shuffling in general

[walkingdude]

Something that’s worth noting is an overlooked fact about rifle shuffling and why some piles are needed. Most tables are not clean. It they are wood, there is varnish on them. If they are general tables, odds are there is old food on them. Even if it looks clean there is probably gunk.
Spells tend to sit in your hand library or graveyard, but permanents sit on the table and get rubbed against the table when you tap them. This sitting and rubbing action cause some of the table gunk to stick to permanents and even if it’s a very small amount it effects their stickiness relative to the rest of the cards in your deck. The result is that if you just riffle shuffle your permanents will clump together more than one would expect based on true randomness or statistical prediction. The result is you either A) get mana screwed more often or B) get the nuts affinity draw more often depending on weather you want a front load of permanents or an even mix of lands and spells.
The solution is to either change sleeves regularly, or always use a playmat that you are sure is clean and that gets washed frequently. If you play on tables with old sleeves you are not really randomizing no matter how much you want to.

edit: thumbs up to english

[jdl]

The solution is to either change sleeves regularly, or always you a playmate that you are sure is clean and that gets washed frequently.

Indeed!

So far, the best point made in this thread is that randomization != even distribution of land.  If your deck is random, it will have land pockets.  It's just how random a deck really needs to be that is the issue with the floor rules.  How does a judge decide what is random and what isn't?

[Rainula]

I would imagine a judge would find a deck to be insufficiently randomized if there was an algorithm that could predict the next type of card in a deck.  Something on the order of land spell spell repeat or no two lands together.  Interestingly enough, if a deck was to be totally randomized, it could still be very organised in any such way.  I belive that the clear signal would be a high amoung of order because the number of times a deck is well ordered after a randomization is so staggeringly small compared to the other possible outcomes that foul play is almost a given.

[AIcOPed]

It was proven mathmatically that 7 rifle shuffles thouroughly randomizes a 52 card poker deck, and that any higher number in no way unrandomizes(or any other such craziness). keep in mind however that 7 perfect rifle shuffles will put the deck in the same exact position. Assuming a person shuffles by splitting his deck approx in half and does a rifle shuffle accurately, then he will get on average exactly what he should over an infinite time frame. you can figure out the exact probabilities for no land hands, 1 land hands, 2 land hands, etc all the way up to seven land hands with any mana ratio. note: you should shuffle at least 1,000 hands to see if you are shuffling properly using this method. 100 will not give as accurate results, but will be fairly accurate for the middle ranges(ie 2-4 lands).

Any person that never mulligans is either cheating or keeping subpar hands.

[Gabethebabe]

To the originator of this threat I would like to say:

20 land in a ponza deck is not enough.

I don´t know how you get 1-land hands all the time. Drawing 7 cards from a deck of 60 cards containing 20 lands you should have:

0 land: 5%
1 land: 20%
2 land: 32%
3 land: 27%
4 land: 12%
5 land: 3%
6 land: 0.4%
7 land: 0.02%

[Machinus]

Here is the formula for calculating the exact probability of drawing a specific mana/spell ratio:

S = number of "spells" in library
M = number of "mana" in library
s = number of "spells" drawn
m = number of "mana" drawn

[(S+M-s-m)!*S!*M!*(s+m)!]/[(S+M)!*(S-s)!*(M-m)!*s!*m!] = probability of drawing a hand with the given properties.

Note that you can adjust total library size to be over sixty, or adjust your opening hand to be seven, eight, or whatever you want. I just tinkered this up so if anyone feels like checking my formula, let me know if you find any errors. It does give the results posted by Gabe, however.

[SliverKing]

I think the 'randomization' of shuffling is part of whats worst in Magic...

If we all had the same set of hands shuffling all our decks for us in the same way, things would be ok. Still luck based, but at least even.

As it stands, the system encourages people to cheat and punishes people who really randomize.

I've said many times (as I stare at my wasteland, mox pearl, force of will, no blue card hand)  that if I could invent a perfect randomizing machine that could handle sleeved cards withotu damaging them, I'd be rich.

on a more realistic note, i've started doing excessive-number-of-pile pile shuffling. as many piles as I can fit in my play space.  and then picking them up in a random order.  the idea being that hte only true randomization method would be a '52-card pickup' method, and 20-30 piles picked up at random and then riffled a few times is as close as I can get.

[Matt]

That sounds interesting. Does it work well?

[AIcOPed]

the excessive pile shuffling is very close to being perfectly random after two or three shuffles since if you could do 60 piles and randomly pick each card that would be perfect "shuffling"{this is how computers shuffle}. Since you are dividing into 20 piles the individual  piles will have approx three cards thus a few shuffles are needed to distribute the cards from the piles they were in.

[Zherbus]

Moved. Not because it doesn't have good posts, but because of its basic nature.[/color]

[Machinus]

n00bs can do factorials?