[Math] Gaea's Blessing, with arbitrarily large number of Brain Freezes

[Harlequin]

I would like to take a moment to consider an unanswered question in Magic. Consider the following gamestate:

I have an arbitrarily large amount of storm - say 1,000,000 (Tidespout Tyrant + 2  mox, or Salvager + lotus).  Now I cast brainfreeze on my opponent, and discover they have Gaea's Blessing in thier deck. 
- If we were to 'play it out' each time a copy of brainfreeze resolves that mills the Gaea's blessing, it will immediately trigger on top of the other Brainfreeze copies.  So it will shuffle Mid-stack, and you will continue to resolve brainfreezes on the newly complete and reshuffled library (minus cards in play, hand, and RFG).  As millions of copies of brainfreeze resolve, gaea's blessing will trigger hundreds of thousands of times. 
- Assuming we continue to play out the million copies, at some point we will approach the "End State."  The Graveyard will contain  either 0, 3, 6, 9, ... , up to the decks greatest multiple of 3.  Because there is a chance that the final brainfreeze will resolve and include Gaea's Blessing, and there is also a chance that the final brainfreeze will reveal 3 cards, with brainfreeze remaining in a tiny deck. 
-- The person with brainfreeze is generally hoping his opponent ends on a small deck.
-- The person with Gaea's blessing is generally hoping to have a big remaining deck
--- In both cases the cards left in the deck are of interest to both players.

So the purpose here, is to take a moment and apply some basic Probability and Statistics theories to this example.  The goal is to create a "Comparable Probability Model" to shortcut the End State. 

Let’s start with Definitions - these are going to be important if you intend to follow my logic.
D = Number of cards in the deck + graveyard at the beginning of the loop.  Often I refer to the "Deck" below, and really I'm talking about the remaining deck (Registered deck minus cards in play, hand, and RFG).
D0 = Number of cards in the LIBRARY when brainfreeze is actually cast.
D' = Number of cards left in the Deck when the final brainfreeze resolves.  In essence: THE END STATE!

Event G = hitting a geae's blessing
Event G' = not hitting geae's blessing.  In chains I'll denote this as "-"  So for example the chain -G---G would be 1 miss, 1 blessing, then 3 misses and a blessing.
G and G' are mutually exclusive and exhaustive... because in 3 cards you either hit blessing or do not hit blessing.

I = the total number of brainfreezes to resolve
i = the number of brainfreezes that have resolved.
x = the number of Events G' since the last event G

Gx = hitting a geae's blessing on the x-th brainfreeze from the last time event G occurred.

A High level look at Dependence and Independence:
Prob (Gx) = f(D, D0,  I)
* the probability of G is a function of I and D

Once the first Blessing is hit ...
Prob (G | X=x) is independent of i for all x

Using the variables:

Consider a deck of 6 cards, with 4 cards in the yard.
D = 10
D0 = 6

There are essentially 4 possible ends states:
D' could be: 10, 7, 4, 1

Consider I = 3

For i = 1, Prob(G) = Prob(G') = .5
Meaning of the 6 cards remaining in the deck Blessing is either in the top 1/2 or the bottom 1/2.

For i = 2, Prob(G) is dependant on the outcome of i=1.

Prob(G | i -> G) = Prob(G|x=0) = 0.300 = 3/10
Prob(G | i -> X) = 100%

For i = 3 Prob(G is dependant on X)
Prob(G | x=0) = 0.300
Prob(G | x=1) = 0.428 = 3/7

Possible Paths: End State

Code:

GGG: 10 -> 3/6 * 3/10 * 3/10
GG-: 7  -> 3/6 * 3/10 * 7/10 
G-G: 10 -> 3/6 * 7/10 * 3/7
G--: 4  -> 3/6 * 7/10 * 4/7
-GG: 10 -> 3/6 * 1/1 *  3/10
-G-: 7  -> 3/6 * 1/1 *  7/10

Possible End state Probability Distribution with

Code:

Prob(D' | D0 = 4, D = 10, I = 3)
10 = 0.345 = 69/200
7 =  0.455 = 91/200
4 =  0.200 = 40/200
1 =  0

So what does this tell us?  It says that in the given size 10 deck situation with 3 brainfreezes that after you resolve all three brainfreezes you a  34.5% chance to end with all 10 cards in your library, a 45.5% chance to end with 3 cards in your yard and 7 cards (including blessing) in your library, and a 20% chance to have 6 cards in your graveyard, and 4 cards (including blessing) in your library.  There is no possible way to end with brainfreeze being the last card of your library.

Here is an interesting observation.  Lets examine the same scenario (D0=4, D=10) but with I = 4...

Prob(D' |I=4) = Prob(D'=d|I=3) * Prob(G |x=X)
Ok, the math syntax isn't 100% right on that, but the idea is that if you start with each D' of I = 3, you can multiply by the appropriate probability of G or G' to generate the I=4.

