Quantum mechanics is a deterministic theory. In fact, you can call it the "most deterministic theory", as it has a method to transform every non-deterministic theory in a deterministic one*. Just split the world in multiple parts, one for each possible "outcome" of anything which might appear random. This directly leads to many worlds and can make every theory deterministic.
This is not many worlds, and not how many worlds works. This implies you can get the probabilities by simply counting up the worlds- which doesn't work. So I'll outline a bit of history:
Standard quantum mechanics rests on a set of axioms. One group of axioms tells us that we represent our objects as wavefunctions, another group tells us how the wavefunction evolves (according to the famous Schroedinger equation).
The final axiom relates to measurement- but its a very important one. Its how you connect the theory to experiment! This is where the probabilities creep into quantum mechanics. A wavefunction can be in multiple positions, momenta, or energies, but we only seem to measure one. So, Born, and later Von Neumann showed us that we can interpret the magnitude squared of amplitudes as probabilities. This is known as the Born rule.
This isn't problematic for the theory mathematically, but it is physically. We expect quantum mechanics to be the theory underlying macroscopic behavior- but we have to add a special rule for measurements where particles behave differently.
Enter Hugh Everett- http://www.univer.omsk.su/omsk/Sci/Ever ... r1957.html who said 'well, what happens if we just get rid of the measurement process and the Born rule.' In this case, the entire universe is a giant wavefunction. Everett (and DeWitt and Hartle, among others) noticed two things- 1. large portions of the wavefunction evolve independently of other portions of the wavefunction. 2. In the limit of infinite measurements,every one of these independent branches of the wavefunction obeys the Born rule. So Everett interpreted this to mean that each independent branch of the universe exists as a separate 'universe' AND that he had successfully derived the Born rule.
This is fantastic work- but there is a huge problem. When you DON'T have infinite measurements, then there are lots and lots of universes where the Born rule fails. In fact, there are orders of magnitudes MORE universes where the Born doesn't WORK. This is obviously a huge problem because the Born rule has been empirically verified over and over again.
So- can we fix the problem? Maybe. Deutsch said 'wait! We don't need to show that most universes obey the Born rule. Instead, we can use a bit of game/decision theory to show that a rational observer will play the game AS IF the Born rule were valid' http://uk.arxiv.org/PS_cache/quant-ph/p ... 2157v2.pdf (not the original Deutsch paper but an easier to follow demonstration of the same thing by Wallace).
Unfortunately, this runs into problems to- the first is philosophical. Is quantum mechanics to be a theory of how the world works, or a theory about our beliefs? Deustch's ideas tangle these two things up.
The second problem is more technical- Deutsch's proof rests on some specific definitions of rational behavior. See this: http://arxiv.org/PS_cache/arxiv/pdf/090 ... 0624v1.pdf for a summary of some of the criticisms.
So- many worlds is an attempt to kick away the Born rule/measurement postulates. Its a noble attempt- but when we do that WE NEED A WAY TO GET NUMBERS OUT OF THE THEORY. If we can't, we have built a mathematical edifice, but not a physical theory. Everett thought he had a way to recover the Born rule- and indeed he has the tantalizing start of one. Unfortunately, his proof fails for an finite number of measurements, and no one has been able to recover a way to get numbers out of the theory.
This is why no one actually uses many worlds to do calculations. Literally no one. Most use Copenhagen, and some use a consistent histories or path integral formulation. Even the believers of the interpretation can't use it- because there is no method to make actual predictions with the interpretation. So while its a tantalizing collection of ideas, right now the many worlds interpretation is not a physical theory.