Quote from deadlineLet me try to be more rigorous in explaining my perspective. I would specifically like to refute your claim that "a weaved deck will have less impact on the final result than a fully stacked deck." I love examples, so here goes:
I write a computer program that randomizes a virtual "deck" composed of 20 Mountains and 40 Lightning Bolts.
- I stack the 20 Mountains on top of the deck and the program randomizes.
- I instruct the program to find the largest land clump in the deck.
- I repeat the first two steps 100 000 times, and find the average largest land clump.
All the same, except the input is a mana-weaved deck.
I believe that whether the deck was weaved will have zero impact on the final result.
I am absolutely willing to write this computer program if this would settle the debate. If it would not, I would find it very helpful to understanding your position if you could modify my proposal or write your own experiment that would express concrete, objectively observable results that would support your claim. I truly want to know if GAThraawn and I are wrong, and we have the tools to find out for sure.
I'm glad you're willing to put effort into this. Personally, I don't have the expertise or resources to create the necessary simulation myself. Just creating the randomization algorithm alone would take weeks of research for me to do.
I don't know your background with this sort of thing, but the most important thing you should ask yourself when creating a simulation is "Does this accurately describe reality?"
I can't answer that right now, because you haven't elaborated on what method you plan to use to randomize the virtual deck. Suffice to say, a simple RNG algorithm would not reflect what actually occurs when you shuffle a deck.
This can be seen by comparing a virtual deck randomized by an RNG algorithm to one that's been given a single iteration of a physical shuffle. You will see that with the virtual deck, any card can end up in any position but with the physical shuffle, there will be certain cards that cannot reach certain positions (eg. the top cards of a single mash shuffle cannot finish at the bottom of the deck).
For it to be accurate, it needs to mimic common shuffling methods. Good candidates are the mash shuffle and the riffle shuffle, which are specifically mentioned in the MTR.
Because physical shuffling is iterative, you need to be able to apply the method several times. Ideally, you should be able to record the data after each iteration (see below for why).
When recording data, too little is poison for good conclusions. You should record as much as reasonably possible! Especially if you're intending to thoroughly investigate the subject.
In this case, you should not just record the largest land clump, but the entire distribution of land and nonland clumps. That way you will have not just the largest value, but the mean, median, mode, lowest value, and other statistics that relate to the distribution of both halves of the deck.
Also, you should record the values for each step of the iterative process, so you can compare each iteration to both the original order of the deck, and to the same stage of the sister deck.