Lets take a look:
d -> Prob(D'=d|I=4) = ...
Endstate: Prob -> derivation

Code:

7: Prob(D'=7|I=4) -> Prob(G'|x=0) * Prob(D'=10|I=3) 
4: Prob(D'=4|I=4) -> Prob(G'|x=1) * Prob(D'=7|I=3)
1: Prob(D'=1|I=4) -> Prob(G'|x=2) * Prob(D'=4|I=3)
10: Prob(D'=10|I=4) -> 
 = Prob(G|x=0) * Prob(D'=10|I=3) 
 + Prob(G|x=0) * Prob(D'=7|I=3)
 + Prob(G|x=0) * Prob(D'=4|I=3)

An Alternate way to define D':
The exact position of blessing in the deck after each shuffle is uniform... there is equal chances that it will be the first card, the last card, or any specific card in between. 

Lets look at new random veriable A.  Defined as the number of cards flipped before you hit blessing.  If D Mod 3 is 0, then the probability is uniform; but more generally The probability of A=a is a composite uniform distribution.  For example in a 61 card deck, its uniform from 1 to 20 at prob(A=a) = 3/61.  The final prob(A=21)=1/61.
 
Lets also consider the r.v. N ~ the number of times you hit gaea's blessing over the course of I. 

Using these rv's we can express D' ~ f(N,A).  I'm not sure that really helps us though... I think it could help us solve the expected value of D' - but that's not really useful to us since we are after a probability function not the moments.

So anyway, Lets take a look at some theory:

- If I > D'/3 then you -will- Blessing at least once.
- Once you blessing once, D0 really matter for future probabilities of G ... but it still could matter for the final result D'.

Deeper Dive into Probability:
Consider you are asked to bet a $1 on an arbitrary brainfreeze; say brainfreeze # 1000.   No brainfreezes have yet resolved, and You are betting on the cards left in a 60 card deck after Brainfreeze #1000 is done.  So your choices are number 60, 57, 54, 51, ... , all the way down to 3.  What number do you bet on (assuming you win the same amount for each winning bet)? 

The answer is 60.  Essentially you are betting that brainfreeze #1000 -WILL- have a brainfreeze in it.  Why is that?  The reasoning is a bit hard for me to explain but here goes:
Think of the entire string of brainfreezes as a time series, assuming each brainfreeze is evenly spaced in time. you want to think about how much time the deck spends in each given state.  So suppose you have the following 25 events in your serise:
---G- G---- ---G- ----- --GG-
*I broke it up by 5's just so it's easier to follow...

So consider the state of the deck:
60,57,54,60,57;  60,57,54,51,48;  45,41,38,36,33;  30,27,60,60,57

So the only way to get to 57 is to have a sequence that goes G- The only way to get to 54 is G-- and the only way to get to 48 is G----
and for every time you pass though to a number less than 60 you spend _exactly_ 1 interval at the number before it.   60 is a little different Every time you restart the deck you have to spend at least one interval of time at 60.  For each time the sequence goes "GG" you are spending essentially double time at 60.  Here is were you gain your advantage by betting on 60.  For every unit of time you spend at 57 you spend one unit at 60 as well... however it _is_ possible to go from 60 to 60.  And the small probability of "GG" is why you bet on 60.

Ok, same problem but now you cannot bet on 60.  What do you bet on now?  the answer is 57... by much the same logic.  57 will be reached more than 54 because of all the times you hit the sequence "G-G" You spend one unit of time at 57, and no time at 54.  But every sequence that spends time at 54 will also spend 1 unit of time at 57.

This "time spent" concept is what drives your Bet.  If you know its going to spend more time at a given place you should bet your $1 there. 

So what does all this betting have to do with the problem?  It is saying that the probability that D'=60 is greater than that of D'=57, which is in turn greater than that of D'=54... etc. *please note that this is NOT saying you will "always end with a full deck" its not even saying you will "Likely" end with a full deck (simulation shows that its around 10%).  But what its saying is that the probability of ending on any selected D' will be smaller as D' decreases.   

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So to restate purpose here: I want to examine possible comparable probability shortcuts to fast-forward (so to speak) through an arbitrarily large brainfreeze to the endstate.  Because lets face it... taking into account complete deck composition there are practically countless possible endstates... some of which are favorable for the caster of brainfreeze (ei 21 cards in the yard which contain all the win conditions,  will, and not blessing), some of which are favorable to the owner of blessing (ie 45 card in gy with all sorts of nasty mana and stuff but will and tutors still remain in deck), and many of which grant no particular advantage to either player.


Possible Models that I can think of ... none of which have probabilities associated:

Today) "The F-it Plan"
From what I understand the current method is just to shuffle up the geae's blessing into a finished deck and say that's the end state.  This is supported by the "highest probability" of that to occur, but It basically provides no possibility of advantage to the person casting brainfreeze.  In essence it makes Gaea's blessing a better card than it should be... because the brainfreeze player literally has zero chance to affecting you.

A) "Direct Endstate Probability Matrix"
Step 1 - Roll a D100 and compare result to a table based on size of Deck after the first blessing resolves.  This will determine the final end state.  So the table would look something like:
D100 -> Result
1-11 -> 0 cards in GY.
12-20 -> 3 cards in GY.
21-28 -> 6 cards in GY.
...
98-99 -> all but 6 cards in GY.
100 -> all but 3 cards in GY.
Then the strategy would be to remove the blessing from the deck.  Shuffle it up, and mill the correct number of cards given the result.   The shuffle the remaining cards in the library PLUS THE BLESSING together.

