Syntax error in BASH script near `%` operator - bash

Question

I am writing a simple bash script to count the number of occurrences of random draws of cards. I store those in an array, and when printing out the results, for every 10 times that card is pulled, I print one single '*' in a sort of Histogram style of output.
Although, I keep receiving this error when compiling on Terminal:
"task1.sh: line 29: % 10 : syntax error: operand expected (error token is "% 10 ")
task1.sh: line 33: % 10: syntax error: operand expected (error token is "% 10")"
Can't seem to figure out why though. Thank you in advance for any help.
#!/bin/bash
randomdraw(){
Suits="Clubs Diamonds Hearts Spades"
suit=($Suits)
Denominations="2 3 4 5 6 7 8 9 10 Jack Queen King Ace"
denomination=($Denominations)
num_suits=${#suit[*]}
num_denominations=${#denomination[*]}
declare -a numoccurences
declare -a suitoccurences
for ((x=0 ; $x<$loopnum ; x=$x+1));
do
(( numoccurences[$(( RANDOM%num_denominations ))]++ ))
(( suitoccurences[$(( RANDOM%num_suits ))]++ ))
done
}
echo "How Many Random Draws?: "
read loopnum
randomdraw loopnum
for ((x=0 ; $x<$num_denominations ; x=$x+1));
do
let "rounder=$(( ${numoccurences[x]} % 10 ))"
if [ $rounder -ge 5 ];
then
let "starnum=$(( $(( ${numoccurences[x]} / 10 )) + 1 ))"
else
let "starnum=$(( ${numoccurences[x]} / 10 ))"
fi
echo "${denomination[x]}: "
for ((k=0 ; $k<$starnum ; k=$k+1));
do
echo "*"
done
done

Answer 1

Your num_denominations array is mostly empty and the
let "rounder=$(( ${numoccurences[x]} % 10 ))"
is evaluated to
let "rounder=$(( % 10 ))"
Print numoccurences and suitoccurences before asking for loop number for debugging.

Answer 2

You should try to be consistent in the way you write arithmetic expressions in bash. You don't need to use $ to introduce a variable inside an arithmetic expression. And you don't need to use ${array[idx]} either. There's no reason to use let if you have arithmetic evaluation, either. So instead of
let "rounder=$(( ${numoccurences[x]} % 10 ))"
You could write:
(( rounder = numoccurences[x] % 10 ))
These don't quite do the same thing. In the first one, ${numoccurences[x]} will be substituted with nothing if numoccurrences doesn't have a value corresponding to the key $x. In the second one, numoccurrence[x] will be replaced by 0, which is what you actually want. (That has nothing to do with the unnecessary let, since the $((...)) arithmetic expression is evaluated before let is run.)
There are many other places in that script where you would be well advised to simplify your style. For example,
let "starnum=$(( $(( ${numoccurences[x]} / 10 )) + 1 ))"
would be more robust and more readable as
(( starnum = numoccurences[x] / 10 + 1 ))