Using String.prototype.split

split method of Strings allows you to "split" a string by a delimiter into an array. Take this example:

'1,2,3'.split(','); // => [1,2,3]

Answer to your question using split:

var string = 't0=16,21,32,8$t1=15,33,46,4$t2=26,27,37,5$t3=9,29,40,8';
var obj = {
  bets: []
};
string.split('$').forEach(function(x) {
  var o = {n1: '', n2: '', n3: '', s1: ''};
  x.split(',').forEach(function(y, index) {
    o[index < 3 ? 'n' + (index+1) : 's1'] = index == 0 ? +y.slice(3) : +y;
  });
  obj.bets.push(o);
})

Lemme explain the code, it might seem complex at first.

First we split the string by $, the delimiter of our yet-to-be-bets, then we split each part by , in order to get our numbers out.

Now what's happening at [index < 3 ? 'n' + (index+1) : 's1']?

This is an inline if/else statement, if you're not familiar with them, take a look at this.

What it does is: check if we're at the third element of our array, if yes, set the key to s1, else, the key will be 'n' + (index+1) which will result in n1 at 0 index and so on.

We have another inline if statement in our value, what's that? Our first element will not be just a number, it will be something like t0=16, but we only need the number, so we check if we're at the first element, if so, slice up the string.

The +y converts our string to integer/float, it's similar to calling parseInt() with a few small differences.

You could achieve this by using split and reduce:

    var data = 't0=16,21,32,8$t1=15,33,46,4$t2=26,27,37,5$t3=9,29,40,8'.split('$');

    var result = data.reduce(function (mem, curr) {
        var d = curr.split(',');

        mem.bets.push({
            "n1": +d[0].replace(/t\d+=/, ''),
            "n2": +d[1],
            "n3": +d[2],
            "n4": +d[3]
        });

        return mem;
    }, {"bets": []});

Using a combination of String.prototype.split() and some basic regex

var input = 't0=16,21,32,8$t1=15,33,46,4$t2=26,27,37,5$t3=9,29,40,8';
var objs = input.split('$');

var result = { bets: [] };
var re = /^t[0-9]+=([0-9]+),([0-9]+),([0-9]+),([0-9]+)$/i;
for (var i in objs) {
  var matches = re.exec(objs[i]);
  result.bets.push({
    "n1": matches[1],
    "n2": matches[2],
    "n3": matches[3],
    "s1": matches[4]
  });
}

console.log(result);