This next post is from a study done by Kahneman, D., & Tversky, A. (1979). It is an amazing study that looked at why people make risky decisions. The found out that people make decisions based on losses and gains as opposed to the probability of those losses or gains. An example:
"Imagine your country is preparing for the outbreak of a disease expected to kill 600 people. If program A is adopted, exactly 200 people will be saved. If program B is adopted there is a 1/3 probability that 600 people will be saved and a 2/3 probability that no people will be saved."
In this example more people chose option A (72%) because the example is presented in gains. The same example just presented in terms of loss:
"Imagine your country is preparing for the outbreak of a disease expected to kill 600 people. If program A is adopted, exactly 400 people will die. If program B is adopted there is a 1/3 probability that no one will die and a 2/3 probability that 600 people will die."
Here more people chose option B (78%).
So from the examples we learn that people don't really care about the odds but are more concerned with how it is worded or in other words what are they going to lose.
When writing our stories we need to see how we are presenting ultimatums. Are we looking at them from the perspective of odds or from gains and losses. The character is more likely going to make the choice depending on how it is presented rather than the odds of success or failure.