of finding at least 4 ONH in 20 tries is 13.3% Where did I get that number, you might ask? Well, I cheated and used an advanced concept called Binomial Distribution, but sadly (or happily?) it is beyond the scope of this article.
The chance of finding zero ONH at all through 20 tries is determined through converse probability:
10% chance of finding item on each kill means 90% chance of not finding it (0.90).
Chance of not finding it through 20 kills = (.90)^20 = 12.2%
So there is about the same chance of finding 4 ONH in 20 tries (13.3%) as there is finding zero ONH in 20 tries (12.2%). Not yet cause for justified panic.
To really determine if you should panic, you need more info. You need lots of data points from your testers in order to draw an informed, statistically-based conclusion (OK, I’m jumping ahead to part 2. Indulge me.)
Let’s say you collect info on 100 play sessions, each of which involve 100 kills. That’s a respectable amount of data. If out of those sessions, players are finding ONH a lot less or a lot more than 10% of the time, then you probably have a bug that is affecting your reward rates. In that case, panic with all haste! Tip: Sprinting around the office screaming “No!” generally gets quick results.
Q2) 2x-3x-4x+ Critical Hits
The chances of doing at least 2x damage are found by the conditional probability of hitting twice in a row:
Chance of 2x or better = 0.75 x 0.75 = 56.3%
Chance of 4x or better = (0.75)^4 = 31.6%
Wow. Players will do 4x or better damage almost 1/3 of the time. Fix your system, dude/dudette! Either drop the base hit percentage or make the successive critical levels harder to achieve.
Q3) Will Flip Coins for Money
This question is a silly trap, not-so-elaborately laid. First you give the player help by showing them the last 20 flips, then you need to shore-up your system to present exploits. Sheesh!
The answer, of course, is that providing the player with this 20-flip history changes nothing about the fact that each coin flip is a 50/50 proposition****. Let the player wreck himself with the Gambler’s Fallacy.
Heck, I even recommend paying out less than even money every time a player bets “heads” after 2 successive “tails” results. Just tell ‘em you are adjusting to their unfair advantage of knowing “heads” is due. They’ll believe you, they will...
****Natch, discounting any flaws in your random number generator that simulates the coin flip.
What are the Chances that this Article was Interesting?
I may be a gambling man, but I won’t dare to give odds on that.
If you survived the last few thousand words or even enjoyed them, stay tuned. In Part 2, we’ll explore the “Two-Drink Minimum” science of Statistics. And finally, in Part 3 (the riveting conclusion), we’ll look at the anatomy of a number system and explore how your choices as a game designer can sculpt a game’s mechanics into a true work of art. No, really!
Recommended Reading:
Peter Webb’s “Layman’s Guide to Probability”:
http://www.peterwebb.co.uk/probability.htm
The Wizard of Odds (lots of great gambling prob calcs):
http://www.wizardofodds.com
Brian Alspach’s Poker Computations:
http://www.math.sfu.ca/~alspach/computations.html
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