No “DUH” about riffle shuffles precisely because it negates the whole point of the conversation. Riffle shuffles are not good unless you do a lot of them. This is not true for all shuffles. There are many other forms of shuffles I have seen humans do live as well. I have seen people throw cards on the ground then pick them up; I have seen them deal them into several neat piles and then stack them up; I have seen them cut the deck into many small piles and change the order of the piles, etc. All of these will have different stochastic behavior. Some of them are much better than others. Perhaps riffle shuffles are the ironclad norm at casinos or something. I have never been to a casino in my life, so I couldn’t say.
Multiverse theory and life choices are pretty far off topic. I still don’t know why your tree branches off in 20 directions. The only tree that makes any sense for branching goes in 52! directions.
Anyways, the point seems to be about branching paths, but the issue is that the path that the cards took to get to their configuration is irrelevant, the only thing that matters is their final position. You will get the 4 of hearts -or not- based on where the 4 of hearts is after the shuffling is completed, regardless of what route the 4 of hearts might have taken to get there.
Let’s go back to flipping a coin. Assume you have a fair coin. If you flip this coin, you will get heads or tails with a 1/2 probability each. Now, you can flip the coin again and decide that you will leave the same situation you had after the first flip if you get tails, and you will change it if you get heads. This will give you either heads or tails, each with a (1/2)(1/2)+(1/2)(1/2)=1/2 probability each, which you might notice is exactly the same as before. You can keep going on and on like this if you like, swapping your result each time you see heads. Your result will change, but the probability of heads and tails will always be exactly 1/2. The number of possible paths you took, swapping heads and tails at different moments, will grow like crazy, but the probability of each outcome does not change at all.
If, on the other hand, you have an unfair or “loaded” coin, say with a 1/3 chance of landing heads and 2/3 chance of landing tails, then flipping the coin once will give you a higher chance of tails, however, if you flip a second time you will have heads with a (1/3)(1/3)+(2/3)(2/3)=5/9 probability, and tails with a (1/3)(2/3)+(2/3)(1/3)=4/9 probability. You will notice this is closer to even. A third toss will get you to 14/27 and 15/27. If you repeat this over and over again, changing your result each time you get heads, you will get closer and closer to uniformity. If you do this ad infinitum you will converge to the uniform distribution. *
To sum this up, if your initial flip is “good enough”, flipping over and over again does not help at all, however if your initial flip is bad, then repeated flipping improves the result. Of note, with imperfect initial flipping, you will never get to exact fairness, only approximate it better and better.
Riffle shuffling behaves like the loaded coin: Repeating it improves the randomness.
If you have some machine which truly spits out uniformly random numbers in (0,1) then the RPP algorithm will behave like the fair coin. It jumps directly to fairness. Repeating it makes no difference at all.
The only question is whether the MT is a machine which truly spits out uniformly random numbers in (0,1). The answer is no. The MT is deterministic, and if given the same seed it will spit out the same result. If not given the same seed, however, it behaves so closely to uniform randomness that the present state of science has no idea how to tell the difference, even if given runs of hundreds of millions of numbers. The question of whether patterns will emerge with many shuffles of cards is the same as the question of whether patterns will emerge with large datasets in the MT. It has been studied very seriously by very smart people with absurdly large sample sizes, and no patterns were found.
The issue of the seed being the same is not a problem; you just change the seed each time. You will not run out of seeds because the number of possible seeds is a number so mind bogglingly huge that there is no physical phenomenon you could ever compare it to (typically we say “quadrillions of times bigger than the number of atoms in the universe”, but even that is still way too small to give any meaningful reperesentation of such an obscenely large number). Picking a seed is also no big deal. By default your computer will set the seed by using the output from the last time the MT was used. If the MT was never used, it sets the seed using the system clock. This is hardcoded into all modern computers. Older computers (pre 2000) were not as good (In the 80s it was common to have computers start with the same seed each time they booted up, and they also had much weaker RNG).
As an addendum, it is possible to override the seeding behavior of a computer, and it is OK to do this in really dumb ways. For instance, there is no tractable relationship between the number MT gives you with one seed and the one it gives with the seed that comes immediately after (for instance seeds 45926184 and 45926185). They are just as unrelated as if the seeds were not similar.
*By the way this works regardless of how unfair the coin is, so if you have a coin that you don’t trust you can toss it 20 times, swapping every time you get heads, and you will end up with something that is extremely close to the result of a fair toss.
