Avni designs a game in which a player either wins or loses 4 points during each turn. Which equation represents all numbers of points, p, a player may have after his or her first turn of the game?

In Avni's game, a player either wins or loses 4 points during each turn. Let's denote the initial number of points a player has before the first turn as \( p_0 \).

After the first turn, the player will have either:

1. \( p_0 + 4 \) points if they win 4 points.
2. \( p_0 - 4 \) points if they lose 4 points.

Thus, the equation representing the possible points \( p \) after the first turn is:

\[
p = p_0 \pm 4
\]

However, since we are considering the outcome after the first turn and assuming \( p_0 = 0 \) (starting with zero points), the possible points a player may have can be represented by:

\[
p = \pm 4
\]

In other words, after the first turn, the player can have either 4 or -4 points.

Would you like further details, or do you have any questions?

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Here are some related questions:

1. How would the equation change if the player could win or lose different amounts of points?
2. What is the equation if the player takes two turns?
3. What is the probability of a player having 4 points after the first turn?
4. How does the point total evolve if the game has more than one turn?
5. Can the player’s score ever be zero after the first turn?

**Tip:** When dealing with absolute value in problems, remember that \( \pm \) represents both the positive and negative outcomes of an operation.

Explore how points are calculated in Avni's game where players either win or lose 4 points per turn. Learn the equation representing possible points after the first turn and scenarios involving point changes.

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