*limitation: tables of probability would have to be calculated for every possible # of cards left in the deck... because obviously the table for 10 cards remaining would be much different from 52 cards remaining.   There may be some opportunity to define tables for given ranges.  Also Judges would have to have access to these tables readily
*limitation#2: D100 only allows for a 1% variation... this would probably have to be a D1000 (3D10 of different color that represent defined digits) the D1000 would allow the tables to split on 0.1%.

*Advantages:  You cut right to the end.  And it would take little more than the time required for the judge to look up the correct table and roll some dice. 

B) "Fast Forward to the Tail"
Lets say we prove that Storm = 10,000 is statistically the same as storm = 1,000.  What we would have to do is back into the Storm require to reach a 'significantly equal' probability model.  So lets say we can say ... with it 0.05% storm 28 is the same as all storm values larger than 28.  So it would be fairly easy...
Step 1 - allow the first part of brainfreeze to resolve, and shuffle up the deck.
Step 2 - take the fully shuffled deck and flash forward to the last 28 copies of brainfreeze... and assume that your end states going forward will fit the distributions of the "tail end" of an arbitrarily large storm.
Step 3 - resolve the final 28 copies as you would if you got hit for a storm 28 brainfreeze... and empty the stack.  If you hit blessing, continue to shuffle and resolve copies. 

*Limitation - I can't even begin to imagine what this number will be, but I would guess its probably around 40 to 50...possible up around 100.  So really, in the constraints of a 50 min round this may not be a 'short cut' at all.   You still take lots of time, and also risk doing damage to cards because of multiple shuffling
*Advantages - It requires no tables ... just a magic number that applies to any deck with less than 60 cards left in deck.

C) "Hybridized Probability Matrix"
Basically generate a near tail-end probability table that would (using conditional probability) be similar to the end state probability.  So something like:
d6 -> Tail End resolutions
1 -> 2
2 -> 4
3 -> 6
4 -> 8
5 -> 10
6 -> 12

Step 1 - resolve the first blessing and shuffle the deck.
Step 2 - roll a d6 an get the tailend resolution number.
Step 3 - with the shuffled deck including gaea's blessing, resolve that number of brainfreezes.  So for example if you roll a 4, you simply resolve 8 additional brainfreezes, and then consider the stack empty.  If you encounter blessing during these tail end resolutions resolve them normally.

Limitations:  It may not even be possible to create this type of model.  The complexity here could be enormous.  On top of that proving the two models to be insignificantly different would be equally daunting.  As a judge you would still need to refer to a table (unless its simply like # times 2 as illustrated above).
Advantages: This method shortcuts method-B because at most you have to resolve 12 brainfreezes, and typically you would end up resolving less.  So its a time saver over method-B and not as "have faith in mathematics" as method-C does.




////////////////////////////////////////////////////////////////

Currently I have built excel based simulation tool which alows me to run thousands of trials while controlling each variable.  So if my probability skills are not up to the task - maybe my statistics skill can help back into the probability distribution.

So far the simulations I've run support my claims - but no real numbers or percentages to report.


I'd love to hear more from some mathematicians, statisticians, and Tournement Judges on this!

[Anusien]

The current word from the DCI is none of the above.  It's not a loop that can be shortcut through.  You have to actually play it out and see what result you get.  The DCI does not require its judges to have studied probability in order to be a judge.  Accepting a piecemeal solution like this would lead to uneven judging based on the floor judge or head judge's personal knowledge of statistics.

It's not an unanswered question in Magic, it's been asked and answered.  People just don't *like* the answer.

[Shock Wave]

You may want to contact Dicemanx and have him post his $0.02. This is exactly like the Dragon situation where you can mill infinitely, the ideal circumstance being their Blessing ending up as their last card. I know he has received different feedback from different judges, so he may have something to add.

[oneofchaos]

So what exactly happens in this scenario?

Player A has got a bajillion freezes going off vs Player B's Gaea's Blessing.

Now it's not an infinite combo in the way dragon was, so we can't just end the game in a draw.  Now somebody has to conceed.  Who would do that.

Nobody conceeds.  The arbitrarily large number has to be played out, copy for copy all one hundred thousand.  Now, time in the match of course ends, but five turns are untimed.  Do you give both players a double loss in order to continue the tournament?  I just figure this is an issue that while not incredibly relevant needs to be answered by the DCI due to the confusion it holds (how will the head judge rule, it's his say).

-thanks
Dave

[Anusien]

Now it's not an infinite combo in the way dragon was, so we can't just end the game in a draw.  Now somebody has to conceed.  Who would do that.

Nobody conceeds.  The arbitrarily large number has to be played out, copy for copy all one hundred thousand.  Now, time in the match of course ends, but five turns are untimed.  Do you give both players a double loss in order to continue the tournament?  I just figure this is an issue that while not incredibly relevant needs to be answered by the DCI due to the confusion it holds (how will the head judge rule, it's his say).

