Some remedies include shuffling the randomized portion of a player's deck. However several rounds into the game with the option of multiple scries and maybe even a Duskwatch Recruiter, players can easily lose track of how many cards on the bottom of their deck are considered non-random.
I usually go by the minimum number both players can agree on, but am wondering is there a better way to determine what is the non-random portion in such a case?

Review all the things that have happened in the game.

Did players mulligan?
Are there any Oath of Nissas on the battlefield?
Review the graveyard for cards like Anticipate.

Often times both players will remember details when prompted (Oh my opponent failed to find with their Oath so that's 3 cards, and there was a scry to the bottom from a mulligan, so that's bottom 4). If both players cannot remember exactly, use the clues present to solve.

Edited Jeff S Higgins (June 22, 2016 03:34:16 AM)

I prefer going for the maximum, and when in doubt, round up a little. If the bottom 5 cards are known, the next 5 cards were random, and you don't shuffle the bottom 10 cards of the library… we finish in the exact same situation! However, if the players mistakenly believe that the bottom 5 cards were known, you shuffle the rest of the library, and then they find out it should have been 6 cards, you can't restore that.
Shuffling the non-random portion is bad, leaving the random portion unshuffled and hence still random is not a problem. Just please don't waste too much time on determining the ecaxt amount of cards to be shuffled, unless in very rare corner cases where ir actually matters. Hint: it never does…

Dustin, I have to say I like that logic.

If players are not sure for effects like Duskwatch Recruiter or Collected Company, assume worst scenario - nothing was found, whole set wat put on the bottom. Sometimes you will get partial information when asking how many cards were put from particular effect, like “I hit something from that CoCo but I don't know if it were 2 or 1 creature”, just assume it was only 1.
Like Dustin said, its better to keep more than less on the bottom :)

So, lets say we are into a game with multiple effects organizing the bottom of the deck? start of game scry, a couple of CoCo and (now the tricky part) an unknown amount of duskwatch recruiter activations. Leaving you with a non randomized portion of the deck of unknown size.

While if we are talking about one effect, picking 6 cards for a single CoCo seems fine but when you have to account for the amount that for all you know can be 20+ cards?

Call me over when it happens in a sanctioned Competitive REL event, where no fetchlands have been cracked at all, and it is relevant whether we leave the bottom 15 or the bottom 20 in place.

You should make best estimation. Ask, how many creatures were for sure found through Recruiter, or if players recall how many times it was a miss. You can ask for how long he is in the table and estimate what is maximum number of activation that player could resolve, include there mana spent to cast other spells later. You need to do your best (in timely fashion) to estimate how many times he was activated, add a few cards to that just to be sure and stick to that. Way of doing this will vary a lot, depends on cards involved. If you believe that last 25 cards in library are known to player, when whole library at this point have 30 cards, that viable outcome. Unknown portion or library might be 5 cards size.

Just to remind, always say what you want to apply as a fix before executing motions and ask if both parties are OK with your solution. Players might appeal your way of fixing things and HJ might came with different solution and backing up fixes might be hard or impossible.

Originally posted by Dustin De Leeuw:

If the bottom 5 cards are known, the next 5 cards were random, and you don't shuffle the bottom 10 cards of the library… we finish in the exact same situation! […] Shuffling the non-random portion is bad, leaving the random portion unshuffled and hence still random is not a problem.

That's correct in the rare case when we shuffle a library for no reason, but it's incorrect when we are shuffling a card into the library. Leaving some bottom cards unshuffled increases the probability that the card shuffled in will be drawn.

For example, if we shuffle a card into the top 30 cards of the deck, the chance of drawing it is 1/31. If however, we shuffle it into the top 40 cards of the deck, the chance of drawing it is only 1/41.

Edited Isaac King (June 22, 2016 02:52:39 PM)

Originally posted by Isaac King:

For example, if we shuffle a card into the top 30 cards of the deck, the chance of drawing it is 1/31. If however, we shuffle it into the top 40 cards of the deck, the chance of drawing it is only 1/41.

I'm hoping that, with a minimal amount of reflection, we can all see why this is largely insignificant? and that this doesn't even come close to invalidating the excellent answers from Dustin and Bartlomiej?!?

d:^p

Originally posted by Scott Marshall:

I'm hoping that, with a minimal amount of reflection, we can all see why this is largely insignificant?

I disagree. The probability of drawing a specific card is one of the most important aspects of the game of Magic. It's why we place so much emphasis on shuffling well.

Originally posted by Scott Marshall:

this doesn't even come close to invalidating the excellent answers from Dustin and Bartlomiej?!?

Oh, I wasn't trying to invalidate their answers, my apologies if that's how it came across. I agree that in most cases, it's better to risk overestimating the number of non-randomised cards on the bottom than it is to underestimate it. I was merely pointing out that it's not as simple an answer as Dustin made it seem. After all, if that logic were completely sound, we could extend it all the way through the library and conclude that we don't need to shuffle at all!

Lowering the probability of drawing a card shuffled into the random portion of the deck is the original logic that guided me when choosing to go with the minimum number of cards that both players can agree on is non-random.

From Dustin's answer I take that “Not shuffling the non-random portion”>“The above”

The crux of what Dustin, Bartlomiej, and I are trying to say (I think, I may be putting words in their mouths that they'll quickly spit out!): if you can't be sure if there are 4 or 5 or even 6 “known” cards on the bottom of the library, then setting aside 6 and shuffling the rest is fine.

I'm aware that mathematicians - esp. those who love probability & statistics - will take offense at this, but I'm standing firm: it really doesn't matter enough to waste time determining whether it really is 4, 5, or 6.

Isaac, you took this to an extreme with your example - a difference of 10?! Really?!? I challenge the assertion that our inability to estimate is that poor; in reality, the difference has been 1 or 2 cards. If you insist on throwing this into the corner where a huge margin for error might exist, then I'm out. As you probably noticed, I don't function well in those deep, dark corners. :)

Further, your assumption is that the card we're shuffling away is the one that the player most (or least) wants to draw, next. It's far more likely that, were he to rank the desirability of the remaining 31 or 41 (!) cards, this one could be near the top, near the bottom, right in the middle.

As I said (but slightly mis-worded, my apologies) - with just a bit of reflection, we see that your concern really is insignificant; in reality, what we're trying to say is “it's better to err on the side of caution in these situations.”

d:^D

I actually had this exact scenario come up at GP Pitt this past weekend.

Player flipped the top card of their library over accidentally, “do you know the positions of any cards?”
“The bottom 3/5ths or so maybe, I'm not sure”

no evolving wilds or any shuffle effects anywhere. Player has activated Evolutionary Leap 5-7 times (confirmed by opponent, randomly Reid Duke). Quick investigation gets us to 6 activations.

Recognizing that Evo Leap can't put a creature on the bottom, I look at the contents to see where the first creature is. It's about 35 cards from the bottom.

I'm thinking about how to proceed, my plan is to ask them to estimate how many cards they flipped on each activation, and go with that number if it's less than 35.

Where I get lucky is that at this point I see an Oath of Nissa.
“Was that a turn 1 Oath of Nissa by chance?”
“Yes it was.”
“Do you remember the other cards you saw and put on bottom?”
*away from table* “it was a Hangarback and a forest or a plains, because I took the other Hangarback”

Bottom creature of the deck is a Hangarback Walker, above a forest and below a plains. I erred on the side of caution and set all three of those as the capstone of the “known contents” portion.

I reasoned that random is random, so if I'm shuffling 14 cards instead of 15 cards, they're still random and it's fine especially because only I know the 15th card so it's effectively random as well.