// include this function in your javascript and to be use to send won to backend

function update(won){
    if (won != '' || won != 'undefined') {
        $.ajax({
            url: "gameupdate.php",
            type: "POST",
            data: {"updatewon" : won},
            success: function (data) {
                if ($.trim(data) == 'success') {
                    alert('updated');
                } else {
                    alert('something goes wrong');
                }
            }
        });
    }
}

// when you want to update won
// update(won); <===

gameupdate.php
#########################
<?php
if (!emtpy($_POST['updatewon'])) {

    // validate $updatewon is within 0 to 100
    $updatewon = (in_array($_POST['updatewon'], range(0, 100)))? $_POST['updatewon'] : 0;

    if(!$link = mysqli_connect("localhost", "root", "....", "db")) {
        die ("No connection: ".mysqli_connect_error());
    }

    $res = mysqli_query($link, "select balance from registrations where username='{$_SESSION[username]}'");

    // $Balance = $res;
    if (mysqli_num_rows($res) === 1) {

        //   insert newblc to database;
        if (mysqli_query($link, "UPDATE registrations SET balance = balance + {$updatewon} WHERE username = '{$_SESSION[username]}'"))  {
            echo 'success'; // this output will be send to DOM as data response
            exit;
        } else {
            echo 'upddate failure';
            exit;
        }
    } else {
        echo 'no balance was found';
        exit;
    }
}
?>