This thread is an institution, there is no way I can let it die with the WotC Forums.

First, the [O]fficial explaination of how the MTGO shuffler works, originally provided by Chris Green, president of Leaping Lizards (who developed the thing), preserved by muriban and passed on to Vitalogy1994 who posted it in the last incarnation of this thread:

We have no guarantee the shuffler is identical to the original incarnation of MTGO, but there also doesn't seem to be a reason they would change it.

The primary reasons people think the shuffler isn't random:
Most people are under the misconception that a random distribution means an even distribution. Random distributions have natural clustering.

Experience doesn't match what they are used to in paper; there are many poor (human) shufflers out there. When confronted with *actual* randomness of the computer shuffler, they blame the computer instead of their own faulty shuffling practices. In reality these people have been unknowingly cheating for a long time.

People tend to remember significant events more vividly then normal occurrences. They remember the times when they were horrifically flooded but forget all the normal games in between.

Now, some required reading before you post if you want any hope of people caring what you say:

Stats 101: Am I Shuffling Enough - Or Correctly, For That Matter? - A very good explaination of what a randomized deck *should* look like; it's far different than many think. [Provided by Vitalogy]

The Wikipedia Entry on Knuth Shuffling. Here's a code snipet using the method [adapted from code posted by many]:

Actual OpenBSD code for a strong random number generator using hardware noise. Includes underlying theory [pointed out by slpalmer]

Article describing similar complaints in bridge since they switched to computer-generated deals 30+ years ago. Turns out (suprise!) people weren't shuffling correctly so their expectations were wildly different than should occur with truely random deals. Also discusses how many shuffles are necessary to randomize a deck. [Provided by me]

Math Magic Made Easy - Excel™ spreadsheet I created that computes various Magic math situations. One of the pages produces the probability of drawing so many cards of a certain type (listed as lands) out of N cards drawn from a deck of your choice. This should be useful if you want to try and disprove the shuffler by drawing a set number of cards from your deck instead of comparing the number of land clumps in the full deck as SCG does. [Shameless self-plug]

If you want to try and disprove the randomness of the shuffler, here are some things you MUST do:

Use EVERY trial you do, don't pick-and-choose 'bad' ones and note them.

Run a BARE MINIMUM of 1000 trials. Hundreds of thousands would be better.

Read up on statistical confidence intervals and learn how to conduct a T-Test, Z-Test or similar.

Xtofyr recorded data for several thousand hands. The initial results appeared skewed and prompted more thorough testing by elf. These later tests show the shuffler to behave as expected. Unfortunately, the full discussion thread and results have been lost.

The probability for common MTG cases:

Seven Cards (opening hand):
#land drawn|16/40|17/40|18/40|23/60|24/60|25/60
0|01.86%|01.31%|00.91%|02.67%|02.16%|01.74%
1|11.55%|09.20%|07.20%|13.84%|12.10%|10.51%
2|27.36%|24.55%|21.61%|28.56%|26.94%|25.22%
3|31.92%|32.30%|32.02%|30.29%|30.87%|31.18%
4|19.76%|22.61%|25.28%|17.82%|19.64%|21.44%
5|06.47%|08.40%|10.62%|05.80%|06.93%|08.19%
6|01.03%|01.53%|02.19%|00.97%|01.25%|01.60%
7|00.06%|00.10%|00.17%|00.06%|00.09%|00.12%
2-5|85.50%|87.85%|89.52%|82.46%|84.39%|86.02%

Six Cards (mulligan):
# land drawn|16/40|17/40|18/40|23/60|24/60|25/60
0|03.51%|02.63%|01.97%|04.64%|03.89%|03.24%
1|17.72%|14.90%|12.35%|20.03%|18.07%|16.21%
2|33.22%|31.37%|29.16%|33.38%|32.47%|31.37%
3|29.53%|31.37%|32.74%|27.49%|28.87%|30.07%
4|13.09%|15.69%|18.42%|11.78%|13.37%|15.03%
5|02.73%|03.71%|04.91%|02.49%|03.07%|03.71%
6|00.21%|00.32%|00.48%|00.20%|00.27%|00.35%
2-4|75.84%|78.44%|80.31%|72.64%|74.71%|76.48%

Eleven Cards (5th turn play/4th turn draw):
# land drawn| 16/40| 17/40| 18/40| 23/60| 24/60| 25/60
0|00.1080%|00.0585%|00.0305%|00.2495%|00.1753%|00.1217%
1|01.3574%|00.8413%|00.5035%|02.3378%|01.7801%|01.3392%
2|06.7869%|04.8074%|03.2920%|09.1842%|07.5820%|06.1810%
3|17.8157%|14.4222%|11.2870%|19.9518%|17.8719%|15.7958%
4|27.2476%|25.2389%|22.5739%|26.6024%|25.8834%|24.8220%
5|25.4310%|27.0205%|27.6531%|22.8266%|24.1578%|25.1644%
6|14.7232%|18.0137%|21.1465%|12.8399%|14.8064%|16.7763%
7|05.2583%|07.4493%|10.0697%|04.7247%|05.9490%|07.3445%
8|01.1268%|01.8623%|02.9149%|01.1117%|01.5323%|02.0656%
9|00.1366%|00.2660%|00.4858%|00.1588%|00.2404%|00.3547%
10|<0.0001%|00.0193%|00.0416%|00.0124%|00.0206%|00.0334%
11|<0.0001%|<0.0001%|<0.0001%|<0.0001%|<0.0001%|<0.0001%

NB: booster/tournament packs are NOT random, nor are they intended to be. They are created using card listings called print runs.

