To determine how many different ways a player can roll a total of 4 from two dice, we need to find all pairs of numbers $(x, y)$ where each die result $x$ and $y$ is between 1 and 6, and their sum $x + y = 4$.

Let's examine each possibility:

1. $1 + 3 = 4$
2. $2 + 2 = 4$
3. $3 + 1 = 4$

These are the only combinations that result in a sum of 4. Therefore, there are 3 different ways to roll a total of 4 with two dice.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How many ways are there to roll a total of 7 with two dice?
2. What is the probability of rolling a total of 4 with two dice?
3. If a player rolls three dice, how many ways can they roll a total of 4?
4. How many total outcomes are possible with two six-sided dice?
5. How would the answer change if we used a 10-sided die instead?

Tip: When calculating possible sums with dice, list all possible pairs that add up to your target value to avoid missing combinations.