# Why is probability used to make decisions?

If I am offered two bets to choose one from, and either wins \$100 or losses \$100, I would want to know the chances of winning in order to decide which one to pick. For example, if one bet has a 90% chance of winning, and the other has a 30% chance of winning, I will pick the 90% one

Question: why is the bet with the higher probability "better"? Assuming that I very much want to win the \$100.

Attempt: this makes sense from a Bayesian point of view. 90% is my confidence or belief that I will win \$100. Therefore, I will pick the bet that I am more confident or has higher belief in.

However, this makes no sense using the frequentist framework since 90% chance of winning is interpreted as the proportion of wins if I repeat the bet a "large" or infinite number of times. Since I am only doing this once, what is the reason to choose the one with the higher chance?

• a) just shut up and calculate? b) imagine the problem is about two guns with the probability reflected by the number of chambers loaded with a bullet. now the reason is simply your wish to remain alive. c) probability is label on the sign by the entrance to a bottomless rabbit hole. – nir Apr 16 '16 at 20:27
• d) evolution? imagine two species of lemmings — one wired in such a way that individuals of the species tend to make choices that are likely to keep them alive while the other species is wired in such a way that individuals tend to make choices that lead to certain death. – nir Apr 16 '16 at 20:41
• I find your example to be question begging: you've characterized the games in terms of "chance of winning", then ask "why are probabilities related to my goal (of winning \$100)?". They are related because that is the way you've framed the question. – Dave Apr 18 '16 at 20:26