No player is ever under an obligation to concede to their opponent.  Also, no judge should or would give a double loss just "in order to continue the tournament", although the player who owns Brain Freeze may be looking at some serious slow play issues if they can't resolve all their Brain Freezes in a reasonable time.
That said, this is something that players who play these sorts of decks need to be prepared for.  There is no built in compensation for a player that has the game locked up with Squee, Goblin Nabob + Solitary Confinement against an opponent with 0 outs, and the game goes to time before the opponent can deck.  Consequently if you are vulnerable to Gaea's Blessing, in this way, that's something you're going to have to accept or plan around.
That said, this is the kind of corner case that never comes up, since people often have something better to do than sideboard Gaea's Blessing.

To answer the comment about the DCI answering, they have.  What I'm saying is the Official answer from multiple NetReps.  There is no official shortcut.

[22:45] <EliShffrn> I'd tell you that if you can't resolve one million copies quickly, you get a slow play warning and upgrade appropriately.

[22:49] <EliShffrn> If you insist on saying "I'm gong to sit here milling until time," I'd actually consider stalling penalties.

I should point out that these quotes are part of the answer, but it's more complicated than that and requires looking at whether players are offering draws or not and why, and what the intent behind actions are.

[oneofchaos]

Well assuming you want to deck the opponent you casually say a billion storm, not knowing they have blessing.  surprise!  Now what exactly can you do?  Resolve said million copies?  Concede to avoid penalties?  I just don't see how it looks like the brain freeze player is going to get "punished" for this.  They are the ones on slow play watch, but how do you realistically expect someone to resolve one million copies of something on the stack.  Also I fail to see how it qualifies as stalling, it's not intentional the player is milling against an unmillable deck.

[Zombie Shakespeare]

You may want to contact Dicemanx and have him post his $0.02. This is exactly like the Dragon situation where you can mill infinitely, the ideal circumstance being their Blessing ending up as their last card. I know he has received different feedback from different judges, so he may have something to add.

Here's what SCG's Ask the Judge says about that particular situation:

Q: I have Ambassador Laquatus in play and a method of generating arbitrary amounts of mana at will (and untapping creatures at will). My opponent has thirty-nine cards in his library, two of which are Blessing ">Gaea's Blessing and no cards in the grave. Since the milling and reshuffling could go on potentially forever, could I request that a certain three cards (two Blessings and an island) put left in his library and the rest in his graveyard? This would happen eventually anyway, right?

A: Just because it would eventually happen doesn't mean that you can just jump to that state. It's very different than repeating a set of identical actions with identical results (like mana with Rob Dougherty's Verdant Succession deck). This is one you'll have to play out, and take your actions in a timely fashion. I'd probably put a judge on the match to keep you moving along briskly and so your opponent feels confident that you're not stalling. If you run out of time and get to the five extra turns, I'd put you on the clock (five minutes), like we did in the days of TurboZvi.

Source

[Anusien]

Well assuming you want to deck the opponent you casually say a billion storm, not knowing they have blessing.  surprise!  Now what exactly can you do?  Resolve said million copies?  Concede to avoid penalties?  I just don't see how it looks like the brain freeze player is going to get "punished" for this.  They are the ones on slow play watch, but how do you realistically expect someone to resolve one million copies of something on the stack.  Also I fail to see how it qualifies as stalling, it's not intentional the player is milling against an unmillable deck.

Well here's a question: why build up a billion storm?  1,000,000,000 copies can never be resolved.  You can easily Brain Freeze for less and still mill them, and that many copies you'd be able to resolve.

The end result of all the judge chats seems to be:
A) You can offer an intentional draw or concede at any time
B) As long as there's time on the clock, you might be free to shuffle away (call a judge when the situation comes up; the actual ruling is up to them/HJ)
    Slow play is of course always a possilibity
C) If we're in turns, there's no way we're resolving billions of Brain Freezes and hundreds of shuffles.  The final resolution is up to the judge, but may include slow play penalties or other factors.

Now if you're simply casting Brain Freeze in game 2 to eat up the clock (maybe you know they have Blessing and you want to draw the match), knowing that it can't be resolved; or you intentionally put billions of storm instead of twenty to draw a losing game, then you're guilty of stalling.

[oneofchaos]

Well assuming you want to deck the opponent you casually say a billion storm, not knowing they have blessing.  surprise!  Now what exactly can you do?  Resolve said million copies?  Concede to avoid penalties?  I just don't see how it looks like the brain freeze player is going to get "punished" for this.  They are the ones on slow play watch, but how do you realistically expect someone to resolve one million copies of something on the stack.  Also I fail to see how it qualifies as stalling, it's not intentional the player is milling against an unmillable deck.

Well here's a question: why build up a billion storm?  1,000,000,000 copies can never be resolved.  You can easily Brain Freeze for less and still mill them, and that many copies you'd be able to resolve.

The end result of all the judge chats seems to be:
A) You can offer an intentional draw or concede at any time
B) As long as there's time on the clock, you might be free to shuffle away (call a judge when the situation comes up; the actual ruling is up to them/HJ)
    Slow play is of course always a possilibity
C) If we're in turns, there's no way we're resolving billions of Brain Freezes and hundreds of shuffles.  The final resolution is up to the judge, but may include slow play penalties or other factors.

