I see a lot of questions on software patents, but very few questions about eligibility, post-Alice.
What is the current thinking, particularly in the wake of Enfish and Bascomb?
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There is no technically correct answer under US law because the Supreme Court left patent eligibility a confusing mess.
There is, however, a practical answer. The practical answer is to follow a "cover all possibilities" strategy. As a preliminary matter, consider filing in other countries where the law is better settled. Believe it or not, the patent system in China is becoming more stable and software-friendly. Similarly, consider filing in larger English speaking countries (because translation is expensive) as well as in Germany (biggest EU economy).
As for the US, you'll want to draft as broad a specification as possible. Assume that the specification needs to cover a situation where patent eligibility broadens (a possible outcome if the Supreme Court experiences retirements and Trump replaces some Justices with ones holding the typical conservative pro-private property attitudes), and to cover a situation where patent eligibility narrows (a possible outcome if the infringer lobby continues to succeed in getting Congress to restrict patents and patent enforcement).
Don't file a "track one" application. Instead, file a provisional application (gets you an extra year) followed a year later by a non-track-one utility application. The USPTO will probably sit on it for 3 years or more. That puts you at least four years out. I expect US patent law to be more settled four years from now, and at that point you can amend the claims to reflect whatever happens to eligilibity standards. If the law remains unclear four years out, you can appeal, which adds another four years. Hopefully the law would settle while on appeal, making the case either a winner or loser (and if it is a loser, you can then amend in an RCE).
The bottom line is that your best bet is to hedge your bets. Your ability (or your lawyer's ability) to draft a broad, enabling disclosure will be critical, since your disclosure is going to need to support claims that track the state of the law in the future.
In my opinion, it is inexcusible that Congress hasn't clarified eligibility -- they could do so quickly and decisively. Instead, the Supreme Court is left writing the law itself (seriously, read Section 101 and it looks like everything is patent eligible; all of the restrictions in the Alice and similar cases are pretty much what the Supreme Court guesses Congress would do if Congress could walk and chew gum at the same time). This leads to yet another point of uncertainty -- even if the Supreme Court finally hands down clear guidance, Congress could alter it at any time.
All of which means you need to keep the maximum number of options available. File foreign, the law is in flux in the US in a way that it isn't in other major economies. File a broad specification that will support claims in the US no matter which way eligibility goes. By all means, it is smart to file on something valuable if you think there is a reasonable chance patent law does or will support those claims.
You do need to see a lawyer, though. This isn't legal advice, and you do need legal advice. What I'm trying to do is give you practical issues to ask your lawyer about.
I am not a patent attorney so this advice is probably inadequate. That said, I do have several algorithm based patents so perhaps my insights are of value. My understanding is that abstract mathematical algorithms are simply not patentable. However, the use of an algorithm to solving a specific technical application may be patentable. If you are just automating a series of steps that could otherwise be done manually, don't expect a patent to be issued either. In my case, the algorithm patents I have are the application of unique mathematics to solving a very specific problem where the solution was unexpectedly advantageous over the prior art. This unexpected advantage was a key aspect to convincing the patent examiner of novelty and non-obviousness.