Problem with if condition on a "random walk" script - bash

Question

I'm trying to make the coordinate "x" randomly move in the interval [-1,1]. However, my code works sometimes, and sometimes it doesn't. I tried ShellCheck but it says "no issues detected!". I'm new to conditionals, am I using them wrong?
I'm running this on the windows subsystem for linux. I'm editing it on nano. Since I have a script that will plot 200 of these "random walks", the code should work consistenly, but I really don't understant why it doesn't.
Here's my code:
x=0
for num in {1..15}
do
r=$RANDOM
if [[ $r -lt 16383 ]]
then
p=1
else
p=-1
fi
if [[ $x -eq $p ]]
then
x=$(echo "$x-$p" | bc )
else
x=$(echo "$x+$p" | bc )
fi
echo "$num $x"
done
I expect something like this:
1 -1
2 0
3 1
4 0
5 1
6 0
7 1
8 0
9 1
10 0
11 -1
12 0
13 1
14 0
15 1
But the usual output is something like this:
1 1
2 0
3 -1
4 0
5 -1
6 0
7 -1
(standard_in) 1: syntax error
8
(standard_in) 1: syntax error
9
(standard_in) 1: syntax error
10
(standard_in) 1: syntax error
11
(standard_in) 1: syntax error
12
(standard_in) 1: syntax error
13
(standard_in) 1: syntax error
14
(standard_in) 1: syntax error
15
Always stopping after a -1.

Answer 1

You can do this with bash:
x=$(( x - p ))
or
(( x -= p ))
and you don't need bc.

Answer 2

Replace x=$(echo "$x-$p" | bc ) with x=$(echo "$x-($p)" | bc ) to avoid echo "-1--1" | bc.

Answer 3

One-liner equivalents to the OP's 18-line random walk script, using bash arithmetic evaluation:
x=0; printf '%-5s\n' {1..15}\ $(( x=(RANDOM%2 ? 1 : -1) * (x==0) ))
x=0; printf '%-5s\n' {1..15}\ $(( x=( x ? 0 : (RANDOM%2 ? 1 : -1) ) ))
Sample output of either, (the 2nd column will vary between runs):
1 -1
2 0
3 -1
4 0
5 1
6 0
7 1
8 0
9 -1
10 0
11 1
12 0
13 -1
14 0
15 -1
How it works:
echo {1..15}\ $(( ...some code... )) prints the numbers 1 to
15 followed by 15 instances of whatever result in the $(( ... )) code returns. One flaw with this approach is that with the resulting 15 pairs of numbers, (e.g. 1 -1, 2 0, etc.), each appears to bash as one string, rather than 30 separate numbers.
(RANDOM%2): the % is a modulo operator and here returns the remainder when divided by 2, which is either 0 or 1.
(x==0): $x can be one of three numbers, but if the previous value of $x was -1 or 1 the only legal random step is 0, so we only need a random number if the previous value of $x was 0.
The if logic is replaced with shortcuts of the form (expr?expr:expr); these use the same logic as the OP script.