Now if you're simply casting Brain Freeze in game 2 to eat up the clock (maybe you know they have Blessing and you want to draw the match), knowing that it can't be resolved; or you intentionally put billions of storm instead of twenty to draw a losing game, then you're guilty of stalling.

Pretend it's game 1 and you have no idea that the blessing is there (hell most oath decks cut it when they went the tyrant route).  To what extent would you have to go through these copies resolving in order to reach a conclusion.  Realize that the Brain freeze player game 1 has no idea about the blessing, so he is not stalling.  If he calls a million storm, then realizes the blessing is there, it would be tough to proceed as a judge right?  Now if he realizes he is dead next turn, and this is game 2 and he knows his opponent has/may have a blessing and does this in order to kill time, I see that as being way different than blindly walking into it.

[Vegeta2711]

Pretend it's game 1 and you have no idea that the blessing is there (hell most oath decks cut it when they went the tyrant route).  To what extent would you have to go through these copies resolving in order to reach a conclusion.

...

If he calls a million storm, then realizes the blessing is there, it would be tough to proceed as a judge right?

Why? You chose to cast storm for a million of something, it's still on you to resolve each copy until the game is ended in an appropriate manner.

[Anusien]

Pretend it's game 1 and you have no idea that the blessing is there (hell most oath decks cut it when they went the tyrant route).  To what extent would you have to go through these copies resolving in order to reach a conclusion.  Realize that the Brain freeze player game 1 has no idea about the blessing, so he is not stalling.  If he calls a million storm, then realizes the blessing is there, it would be tough to proceed as a judge right?  Now if he realizes he is dead next turn, and this is game 2 and he knows his opponent has/may have a blessing and does this in order to kill time, I see that as being way different than blindly walking into it.

Let me preface this by saying this is the official DCI policy (no official shortcuts).  It comes up about once a year, and each time this ruling gets confirmed.  So while this is an invaluable resource to educate the player, it's likely not going to change as a result of this thread.

Sure, it's possible to walk into Blessing and not stall.  But now you know about the possibility and what would happen, if you're just trying to deck the opponent, why Brain Freeze for a million instead of 20?
Second, why would it be tough as a judge to proceed?  The whole situation is sort of messy in that it's up to the judge and the players to find a way to keep the tournament running on time.  Many judges feel that if you put a million spells on the stack and can't resolve them all in a reasonable time frame, you're committing slow play (this would get a second Slow Play warning fairly soon after, resulting in a Game Loss).  Some judges have other remedies.  If you can't end a game at a reasonable pace, you always have the option to offer an Intentional Draw or to even concede.  You could even try to negotiate some sort of shortcut for most of the Blessing copies; you could say, "Let's just shortcut past all but the last set of Brain Freezes and Gaea's Blessing."

The more complicated form of this is "I have Ancestral Recall in my hand, and I want to Freeze them through Blessing until Blessing is in the last (Library mod 3) cards.  There's no official shortcut for this, and it's likely you and your opponent won't be able to come up with an acceptable shortcut.  So, good luck with that.

Luckily it's an event that gets talked about a lot but rarely comes up in sanctioned play.

[Harlequin]

The whole situation is sort of messy in that it's up to the judge and the players to find a way to keep the tournament running on time.  Many judges feel that if you put a million spells on the stack and can't resolve them all in a reasonable time frame, you're committing slow play (this would get a second Slow Play warning fairly soon after, resulting in a Game Loss).  Some judges have other remedies.

Ok, right there.  That's the point of this mathematical examination.  To sort of, give players and judges who read this and agree with the grounds it was created on an alternate method of fairly resolveing the stack.   Because seriously what is "Fair" about "ok you now have a choice between draw or DQ without prize."  Which is how I've come to understand the "offical no shortcut" DCI pollicy. 

[dicemanx]

The whole situation is sort of messy in that it's up to the judge and the players to find a way to keep the tournament running on time.  Many judges feel that if you put a million spells on the stack and can't resolve them all in a reasonable time frame, you're committing slow play (this would get a second Slow Play warning fairly soon after, resulting in a Game Loss).  Some judges have other remedies.

Ok, right there.  That's the point of this mathematical examination.  To sort of, give players and judges who read this and agree with the grounds it was created on an alternate method of fairly resolveing the stack.   Because seriously what is "Fair" about "ok you now have a choice between draw or DQ without prize."  Which is how I've come to understand the "offical no shortcut" DCI pollicy. 

I totally agree with this. The judge's decision is the least intuitive, because they threaten punishment for playing the game with the intention of making progress. Resolving Brainfreeze triggers with the demonstrable intention of making progress shouldn't be punishable.

This decision is actually even less intuitive for the Laquatus (in WGD) versus Blessing where it is possible to put Laquatus mills on the stack indefinitely, so the probability of leaving a Blessing as the final card approaches 1. The judges at a SCG event actually told me that if I can prove mathematically that an event will eventually happen then they would reverse the ruling. I opted to go with Witness over Laquatus at that event instead and the rest is history. 

