Is there a mathematical scenario in the game of snooker where deducting points from Player A instead of adding points to Player B would change result?

Question

Context

During a game of snooker I was playing in, I committed a foul resulting in 4 points being added to my opponents score. However, the friendly but inexperienced scorekeeper deducted 4 points from my own score.

This led to an unresolved discussion about whether the addition or deduction of points could lead to a different mathematical result in the game.

Quick overview of Snooker

Snooker is a game played on a table with different coloured balls akin to pool but with more complexity. Players take turns attempting to pot a red ball (1 point) which then allows them to take an immediate second shot on a coloured ball that is not-red. the red ball is not replaced and the total can only diminish. The colours available are yellow (2), green (3), brown (4), blue (5), pink (6), black (7). If a coloured ball is successfully potted, the coloured ball is replaced and the player may take another shot on a remaining red ball, repeating the pattern until they miss or all balls are potted.

The total score available to a single player (without being gifted foul points) is 147 points.

If a player fouls then their opponent is given the points depending on the nature of the foul (never less than four points but up to seven points).

A snooker game can not result in a tie. The game will continue until a winner is declared.

Recap and Summary

This question centres on the argument that points deducted from the fouling player would result in no different game outcome than points added to the non-fouling player instead.

Answer 1

The difference between the scores of the two players will stay the same.

This means in particular that if player $A$ has more points than player $B$ in the scenario where points are added to the score of $B$, then player $A$ will also have more points than player $B$ in the scenario where points are subtracted from player $A$.

In short: The game would have the same result.

However, subtracting points might lead to negative scores: If a player makes a lot of fouls, and the judge keeps subtracting points, the score can become negative. If in this scenario, the judge does not subtract points, but stops subtracting at 0, the difference in scores changes between the two scenarios.

Therefore, I think adding points to the other player is preferable, as negative numbers are a needless complexification of an already quite complex game.