# Comparing Game Strategies Using Expected Values: Process & Examples

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• 0:01 Games and Expected Values
• 0:56 The Process
• 1:43 Betting for a Card
• 3:08 Insurance Rates
• 4:01 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

While statistics and probability leave a lot to chance, we can use expected values to help inform our decisions. This lesson shows us how to use expected values to make the best determinations possible.

## Games and Expected Values

If you've been studying statistics and probability for a while, you probably feel that, to some degree, these can be shots in the dark. After all, you can roll a die, but you know it's going to have one of six options. As long as you don't bet on number 7 to come up, you should be okay.

However, that doesn't mean that statistics is utterly useless when it comes to trying to predict events that may not obviously have a link to math. In fact, there is a whole field of analysis called game theory that is based on using math to help guide logical decision-making. In this lesson, we're going to look at how to use game theory to inform various strategies by using expected values. Expected values are exactly what they sound like - they are the results that we can anticipate having when a particular event takes place. Afterwards, we'll look at two very different examples to see this all in practice.

## The Process

First things first - if we're going to use expected values to see what the best course of action is in a particular game, we first have to define the game. Earlier, I joked about rolling a six-sided die and hoping for a seven, but the fact is that it is vital for us to know that our die indeed only has six sides. From there, we have to establish our expected values. We know that if we roll a die, it has a 1 in 6 chance of returning any given side. Therefore, those are our expected values. With this information in hand, we can frame the situation so that we can take in all of our options. This means we have to think them through, but as you'll see in these examples, that isn't as complex as it is often made out to be.

## Betting for a Card

If you're ever in Vegas and want the highest chance of beating the casino, blackjack is the way to go. This is because the casino has to rely on the same numbers you have in order to win. In case you're not familiar with the rules, the goal is to get as close to 21 without going over. An ace counts as either one or 11, while all face cards count as 10.

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