A coin landing on heads 100 times in a row might only "call out" for an explanation if one has some existing beliefs about the coin, creating the (failed) expectation that it would land on heads roughly half the time. Without such beliefs or expectations, neither explanation "calls out" for an explanation any more than the other.
What's actually going on is that we have existing beliefs (or hypotheses), based on experience, that:
- The coin is fair (based on coins usually, but not always, being fair).
- Tossing a coin is chaotic enough to result in a random distribution.
If the above were true, it would be an unlikely outcome to get heads many times in a row (we can model this via confidence intervals). So we might suppose that either or both claims are false, and we can consider whether and how competing claims may better explain the evidence (be that the coin being weighted or a coin-toss not actually being as chaotic as believed).
Though note that a coin being fair and a coin being weighted are both designed, because essentially all coins are designed. Calling the latter "rigged" suggests intent (i.e. "more" design). In the case of a coin, being weighted may be intentional (whereas being fair may merely be a side effect of design). But this isn't, as such, a principle we can generalise to determine whether something was designed (though it may relate to other such principles). Naturally-forming things could lean towards some outcomes above others due to simple asymmetries in how those things formed. Coins are usually designed to be roughly symmetrical (fair), but any given natural forming process may or may not produce symmetry. And some natural things (e.g. physical laws or physical constants) may not have formed at all - they may just always have been that way.
So, what is a "robust" explanation, then?
The concept of a "robust" explanation is not particularly robustly defined.
Though we could define it in terms of having high explanatory power, such as having greater predictive power, fewer surprising facts and fewer additional claims to retrofit the explanation to the evidence.
In the case of flipping a coin, the fair-chaotic-coin explanation would predict that we're get a roughly-even distribution between heads and tales across many flips, and it would be surprising if we get either heads or tales exclusively or many times in a row. With a weighted coin, this is less surprising and we may correctly predict this outcome going forward, if indeed it's weighted.
There may be additional claims required to explain how you ended up with a weighted coin, or a fair coin for that matter, in the first place. But both of these things are fairly common occurrences*, so neither would be too extraordinary of a claim to add to our explanation. If the existence of a weighted coin were near impossible, it may still be more likely that what actually happened was the exceedingly unlikely possibility that a fair coin landed on heads many times in a row.
* A coin being fair is more common than it being weighted. The former would often be the default explanation, the null hypothesis that we'd need to reject, based on the evidence, to accept that the coin is weighted. Though in certain settings, weighted coins may be more likely and there may be reasons to mitigate that possibility, e.g. a casino wouldn't let you bring your own coins (or dice, rather), because they'd lose a lot of money if it ends up being weighted. And you'd win a lot of money, which would make it more likely for someone to bring weighted dice.
Never mind that we also need to consider the ways we could end up with a weighted coin. For a coin in particular, we generally broadly have 2 main possibilities:
- The coin was intentionally made to be weighted.
- There was an inconsistency in the production process (or being weighted was a side effect of patterns on the coin).
The former may be more likely, but neither of these are particularly extraordinary. Note that the latter doesn't entail intent (at least not in the design of the coin, specific to it being weighted).
We wouldn't say e.g. the coin being fair is unlikely, therefore it was zapped into existence by a unicorn (unless you already have strong evidence that said unicorn exists and has a habit of zapping coin-like things into existence). We wouldn't say that even if we didn't know how weighted coins could come about.
For other things for which people say "this would be unlikely, therefore this other explanation [of it being designed this way] is correct" (in particular in relation to a god's existence, i.e. fine tuning, which has other issues):
- We need to consider how extraordinary (or otherwise justified) this explanation is.
- We also need to consider competing ways that this "weighting" could've happened.
Just because someone comes up with an explanation to avoid some improbability, doesn't mean they're correct.