[Harlequin]

http://www.themanadrain.com/index.php?topic=27883.0

On reply #5 I post my probabilities for the Laquatus problem.  And that math invovles TWO geae's blessings ending in the bottom 2-4 cards (with double deep anal). 

The interesting thing, is that the probably never actually becomes 1.  However with a sufficently large number of trials it is "statistically insignifigantly" differant than 1.  In that example, I show that with X mana you have a better chance of rolling 200 D20's and having them all come up as 20 then me failing to hit blessing.  Hell, if you had a number to attach to it, you could calculate the mana needed such that the odds are greater that Chuck Noris will bust in the door and say "Ride with me into the sunset!" and I will concede because I am about to be swept up into a round-house kicking adventure!

Basically my point is, give me any number you can immagine that is not 1, but close to 1 - I can back-calc the mana needed to give you "better" odds of success.

-------------------

The infinite storm problem is much more complex - because it doesn't approch at 1:0 probability.  It instead approaches a probability distribution.  Here is my point:
- Some end states will be advantagous to the owner of blessing
- Some end states will be advantageous to the caster of brainfreeze
- Some will yeild no particular advantage to either player... and the game will continue, and be decided by future plays that are dirrectly influenced by the gamestate that has been reached.  But all in all the game will continue.

How is that a draw??  Thats like saying... well if I lose this mana crypt roll you win, and if win the flip I win - Therefor I declare this game is a draw!

[Anusien]

Close to 1 is not 1.  You can't say, "Well the chance that I don't win the game here is incredibly minor, so judge please give me the win."  Magic only recognizes two probabilities: 1 and not 1.
How would you like to be playing a game; you're in the finals of a Legacy Grand Prix (since Tidespout Tyrant and Lotus Petal are both in Legacy).  Some large amount of money, maybe $20,000 is on the line.  You're down a game but the match favors you.  Ahead on board, your opponent finally Show and Tells out a Tidespout Tyrant, plays two moxen and builds infinite storm and casts Brain Freeze.  Fine, you've got Blessing in your deck.  Your opponent shows you Careful Consideration and calls a judge.
How bad can it get from here?
A) You don't understand statistics and you have no chance to defend yourself to the judge.
B) Your opponent gets the game win and therefore the match win even though they didn't automatically win.

Can you imagine B?  Losing an important match because your opponent convinced the judge that even though they didn't automatically win, they should be given the match?
Yes, the current answer is kind of bad in a lot of ways, but at least it does not have judges giving matches away.

The DCI does not require its judges to have studied probability in order to be a judge.  Accepting a piecemeal solution like this would lead to uneven judging based on the floor judge or head judge's personal knowledge of statistics.

What level of statistically insignificant for a loop is okay?  1%?  .1%?  .01%?  What if the principle gets applied to things it shouldn't, or we start handing matches away because of a math error?

The infinite storm problem is much more complex - because it doesn't approch at 1:0 probability.  It instead approaches a probability  distribution.  Here is my point:
- Some end states will be advantagous to the owner of blessing
- Some end states will be advantageous to the caster of brainfreeze
- Some will yeild no particular advantage to either player... and the game will continue, and be decided by future plays that are dirrectly influenced by the gamestate that has been reached.  But all in all the game will continue.

Yes, but that's Magic.  Solutions to tricky game states that involve the game Magic are better than solutions to tricky game states that require Ti-82+s.

To sort of, give players and judges who read this and agree with the grounds it was created on an alternate method of fairly resolveing the stack.   Because seriously what is "Fair" about "ok you now have a choice between draw or DQ without prize."  Which is how I've come to understand the "offical no shortcut" DCI pollicy.

You're not given the choice between draw or DQ without prize.  I explained the options.  First, you got yourself into this situation by playing Brain Freeze with 10000000 storm, and you do have the option to offer the draw.  The only way you're getting a DQWOP is if you're Stalling or Cheating in some way (which is true across the board).  I don't think it's unreasonable to say, "If you create a game state that physically cannot be resolved in 50 minutes, you're doing something wrong."  I should remind you, I presented a shortcut that might not be unreasonable to players and the judge.  If you just shortcut away all the Blessing triggers/Brain Freeze copies and just mill them through once; whatever the math works out to.

It's not like Extirpate hasn't been printed or something.  It's not the DCI's responsibility to make sure your archetype works the way you want it to.  All strategies in Magic get trumped, and if you lose because the opponent has a single card in their deck...
It's like saying, "I have Mindslaver + Academy Ruins so I control all their turns, make them concede."  Well no.  You're not guaranteed to win.

Edit: I've tried to present the position of the DCI.  I should stress, this is the position of the DCI.  If you want to get it changed, you can't stop anywhere short of talking to the DCI.  No judge should overturn this ruling.  If you still have issues, I suggest you talk to Customer Service and they can get your feedback directed in the right place.
http://wizards.custhelp.com/

[Apollyon]

The whole situation is sort of messy in that it's up to the judge and the players to find a way to keep the tournament running on time.  Many judges feel that if you put a million spells on the stack and can't resolve them all in a reasonable time frame, you're committing slow play (this would get a second Slow Play warning fairly soon after, resulting in a Game Loss).  Some judges have other remedies.

