Aren't you using it wrong? Radio buttons are used more to select one option out of many, and checkbox is used more for multiple selection, so you should not have a name as an array on the radio button. Then a simple check if the old value is the same as the one selected you should print out checked.
<input type="radio" name="radio" value="1" {{ old("radio") == '1' ? 'checked' : '' }}>
if you use checkbox instead or the name as an array just check if the value is contained in the array.
<input type="radio" name="radio[]" value="1" {{ in_array('1', old("radio")) ? 'checked' : '' }}>
Let me know if it works.