Let's explore how to figure out a goal's value. So, here's our first choice. We can aim for drawing the triangle or the square, and both give three points.
There are three cards to draw from, one triangle, two squares. Since there's a higher probability of choosing the square, then the square is a more valuable reward. Here's a different deck. We can either try to draw a circle for three points or a square for four points. Since there is only one of each shape in the deck, there's an equal probability of 1/4 for drawing either.
Since the probability is the same, the goal with the higher reward is more valuable. In this next deck, the first goal is to draw a card with a value of two or more for four points. The second goal is to draw a star for three points.
There are three cards with a value of two or more and two cards with stars.
So, there's a higher probability of drawing a card that is greater than or equal to two. This goal also has a higher reward, so it's more valuable.
When choosing a goal, we have to consider both the reward and the likelihood of getting it. When the probability is equal, the bigger reward is always the better choice. Let's try another. We can get a circle for three points or a card with a value of four for four points. For the first goal, there are two circles, which gives us two out of four, or a probability of 1/2. For the second goal, there are two cards with a value of four, which also gives a probability of 1/2. Since the probabilities are equal, the goal with the larger reward is more valuable.
This last one is a bit different. The first goal is a triangle for five points. The second goal is a circle for four points. The probability of drawing a triangle is 1 out of four, while the probability of drawing a circle is three out of four. 3/4s is a much higher probability. So on average, you're much more likely to draw a circle. So even though the reward is slightly smaller, it's a more valuable reward.
A much higher likelihood can make up for a smaller reward because you're more likely to win.
