# Negative mathematical expectation of options. probability - Math Expected Value? - Mathematics Stack Exchange

Expected Value - Explanation and examples Playing with chances and values What is expected value? Expected value is the probability multiplied by the value of each outcome.

All decisions involve potential tradeoffs and opportunity costs. The question is, how can we make the best possible choices when the factors involved are often so complicated and confusing?

We can use this framework to work out if you should play the lottery. Without using expected value, this is a nearly impossible question to evaluate. This is true of most lotteries in real life, buying a lottery ticket is just an example of our bias towards excessive optimism.

Examples of using expected value It turns out that all events have some aspect of risk and value. Insurance companies use this to determine how much to charge you for your premiums. They add up everyone in your reference classand determine how much it costs them on average in payouts.

They then add a little on the top to make a profit, which makes buying insurance net negative the costs minus the benefits to you on expectation, just like buying a lottery ticket.

Another way to put this is that we have diminishing marginal returns to extra money or concave utility functions, for the mathematically inclined.

Humans all bet with their lives either that God exists or that he does not. Pascal argues that a rational person should live as though God exists and seek to believe in God. If God does actually exist, such a person will have only a finite loss some option levels, luxury, etc.