# Dead of Winter Probability of Avoiding Death

In the board game Dead of Winter, certain actions a player can take result in rolling a 12-sided die. On one face of the die, there's a tooth, representing instant death by zombie. Two faces of the die result in a frostbite wound, and three faces of the die result in a regular wound. Half the time one rolls the die, there is no e ffect. Suppose the game calls for a player to roll the die three times in a row. Assume that if a tooth is rolled, death occurs and no further rolls are made. Assume also that if three wounds of any kind are rolled, death occurs. What is the probability that a player rolling the die three times escapes death?

I tried (11/12)(11/12)(6/12), but I don't think that this accounts for the order of the die. For example, if I rolled a non-wound on the second roll, wouldn't that change my third probability?

• frost bite = regular wound in this exercise ? – marmouset Sep 14 '16 at 13:06

First of all, you must avoid that tooth three times running. The probability of that is $\left(\frac {11}{12}\right)^3$.
Now, let's suppose that you have dodged the tooth. That means that each of your three rolls is one of the other eleven options. Five of these are wounds, though, and you mustn't get three of those. What is the (conditional) probability of getting three of those? Well, it's $\left(\frac {5}{11}\right)^3$. Therefore the conditional probability that you don't get three wounds is $1-\left(\frac {5}{11}\right)^3$.
As you need both things to occur the final answer is $$\left(\frac {11}{12}\right)^3\times\left(1-\left(\frac {5}{11}\right)^3\right)=0.697916667$$