Using get_current_user_id() Inserted into my WPDB table.

So I would like my plugin to insert the current user’s ID into my table, “wp_ml_char”.
The problem is, it’s failing to actually insert it; nothing happens and no errors are displayed. This form is only asking me to put in a name, but it also has a “hidden” input type which grabs whatever user ID is currently present. I can’t pinpoint where the cause is exactly, but it might be the “hidden” input line I made. Thanks in advance to anyone that can help!

// Character creation form. Grab the current user's ID.
require_once('/home/mythlarp/public_html/wp-includes/user.php');
$wpid = get_current_user_id();

function html_form_code() {
    echo '<form action="index.php" method="post">';
    echo '<input type="hidden" name="wp_id" value="<?php echo $wpid; ?>" />';
    echo '<p>';
    echo 'Character Name (required) <br />';
    echo '<input type="text" name="ml_char_name" pattern="[a-zA-Z]+" value=""' . ( isset( $_POST["ml_char_name"] ) ? esc_attr( $_POST["ml_char_name"] ) : '' ) . '" size="40" />';
    echo '</p>';
    echo '<p><input type="submit" name="cf-submitted" value="Send"/></p>';
    echo '</form>';
}

// Insert form data.
$wpdb->insert('$table_name', array(
	'ml_char_name' => $_POST['ml_char_name'],
	'wp_id' => $_POST['wp_id'],
));