Ok, right there.  That's the point of this mathematical examination.  To sort of, give players and judges who read this and agree with the grounds it was created on an alternate method of fairly resolveing the stack.   Because seriously what is "Fair" about "ok you now have a choice between draw or DQ without prize."  Which is how I've come to understand the "offical no shortcut" DCI pollicy. 

The problem with relying on any math model, such as this, is that it requires everyone involved to have a good basis in math. While many of us are, at the least, passable in math, doing out a formal proof requires a good amount of time and understanding. In a tournament situation, the judges might not necessarily have enough of either.

Given that one of the DCI's policies is 'consistent enforcement'. That's the goal of Sanctioning; to allow players to play in tournaments with equal levels of rules enforcement and consistent policies. I can go to a FNM in Japan, France, Iowa, California, here, Russia, or anywhere else, and expect to see the same set of rules as any of those other locations. I don't see how any solution like this accomplishes that policy.

When you discuss fairness, is it fair for the judge to GL your opponent because it's likely that you are going to win? Arguing that because it's "very likely" or "extremely likely" goes down a slippery slope. If I'm playing in a type 4 game and the board is: my opponent with a Darksteel Colossus, the shared library having 200 cards left, I'm at 3, he's at 4, and the only answer to it left is a Psi Blast, can he say that because the probability of him winning is 199/200th, that we can just agree that he wins because it's 'likely' that he'll win. Or how about if CF sits down across the table from 12 year old Timmy in a Sanctioned Standard match? Can he say "My rating is 2100. His is 1400. Therefore, it's extremely likely that I'll win, so want to just give me the win, judge?"

[dicemanx]

The problem with relying on any math model, such as this, is that it requires everyone involved to have a good basis in math. While many of us are, at the least, passable in math, doing out a formal proof requires a good amount of time and understanding. In a tournament situation, the judges might not necessarily have enough of either.

This isn't an actual problem. Only one person needs to "understand the math", and that is the decision-maker when it comes to DCI rulings for specific cards or card interactions. The judges can use the rule as reference, stating to a player that the ruling has been established mathematically even if all parties at an event don't have an understanding of the math.

When you discuss fairness, is it fair for the judge to GL your opponent because it's likely that you are going to win? Arguing that because it's "very likely" or "extremely likely" goes down a slippery slope. If I'm playing in a type 4 game and the board is: my opponent with a Darksteel Colossus, the shared library having 200 cards left, I'm at 3, he's at 4, and the only answer to it left is a Psi Blast, can he say that because the probability of him winning is 199/200th, that we can just agree that he wins because it's 'likely' that he'll win. Or how about if CF sits down across the table from 12 year old Timmy in a Sanctioned Standard match? Can he say "My rating is 2100. His is 1400. Therefore, it's extremely likely that I'll win, so want to just give me the win, judge?"

The slippery slope argument can be made irrelevant because you can set an arbitrarily high cut off (for instance, if the probability of an event is greater than  0.9999..... with 10^100 nines, that can be the cut off where you say, "OK, the event will happen".). In such a case, very few scenarios will apply (namely, 2). In fact, the only scenarios that would apply are those that have been mathematically established beforehand and have been accepted as official DCI rulings. If new scenarios arise, they would have to be submitted to the DCI for ruling decisions with accompanying mathematical proof.

[Anusien]

Okay, talk to the DCI.  Get it accepted.  We can't change anything with this chat.

[Harlequin]

First of all, I'm not really trying to change to offical DCI ruling.  Personally, I only play unsactioned vintage.  So when it comes down to brass tacks - I honestly do not care what the DCI ruling is.  This occured at the last Myriad Game tournement. Dan rule that the Gaea's blessing would be shuffled into a clean library and the GY would be empty, and the stack would be empty.  Honestly, that answer is more statifing to me than "Silly player, why did you make so much storm? I have to punish you now..."  Even if Dan gave Jer a warning for "Failure to keep storm reasonable" and told him that if he makes that much storm again he would be punished.  That would be more acceptable to me as well.  

Secondly, this "there's no probability in MTG" is not correct.  Take a card like mana crypt.  Or better yet take... look at the begining of the match when you 'roll for choice.'  Sure it's intuative that if we each roll the same dice, we each have an equal chance to win.... but guess what, you need conditional probability (almost -exactly- like I post above) to -prove- that both players have an equal chance to win.  Infact you actually need an infinite geometric serise for the prove the 50:50 final outcome because - in theory there is a 1 in 6 chance that I will roll the same number as you, and there is no mathematically law that states we won't continue to roll the same number from now until the rapture.

Also, when we flip a coin, it's actually completely IMPOSSIBLE to know if the coin is "fair."  There are entire divisions of mathematics that are devoted to proving signifigance.  Consider 'testing' a coin to try and decide if it's fair.  You flip it once and it comes up heads.  So did that prove the probability model 50:50?  100:0?  pi:1-pi?  ok how about flipping it twice? you get HH... what does that prove? 50:50? 100:0?  The point is, even if you flip it until the copper has worn off each face so you can't tell if its H or T... and even if that comes down to an exact 50:50 statistical distribution - you still haven't proven anything.  

