I mean for example look at this... with over 40 games in the sample where he drew 12 our of 12 lands and lost (surely a concession, but that doesn't really matter). Note: that he basically never drew 0 lands. That on it's own is a shocking result - as I would expect a lower amount of games lost for 12 out of 12 lands than lost for 0 out of 12 lands. Probability of 0 is supposed to be much higher.

In any case, even if I remove the low end tails I get similar results - e.g.: games where he drew too few cards.

If I cut every trial below 16 cards (inclusive) the data still rejects the true mean with 99% confidence.

Mean: .4678754
SError: .008845
Confidence Interval (.443495 .4922557)

1059 Observations btw in that sample.

Probability true mean is .43333333 is basically 0

That should be impossible.

I have a hard time reading your graph on the x axis DJ.. the 20 games in that sample, did he draw less than 10% lands or 15 % lands for example? The expected value for a n = 12 drawing strictly less than 2 land is 0,002 , whilst strictly less than 3 is 0,036, so you can see that it is quite important to represent those percentages accurately, to see how much they are skewed from the expected results; the mean gets incredibly twisted from the top end flood, but the screw ratio also seems off, but without understanding your x axis better, no way to be sure.



LSO : Dmann and Eon, i've reported both of you, this is ludicrous.

Well if so, your plots confirm what I stated earlier, that it's clear that they managed to both screw up the manascrew and the extreme flood... both are off by alot.

The mean is skewed because of the extreme likelihood of flood, but the screw is also higher than expected.

I would like someone else to chip in though, It's been years since I had to interpret these type of results.

yes that's true, duels is rarely over by t5 due to having a BUSTED hand, so I'm guessing what you say represents a majority of games within that sample. What's the sample size for my initial proposed n of 16/17?

So the conclusion is to build decks that can work with few lands and have ways to cycle excess lands or include large amounts of fixing/ramp. That's kind of what most people actually do already.
But good work Dj!

Could it be that the algorithm has been tweaked somehow to accommodate the fact that we get that extra full/free mulligan? Could it be the other way around, that the whole extra free mulligan thing is just a band-aid fix to accommodate a flawed system that got passed off as a "feature"?

@ Dmann : But why would you do that ? It's perfectly trivial for them to use code that is capable of approaching 'predicted' distributions... I mean WOTC runs magic online which never displayed these issues, and ffs, code that comes close to randomization is freely available ???

Okay, so some things that come off immediately. We can reject with 99% confidence that the true mean of the population is .43 at basically every level of n except a couple. That's an odd finding, since we know that the true mean is .43. This isn't an indication of a broken shuffler with fat tails, this is an indication that the shuffler consistently prefers to put land toward the top of the deck - in other words a 26 land deck is closer in terms of its performance to a 30 land deck.

That's not just a problematic shuffler, that's a complete systematic failure.

I'm not trying to start trouble here, but are you sure the deck had 26 lands in it? And no ways to consistently draw additional lands. Because if not, the duels shuffler doesn't work at all. And I don't mean slightly broken, I mean completely and obviously broken.

If you hadn't told us that the deck had 26 lands in it I would reject that possibility with near certainty. The minimum number of lands I'd even believe (had you not explicitly told me otherwise) is 28, but the data indicates 30.

Mean:.4956765
SError:.0124345
99% CI: (.4619118 .5294411)

FYI, I clustered the data by cards drawn, as it was supposed to be, in case you want to find how I got the exact numbers - doing so increases the Confidence Interval, so if we don't think it's necessary, then the rejection is even stronger.

For the record, these are shocking results.

Let's be a little more clear here: this absolutely suggests that you would always expect to draw too much land. It's not suggesting that low lands lead to few land draws, or high lands lead to high land draws - it's suggesting that no matter what you'll draw too many lands. It damn near suggests that mana screw (not flood) is extremely unlikely - should basically never happen.