[Sub-randomness](https://en.wikipedia.org/wiki/Low-discrepancy_sequence https://en.wikipedia.org/wiki/Low-discrepancy_sequence ) (or apparently Wikipedia uses t

[Sub-randomness](https://en.wikipedia.org/wiki/Low-discrepancy_sequence https://en.wikipedia.org/wiki/Low-discrepancy_sequence ) (or apparently Wikipedia uses the term "low-discrepancy sequence" now) is one case where a random-generator is designed to make the gambler's-fallacy non-fallacious. And I think some simple computerized random-generators were designed sub-random. Some designers have argued that players find it more "fair" when the results of "random" rolls are more predictably evened-out; some players may want some level of variation/unpredictability, though extreme results (extremely good or bad luck) might seem unfair. Also, say you're about to flip a coin 100 times. Then, your future-self advises you that you're 50% likely to get Heads on any particular flip. Then, sure, that'd seem to imply that you're going to get 50 Head's and 50 Tail's, so switching would often make sense as getting one result would tend to reduce that result's likelihood. In particular, you should be able to guess the last flip with certainty, as you know that you ought to get a total of 50 Head's and 50 Tail's. However, if you're flipping a coin 100 times and estimate a 50% likelihood of Head's, then that's a different scenario. I mean, yes -- you're still working under the assumption that Heads is 50% likely, but it's not the same thing. You wouldn't know that the final distribution would be 50 Head's and 50 Tail's, such that getting one result wouldn't have the same implications. Finally, "the gambler's fallacy" is named after a stereotypical scenario wherein a gambler who keeps losing argues that they'd be a fool to quit because they're "overdue" for a win. In that case, it does tend to be a fallacy. So if you come up with a situation where such an argument wouldn't be a fallacy, then presumably you're looking at something other than the gambler's-fallacy.