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I have a suggestion, to make it more detectable, and clear, when someone cheats a game, by altering the RNG to increase the luck.

Best to "solve" such problems in the future, would be to have some "speedrunning mod" or similiar (that SDA could officially create) that players must insert in their game, that alters the RNG seed to depend on movement, time, the world seed or other form of input, but still give the same percentual drop rates. In this way, you can require that the speedrunner submits his input sheet, and then the exact gameplay can be replicated on the moderator's side. Comparing this with a live stream where the keyboard or controller is visible in the frame, would with 100% conslusion either tell if they are cheater or not, without having to analyze RNG drop rates.

Because, then, an unmodified game, with the speedrunning mod, with the same world seed, should, given the speedrunners input sheet, give a completion of the game in the time claimed. If not (ergo, the speedrun becomes "desynced" just because the RNG drop rates does not match), then the original game has been modified. And in the same way, if the input sheet doesn't match the claimed stream (with the keyboard or controller visible), then the input sheet has been TAS'ed to give unfair advantage.

There is a kind of problem with analyzing RNG rates, and that is that its possible to say its impossible to win on the lottery = you cheated when you won on Jackpot with that 8 digit number matching your ticket. and thus forfeiting your monetary win. So its kind of difficult to prove that a random number generator was tampered with, unless you get to analyze the exact RNG - thats why official lotteries have their RNGs analyzed and then sealed with a tamper evident sticker.
So nobody can claim the generator was cheated if the number of lottery tickets that won, is lower than the "expectation".

In the case with Dream's rum, its more clear-cut, but imagine if Dream would just up' their drop rates with a little bit, causing the rates to not be "impossible" or "unobtainable".

Thats why I suggest that a "speedrunning mod" should be used to submit speedrunning samples, which is then a official SDA mod that MUST be used when submitting speedruns.
This could then apply to all games were a RNG affects the run in such way that it would affect speedrunning.
Note that the mod itself doesn't need to be in any way "verified running" or "verified unmodified" - because when the speedrunner submits the input sheet and stream - the moderators just set up a identical setup on their side, meaning the run can be verified. If anything is modified or cheated with - the run will not complete successfully on the moderator's side.

And in this way, the actual run, can be replicated with 100% accuracy on anyone verifying the speedrun, giving more credibility even if something unlucky happens.
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As far as I know, it's not a trivial task to hack something like that into a game (if it was, more games would have input-based demo systems I guess, and that's something devs can do having the source code). So you're not wrong, but it's just far more work than you think. I think just reading the inputs from the user's side isn't enough because it doesn't account for varying amounts of lag.

Luckily it's not very attractive to submit cheated runs on SDA seeing how relatively little exposure it might get through us as things stand. This isn't a site that's considered very glamorous by those kinds of people. If you're submitting a run on SDA, you're probably doing it because you like to set yourself challenges etc. It's ultimately not very easy to stop cheating if someone really really wants to cheat. That's kind of a "get a life" situation more so than anything. Also most runners don't either even know about SDA or do know but don't care, and as such, would probably want to solve such questions within their own secluded communities. It's honestly better for us, too, if some other runners have verified (by whatever means) the legitimacy of the runs, or come over here to do it in the verification. SDA's process just relies on whoever comes in to verify.