Tuesday, February 23, 2016
Open Maw Settlement Event Probability Analysis
Since our last one was such a hit, me and Jeff decided to take a run at (haha) some quantitative probability analysis of the "Open Maw" settlement event.
Our analysis presents the probabilities for death and success while rolling two dice through nine dice: after nine dice, you're practically guaranteed to lose the survivor.
Jeff computed probabilities for two through six dice and estimated probabilities for seven through nine dice using the Law of Large Numbers, and the high-level result of our analysis is that if you want to live, you definitely do not want to roll more than four dice.
Which is to say that if you do plan to run into the Maw, your best chance to get a decent reward and make it out alive is to cap your dice at four.
At four dice, you're (just barely) under 50% probability of death and you're essentially flipping a coin: if you choose to roll five dice, you're going to lose the survivor 70% of the time.
So stay at or under four dice if you want to live and try not to get distracted by the promise of the Lantern Sword or the Iron Will fighting art, because, statistically speaking, there is almost no chance that you are going to get either of those rewards.
According to Jeff's analysis, your best bet for pulling either of those rewards is to roll five dice, which only gets you a a little bit better than a 6% chance of success at a 70% risk of death.
At six dice, you're slightly more likely to get the sword or the fighting art and almost 15% more likely to die.
And I don't care how risk averse you are or aren't: six dice get you a 15% chance of success with an 85% chance of death, which is basically a guaranteed -1 population.
Finally, if you're interested in what your odds are over recurring Open Maw events--i.e. how your odds improve if you pull the event card multiple times--you can check out this breakdown for four, five and six dice that Jeff put together.
 The summary of the detailed breakdowns is this: if you plan to run into the Maw every time the card comes up, you should roll six dice when you do. You're likely to lose a lot of survivors, but after pulling the card about 11 times, you're statistically likely to get a Lantern Sword or the Iron Will fighting art.[/edit]