Ambassador Laquatus + Gaea's Blessing

[Lunk]

I sent this in to the SCG ask the judge, but overcomplicated the question (and made several errors in the way I put it), and was basically told "uhh, in sanctioned play, you're screwed."  I know that Blessing is a fairly common answer to Laquatus (or was), and yet no one I talk to seems to know what happens :p

My opponent mills me a lot (1,000,000 times) with Laquatus.  I have a Gaea's Blessing in my library.  What happens?

I'm fairly certain a few months ago I saw a post by one of the resident rules gurus explaining an accepted simulation method to cut down on the actual number of millings necessary, but I've searched high and low and haven't found it.

Thanks!

[Jebus]

This isn't that hard.

Assuming you had an arbitrariliy large amount of Mana (such as from the Dragon combo) you mill them until you hit a Blessing.  Blessing triggers.  YOu can respond to the Trigger by milling some more.  Repeat until you either stop milling or they have no library.

At this point, you have to begin resolving the Blessing trigger(s).  Each one will shuffle the graveyard back into the library.

The only way to win in this situation is to mill them out, then use an instant speed draw spell such as Ancestral Recall to force them to draw.

[Lunk]

But if you don't have a Recall or some other way to draw them out (i.e. you went with Laquatuss without realizing they had blessing), what's the proper resolution to decide what ends up in my library and what ends up in my grave if they simply pump all their mana into Laquatus?

[dandan]

On average there would be more than half your library left as they have to mill in lumps of three. They would only have X mills left after the last time they hit Blessing, all previous million mills and reshuffles being ignored. As X is the number of mills without hitting a blessing after all the nonsense, I would just mill away a third of your library (divide the number of cards into three and mill away a third rounded down of those groups of three) and shuffle any Blessings back into the library in a casual game (you can mill cards to 'replace' the Blessing if you like) (larger activations without hitting Blessing are less likely so you have to skew towards smaller activations, in addition the fact that you mill 3 at once also reduces the average (think of 3 cards left in the library as the extreme case, the only possible result is X=0, a full library)

Of course in a sanctioned match you can't do the above and either player could insist on playing out all of the mills to determine the correct end state making the game fail to finish on time.

I hope the explanation of how to resolve it in a casual game makes it clear why you couldn't resolve it that way in a sanctioned game!!!

[Jebus]

I suppose you could use the Formula for calculating what to do in case of a Brain Freeze then.

I'll have to dig it up though, so it may not be up until later today.

[brianb]

Suppose you were playing dragon with Laquatus kill and didn't have ancestral to kill with, but you had a couple of counters (or a deathgrip or something to stop hardcast blessings) and a way to sink mana (that can't be used as a kill condition itself).  Your opponent has 47 cards in his graveyard/library, two of which are Gaea's Blessing.  Every time he reshuffles his library, there is a one in 46 times 47 chance (0.05%) that the two blessings will be the last two cards in his library after milling away the top 45 cards.  Given sufficient mana, I can be arbitrarily certain of eventually achieving this game state, from which I can eek out a win.  Can we just skip to that game state or do we have to actually achieve it (which might take a few thousand shuffles and would almost certainly take all the remaining play time + as much overtime as any sane judge would allow)?

[Lockdown]

Most people would probably allow it, providing you have the ability to sink the mana into something like Grim Monolith.

[paradigm]

Your opponent has 47 cards in his graveyard/library, two of which are Gaea's Blessing. Every time he reshuffles his library, there is a one in 46 times 47 chance (0.05%) that the two blessings will be the last two cards in his library after milling away the top 45 cards.

I'm not certain, but I believe the odds are actually lower than 1/47 that this will occur as there exists something like 47^47 different combinations (and thus, much smaller percent that the two blessings are in the bottom three). In addition, the problem becomes that even if the odds were as (high?) as 0.05%, there is a minute probability that it never occurs, and thus, your opponent can chose to draw it out (since the alternative is a loss) by forcing you to prove that it does occur in that fashion eventually.

[brianb]

The precise probability would be 2/(46)(47)--just under one in a thousand.  The exact number isn't important, though.  The occurrance of any small finite probability becomes arbitrarily certain if you do enough repetitions.  If you accept that argument, you could extend it to state that you could choose the exact configuration of your opponent's deck--ensuring not only two blessings left, but the entire graveyard milled out in the exact order you wanted (at least up to groups of three, within which your opponent could choose the order).  If you don't accept it, then the game will almost certainly be a draw that uses up all the remaining time.

