If I presented with an optional task for which I have an outcome independent investment $I$, a probability of success $P$ and a reward for success $R$, then I chose to undertake this task iff $PR > I$.
If I presented with an optional task for which I have an outcome independent investment $I$, a probability of success $P$, a reward for success $R$ and a cost of failure $C$, then I chose to undertake this task iff $PR - (1-P)C > I$.
What if the undertaking of this task has a risk of death? How does one begin to determine the cost? Is the cost of death infinite?
In a situation where there is a one in a million chance of death and a fifty fifty chance of getting £10,000,000, I don't know many people who wouldn't give that a go, but that would imply that the cost of death is finite or no mathematician would ever undertake the task.
I suspect the answer is that the problem required context. Let us suppose you leave the handbrake off the car and it rolls down a steep cliff. In this car is a big sack of lovely cash which you were taking the bank. The tide below is rising and you are certain that you have no time to get help so you are faced with the decision as to whether or not you should attempt to climb down to retrieve the cash. There is a chance you could fail (and lose the money) and there is a chance you could die.
How would you quantify death in context?