If there is anything important you think I missed, let me know.

Credits: Everyone who has contributed their time to the rational discussion of the shuffler in various threads over the years.
Edit (23 Nov 05 19:05 UTC): Added 'Sweet-spot' total probabilities (at least 2 lands + 2 spells in opening hand) and probabilities for a mulliganed hand.
Edit (10 Jul 06 05:53 UTC): Added link to data provided by Xtofyr and Elf.
Edit (18 Jan 08 20:10 UTC): Updated FAQ reference
Edit (15 Mar 10 19:50 UTC): Reformatted with html tags
Edit (26 Sep 15 18:47 UTC): Port to NGA Board

It hasn't changed a bit--it's still just as beautiful as I remember. And just in time for the new scry-mulligan rule to change the classic expected land calculations and ruin everything. I'm not sure when MTGO's going to implement it, but when it does the probability tables might warrant changing up to take it into account.

It should look the same, I just copy/pasted and made spot fixes.

I've been away from Magic for a couple years, so ping me when the Scry change happens so I can update.

I really need to carry this thread around and slap people over the head with it.


Good thread.

this is a nice thread

yeah, when they say that "computer random number generators" aren't random, they mean that they might repeat a sequence after 100s of billions of generations. No one plays MTGO that much.

True randomness should repeat a sequence after 100s of billions of generations to be fair.

True Randomness is any organization of cards that makes me win and my opponent lose.

Wow, when I heard people mentioning the "MTGO Shuffler Thread" I expected something full of confirmation bias and misconceptions about probability. This is 100% the opposite of that. Well done.

**** ****

I still wonder why the test shuffler in the client code is not the same as the server shuffler? At least that is what they are saying when the test shuffler was found to not be random enough.

If this thread is like the original, those will appear quite often.

Indeed. The whole point of the shuffler thread is to (1) consolidate all that idiocy into one thread (any other threads on the topic were promptly locked, and I hope the same will be done here) and (2) preemptively rebut the complaints so we don't have to post the same response repeatedly.

Are you planning on bringing over the history of magic online as well or is that so out of date or too much work?

I was thinking about it, but I didn't want to be responsible for maintaining it. It would be better if someone who wants to maintain it bring it over. I'll do it if no one steps up.

Ironically (or not, i have no idea what irony is), DotP has this thread too. It was one of my favourite reads and I imagine it is much of what the old thread contained.

viewtopic.php?f=38&t=11283

No no no no no no no no no no. Don't make me remember.

I appreciate the reasonable nature of your remarks. I am unclear on what, about the shuffle, I described would be considered a poor shuffle. According to researchers 7 riffle shuffles are enough to mix a deck of cards thoroughly and that more than 7 does not improve the mixing. http://www.nytimes.com/1990/01/09/scien ... umber.html . I listed 5-10 shuffles being done by each player which would mean that if each player shuffled their deck 5 times and their opponent shuffled their deck 5 times each deck would get shuffled 10 times. If the opponent declined to shuffle after you only shuffled 5 times it could be shuffled too little. Since riffle shuffling 7 times is enough to mix the cards thoroughly it shouldn't matter if you stack all your lands on top first but I think that most people will mana weave their deck first and according to Wizards mana weaving is not illegal if it is followed by other forms of shuffling http://archive.wizards.com/Magic/magazi ... /20060707a .

Since we have the statistics of what a random deck should do posted at the top of the thread; 2 or less lands by 11 cards (9.5347%) and 7 or more lands by 11 cards (7.74231%) for a combined percent of mana screw/mana flood of 17.277% for each player. One thing that I plan on doing now to collect data to compare results of shuffling verses MTGO is to count the number of hands, from a 60 card 24 land deck, that have only 2 lands by the eleventh card (mana screw) and those that have 7 or more lands by the 11th card (mana flood). Since it has been proven that 7 riffle shuffles are enough to put the cards in a random order I will always shuffle 7 or more times. Anybody that wants to contribute to the data can keep track of their own games as well. The percentages should become close to these numbers the higher the number of games that are counted if real world shuffling matches a randomized deck.

My friend refuses to shuffle, but rather cuts his deck 2 times, because 2 is closest to the golden number. When I showed him this, he said he thinks it's **** because he doesn't understand math. How should I help him?

My point re: Cheating on the WotC forums is that weaving your cards makes your shuffle non-random. Not merely insufficiently random. If a judge catches you doing that in tourney you will at least get a game loss and maybe more severe penalties. Don't mana weave. 5-10 is a big range. I would say 7-8 is a better range of shuffles. Of course sleeves make it more complicated to shuffle thoroughly without ruining your cards for trading purposes so learning how to do that well is important.

When you see pros shuffling you may see something that LOOKS like mana weaving because they often pile shuffle first but they are not sorting their lands into separate piles. Pile shuffling IS acceptable as long as you are not doing so in such a manner as to create a discernible pattern. Yes there are also cheaters on the Pro Tour and when they get caught it is a big deal and they get huge bans. But those guys are (perhaps slowly) getting weeded out and are not the norm.