Why does a `while` loop never stop after I change the wrong variable?

Compare the variable in the condition with the variable you update. A while loop tests its condition repeatedly and runs its body while that condition is true. It stops when the condition becomes false. [S1]

For example, suppose the test checks count, but the body changes only step:

count = 0
step = 0

while count < 3:
    step += 1

Here, count < 3 remains true because count never changes. Increasing step does not affect that test. The key check is: which exact value must change to make the condition false?

Update count, since count is the value the condition uses:

count = 0

while count < 3:
    print(count)
    count += 1

The condition and its state change trace like this:

1. count is 0; 0 < 3 is true, so the body runs. Then count becomes 1.
2. count is 1; 1 < 3 is true. Then count becomes 2.
3. count is 2; 2 < 3 is true. Then count becomes 3.
4. count is 3; 3 < 3 is false, so the loop ends. [S1]

The ending change is count += 1 taking count from 2 to 3. That makes the next test false. This trace assumes the code runs as shown and that the body reaches the increment each time.

Name the condition variable explicitly and follow its value through every path around the loop. If some path skips the update, check whether that path returns to the condition without changing the value that controls it. The important question is not whether some variable changes, but whether the condition can become false.

For a quick manual trace, write down the condition before each pass, the value it depends on, and the update that happens before the next test. If the same condition and value repeat, inspect the paths that should change that value. For the example above, the value is count, the test is count < 3, and the update is count += 1.

Use this small template, replacing the placeholders with your own condition and update:

Condition: [the expression after while]
Variable(s) it checks: [the values used by that expression]
Update on each path: [what changes those values]
Stop test: [a sample value that makes the condition false]

For the counter example:

Condition: count < 3
Variable it checks: count
Update: count += 1
Stop test: count is 3, so 3 < 3 is false

If you cannot identify a reachable update that makes the condition false, the loop has no demonstrated stopping point yet. This trace explains the shown condition and counter; it does not establish what will happen in code with additional branches or other behavior.