How random is the computer when compared to shuffling real cards?
Whether it's cockatrice, xmage, octgn, vpt or mws. Almost everyone complains about shuffling.
Suppose I build a deck with 30 lands and 30 spells. If shuffling is perfectly random and the distribution of cards if even, most common shuffling result would be land - spell - land - spell .... Stacking all lands or all spells at the bottom should be close to never.
However, it's pretty common to draw or not draw 4 - 5 lands in a row, or the initial hand to contain 1 land and then no lands for 5 turns. And even if I mulligan 2 - 3 times, mana screw or mana flood.
Should shuffling be biased? That is, introduce bias to make the bad shuffling results impossible? From what I know from physics and statistics, there is no known function that is the perfect random number generator.
Suppose I build a deck with 30 lands and 30 spells. If shuffling is perfectly random and the distribution of cards if even, most common shuffling result would be land - spell - land - spell
People complain about shuffling because they're bad at math and worse at statistics. Essentially none of the possible arrangements of that deck have the order "land spell land spell" all the way through.
there is no known function that is the perfect random number generator.
Sure but the Mersenne Twister (what Cockatrice uses) has a period of 2^19937. You could play a hundred games of magic every day for the rest of you life using a single seed for it and never be able to predict the next card drawn (unless you privy to the exact implementation of the shuffling algorithm in which case you'd need "only" a few hundred draws to predict the next draw which would still be irrelevant to any game I can imagine playing). In practice the program runs again every time you shuffle.
Suppose I build a deck with 30 lands and 30 spells. If shuffling is perfectly random and the distribution of cards if even, most common shuffling result would be land - spell - land - spell .... Stacking all lands or all spells at the bottom should be close to never.
While it's true that even distributions are more common then clumped distributions, that's not the same thing as saying that a perfectly even weave is the most likely outcome of a properly random shuffle. Clumps happen, and people overestimate how good of a sample size selecting 8-9 cards out of 60 are. I would expect a fairly even distribution if I took a 6000 card deck, shuffled it according to a random sequence, and drew a 700 card opening hand, but 60 cards are just not enough to make anything statistically significant.
Case in point: On the first try, I went to random.org (which uses atmospheric noise to generate random seeds, thus purportedly being free from the bias inherent to most pRNGs) and got the following sequence when I told it to sort the integer sequence from 1-60.
I went in with the intent to interpret even numbers as lands and odd numbers as nonlands, to simulate your 30-30 split, in which case I would draw an opening hand of 5 lands and 2 spells, then draw lands for my first 5 straight draws. If you go with 0-30 as lands and 31-60 as spells, it's a similar picture - 3 land opener, 1 land on the first draw, then 5 nonland cards in a row. Not bad if your curve tops out at 4, but far from even.
Humans, in general, won't recognize randomness as actually being random. One example I've seen is an experiment where people looked at two squares with dots distributed throughout them. In the first one, the dots were fairly evenly distributed, whereas the second one had areas with large clusters of dots and other areas where there were no dots. Most people said that the the dots in the first square had been distributed randomly. But it didn't - the experimenter had started with the dots being evenly distributed and then moved each dot a little ways (a random, but small, distance in a random direction). The second one had each dot placed completely at random, and some happened to end up near to each other.
This is even worse in the case of card games, since most people are used to using hand-shuffled decks, and hand-shuffled decks aren't that random. If all possible card orders are equally likely, a perfect distribution of lands and spells (land-spell-land-spell throughout the entire deck) is just as likely as having all your lands or all your spells on the bottom of the deck! Over a large number of games, however, you will draw almost exactly the same number of spells and lands, but this won't be reflected in small sample sizes: You've got a 1 in 4 chance of drawing two lands with Divination.
On the idea of a biased shuffling system: The obvious answer would be "no", but if we assume that player-shuffled decks are biased towards a more even distribution of lands and spells, then you could argue that it should be biased.
If a 30 land, 30 spell deck was presented with alternating land, spell, land, spell all the way through, not only is that not 'random', any judge would take that as absolute, conclusive proof of cheating and DQ the player on the spot.
In fact if a 30/30 deck was presented with no string of 5 consecutive cards that were all land or all non-land, that would be strong evidence (not conclusive proof) of cheating. A player that presented such a deck would have a judge observe their shuffling routine in future.
Even a rudimentary implementation of randomness in a computer program is considerably more random than any shuffling routine that can be performed with real cards in the timeframes used in tournament Magic.
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Whether it's cockatrice, xmage, octgn, vpt or mws. Almost everyone complains about shuffling.
Suppose I build a deck with 30 lands and 30 spells. If shuffling is perfectly random and the distribution of cards if even, most common shuffling result would be land - spell - land - spell .... Stacking all lands or all spells at the bottom should be close to never.
However, it's pretty common to draw or not draw 4 - 5 lands in a row, or the initial hand to contain 1 land and then no lands for 5 turns. And even if I mulligan 2 - 3 times, mana screw or mana flood.
Should shuffling be biased? That is, introduce bias to make the bad shuffling results impossible? From what I know from physics and statistics, there is no known function that is the perfect random number generator.
People complain about shuffling because they're bad at math and worse at statistics. Essentially none of the possible arrangements of that deck have the order "land spell land spell" all the way through.
Sure but the Mersenne Twister (what Cockatrice uses) has a period of 2^19937. You could play a hundred games of magic every day for the rest of you life using a single seed for it and never be able to predict the next card drawn (unless you privy to the exact implementation of the shuffling algorithm in which case you'd need "only" a few hundred draws to predict the next draw which would still be irrelevant to any game I can imagine playing). In practice the program runs again every time you shuffle.
Case in point: On the first try, I went to random.org (which uses atmospheric noise to generate random seeds, thus purportedly being free from the bias inherent to most pRNGs) and got the following sequence when I told it to sort the integer sequence from 1-60.
I went in with the intent to interpret even numbers as lands and odd numbers as nonlands, to simulate your 30-30 split, in which case I would draw an opening hand of 5 lands and 2 spells, then draw lands for my first 5 straight draws. If you go with 0-30 as lands and 31-60 as spells, it's a similar picture - 3 land opener, 1 land on the first draw, then 5 nonland cards in a row. Not bad if your curve tops out at 4, but far from even.
This is even worse in the case of card games, since most people are used to using hand-shuffled decks, and hand-shuffled decks aren't that random. If all possible card orders are equally likely, a perfect distribution of lands and spells (land-spell-land-spell throughout the entire deck) is just as likely as having all your lands or all your spells on the bottom of the deck! Over a large number of games, however, you will draw almost exactly the same number of spells and lands, but this won't be reflected in small sample sizes: You've got a 1 in 4 chance of drawing two lands with Divination.
On the idea of a biased shuffling system: The obvious answer would be "no", but if we assume that player-shuffled decks are biased towards a more even distribution of lands and spells, then you could argue that it should be biased.
In fact if a 30/30 deck was presented with no string of 5 consecutive cards that were all land or all non-land, that would be strong evidence (not conclusive proof) of cheating. A player that presented such a deck would have a judge observe their shuffling routine in future.
Even a rudimentary implementation of randomness in a computer program is considerably more random than any shuffling routine that can be performed with real cards in the timeframes used in tournament Magic.