Have a look at the idea of the Boltzmann Brain. Cosmologists are starting to apply the same approach using this idea, as Bostrom used in his version of the simulation argument. You can see an accessible presentation on the controversy about whether Boltzmann brains exist here. This is the context of you 'popping into existence', memories fully formed, in a vast cosmological future. On balance, when you run the numbers, these seem deeply unlikely - the gas in a 1 litre bottle won't randomly all be on one side of the bottle once in the 14 billion years of our universe, so these complex structures without 'causes', seem very unlikely.
'You' in an ontological sense, are your causes and conditions, past and future, and they exist in a vastly complex web which requires every element of the universe that has affected you to be the same. That involves enormously compound unlikely quantum events. So in an ontological sense 'you' in the fullest sense of not only small variations of what actually happens to you, but all your realisable possibilities in this moment, can be recreated in the multiverse, but only very rarely (in the sense of the total probability space, called the Hilbert space), ie when a big chunk of an alternate universe matches ours.
Another framing is, all the possibilities that are realisable from the moments of your life exist in the multiverse, but are forever separated and diverged from the 'you' you consider yourself to be, and not causally linked in any way. You might say there is a branching structure of people that resemble you in different ways, fulfilling the possibilities present in your life (but not impossible things, that's Boltzmann brain territory). I would say alternate 'you's are not meaningfully connected to you, except by you imagining them, and shaping your future actions by learning from that. When you diverge, you cease to 'be' them (see Teletransportation paradox)
In terms of reoccurring in our own universe. Our experiences don't go down to quantum accuracy. It's plausible, likely even according to Bostrom, that your brain and life will be simulated in the future. This can only be done to a certain 'resolution', and it's largely a matter of definitions whether simulations are 'really you'. You could be a simulation now and not know it, which would meet a kind of 'Turing test' analogue, the 'walks like a duck..' test, if you will, for 'really you'. It's hard to draw conclusions about how often these might run and h9w much variation, but thus is really the only way alternate individuals that are meaningfully 'you' could exist.
Probability is slipperier than you imply. The idea all probabilities add up to 1 is called the axiom of 'unit measure' in probability theory, or 'unitarity' in physics. But consider the dice - what about the one time where it balances on a corner or an edge, perhaps have created a pit in the surface from near-infinite rolls? What if the dice has so many sides many of them will never be rolled in the age of the universe, how could you check it's unitarity?
Unitarity is a fiction, a useful and intuitive one, based on imagining counterfactuals: if everything was held to the same initial conditions and repeated infinite times, what fraction would be of each result? We apply limit theory, to move from practical numbers of rolls to mathematically imagining 'as rolls approach infinity'. But in the end, the universe does what it does, and has the final word. Probability is only us imagining 'what if?' and applying simplifying assumptions based on our understanding of a system, invariably limited to simple systems, or else being very unreliable probabilities! (eg. election results)
In quantum mechanics things start to really stretch our understanding. Dirac introduced the idea of using negative probabilities and negative energies in calculations, and predicted the existence of antimatter from this. Feynman argued they need not be thought of as 'real', but as useful book-keeping. And the extended probability ensemble goes further, allowing both negative and beyond unitary probabilities.