To answer the original question, I would do as follows:

Your opponent shuffles his graveyard into his library (as if a blessing had just triggered).  You choose some amount of mana between zero and the number of cards in the library.  The number you choose should have the same remainder when divided by three as the original "infinite" number.  If you were smart and chose the original amount wisely, you avoid mana burn.  Do the last bunch of activations by the book, stacking them as you wish, resolving the gaea's blessings triggers as appropriate.

[dandan]

That is no a good way of resolving it as some decks (i.e. those using Welders, YawgWill) might want a large graveyard. The Dragon player would choose 0 giving their opponent no graveyard.

In a tournament I would not accept a loss because it was very very very probable that my library would end up in a given configuration. Kill me or don't kill me, saying I have cancer doesn't mean I am dead.

[Cuandoman]

If you could infinitely mill them and let Blessings resolve, you could do it over and over again until they have 1-3 cards left. One or more will be blessings. Statistically it WILL happen eventually.

[Lunk]

The problem with that solution is that Dragon has infinite mana, but generally only before Laquatus hits play, afterwards it can't generate more (ok, maybe 3 or 4 more, but you get the idea).  Sure, I can declare that I want to generate 18 billion mana and it's a fairly safe assumption that somewhere in those 6 billion mills Gaea's Blessing will be the last card left.  However, unless it's within 6 mills out of 6 those billion, I'm going to have over 20 mana floating and burn myself to death at the end of the phase, before they draw themselves out.

[dandan]

Statistically you are Chinese but in a few years will be Indian. Statistically we shouldn't exist. Statistically 99.99% of Dragon players cannot tell me how likely it is that I only have 2 cards left in my library after a set amount of milling but a good number could work out that a large amount of milling/shuffling within the time limits in a tournament including enough time to play out another 3 turns will not give a sufficiently high percentage chance of it happening for it to constitute a win. Is it certain? No. Then play it out.

In addition, I am no obligation to reveal the entire contents of my deck to another player, even one with infinite mana. Do you want to mill me? Fine. Again? Fine. Again? Fine. You are the active player, let me know when you have won or you want to resolve something. I am not stalling if you cannot decide how often you want to mill. Seen any Blessings yet? I'll be damned if I tell you if I have any. 1-3 cards left in my library, go ahead. So you need to mill me around 17 times to even see if the Blessing problem comes up, then I need to thoroughly shuffle X times according to how many Blessings I have. Then assuming I have Blessings you need to repeat enough times so that I have the Blessings neatly stacked somewhere in the last 2-4 cards (depending on the original number of cards in my library) and you have to have a way of countering at least one of them. I cannot know if you have such a method or not (damned odd Dragon deck, no Ancestral but counterspells). Play it out.

Lies, damned lies and statistics.

[Jebus]

You can't use statistics to justify stacking your opponent's deck and graveyard in a configuration that is probable at some level to do so.

The method used to determine the outcome must rely on some form of randomness.

[brianb]

However, unless it's within 6 mills out of 6 those billion, I'm going to have over 20 mana floating and burn myself to death at the end of the phase, before they draw themselves out.

That's why I presupposed you have a mana sink or something.

In addition, I am no obligation to reveal the entire contents of my deck to another player, even one with infinite mana.

Seeing your whole deck (less your hand) is the easy part.  I can do that easily without resorting to statistical arguments.

As for getting just the ideal configuration, the opponent is probably justified in turning down the statistical argument to let me stack his deck, no matter how inevitable it is.  So the end result is that we shuffle, shuffle, shuffle until he concedes the point and lets me stack the deck; I find a configuration I like; or time (plus all the overtime) expires in the round.  Which of these happens will depend on the game score, the overall tourney point status, and whether or not the opponent is confident that he can win anyway despite letting me stack his deck (which he probably can in most circumstances).  I just brought this up because it's an odd corner case that slips in between the cracks of the infinity rule and the stalling rule.

[DEA]

to put this colloquially : balls to you
no, you can't stack the deck in ANY manner because you don't know what the card is before you mill it
this is schrodinger's cat all over again
you're using what you *think* is the probable outcome to dictate the actual state of the deck which is basically *bullshit*

play it out

[paradigm]

This thread reflects why Gaea's Blessing is not a great answer to Dragon in a format with Tormod's Crypt, Coffin Purge, and Ground Seal, among the instant speed BEB, STP, and so forth.