Ok one last example:  Ray is known for using Rock Lobster, Scissor Lizard, and Paper Tiger, to "play rock paper scissors for choice?"  and again, anyone who passes thier Probability 101 class will tell you that when the cards are chosen fairly and at random, the final case is 50:50 for either player to win.  
- now the counter arguement here is that his opponent can refuse to play the mini-game... and offer to roll a dice instead.  But I guess the question is: if Ray's opponent can refuse to play R-P-S, can Ray refuse to roll the dice on the grounds that he doesn't know if the outcome is 50:50?   Why is one method considered acceptable where the other is not?  

From the information spewed above, rolling a dice or flipping a coin ... while they seem mondain, are actually no less mathematically complex than R-P-S, or playing a game of war.  And only arguable less complext than the Laquatus or Freeze vr. Blessing example.  So I guess what I'm doing is challenging this line in the sand between acceptable random and unacceptable random.

[Anusien]

First of all, I'm not really trying to change to offical DCI ruling.  Personally, I only play unsactioned vintage.  So when it comes down to brass tacks - I honestly do not care what the DCI ruling is.  This occured at the last Myriad Game tournement. Dan rule that the Gaea's blessing would be shuffled into a clean library and the GY would be empty, and the stack would be empty.  Honestly, that answer is more statifing to me than "Silly player, why did you make so much storm? I have to punish you now..."  Even if Dan gave Jer a warning for "Failure to keep storm reasonable" and told him that if he makes that much storm again he would be punished.  That would be more acceptable to me as well.

Dan SAYS he runs his tournaments as if they would be sanctioned, only they're not.
(A Warning for "Failure to Keep Storm Reasonable" seems ridiculous, but it's not the only thing I've heard of Dan doing that flies in the face of DCI policy.  That's neither here nor there.)
In order to do that, he has to go with this policy.  If you only care about unsanctioned Vintage, your TO can do whatever they want and set whatever policy about it they want.  But even in an unsanctioned tournament, I would recommend sticking with DCI policy.

[Apollyon]

This isn't an actual problem. Only one person needs to "understand the math", and that is the decision-maker when it comes to DCI rulings for specific cards or card interactions. The judges can use the rule as reference, stating to a player that the ruling has been established mathematically even if all parties at an event don't have an understanding of the math.

That's a big problem for judges, who do as much customer service as anything else. Part of being a good judge is explaining your ruling and the logic behind it. If you make a ruling by "judge fiat", which going "I don't know the math, but this is what will happen. Because of math." is, the players can lose respect for you. For lengthy rulings, "Here's how I'm going to rule it, here's the basics, if you want to discuss technicalities, please see me after the match is over." is acceptable. Saying "Here's the ruling, I don't know how it works. See some website for an explanation, if you can understand it." is poor customer service. It doesn't build people's faith that the judges will be able to provide an answer and an explanation as to why it's that way.

The issue is a slippery slope for rulings (This is how it happens. Because.) if you make rulings based upon probability like this, for a minor corner case.

When you discuss fairness, is it fair for the judge to GL your opponent because it's likely that you are going to win? Arguing that because it's "very likely" or "extremely likely" goes down a slippery slope. If I'm playing in a type 4 game and the board is: my opponent with a Darksteel Colossus, the shared library having 200 cards left, I'm at 3, he's at 4, and the only answer to it left is a Psi Blast, can he say that because the probability of him winning is 199/200th, that we can just agree that he wins because it's 'likely' that he'll win. Or how about if CF sits down across the table from 12 year old Timmy in a Sanctioned Standard match? Can he say "My rating is 2100. His is 1400. Therefore, it's extremely likely that I'll win, so want to just give me the win, judge?"

The slippery slope argument can be made irrelevant because you can set an arbitrarily high cut off (for instance, if the probability of an event is greater than  0.9999..... with 10^100 nines, that can be the cut off where you say, "OK, the event will happen".). In such a case, very few scenarios will apply (namely, 2). In fact, the only scenarios that would apply are those that have been mathematically established beforehand and have been accepted as official DCI rulings. If new scenarios arise, they would have to be submitted to the DCI for ruling decisions with accompanying mathematical proof.

Let's say that you have a probability of .9999.. with 10^100 nines, as you suggest. Let's assume, for the sake of argument, that it takes a storm count of 1,000,050 to get that probability. What does the judge say if you have a storm of 1000? What about a storm of 100,000? What about a storm of 1,000,000? In the last case, we are back to where we start, except that now, instead of one policy, there's two. And a number to remember. Now, let's assume that instead of something easy, like 1 million + 50, it's something such as 487,754,549,875. How does a judge remember that? Or do they look it up? And where would that ruling go? The card FAQs? The Magic Floor Rules? The Universal Tournament Rules? The Magic rulebook?

Secondly, this "there's no probability in MTG" is not correct.  Take a card like mana crypt.  Or better yet take... look at the begining of the match when you 'roll for choice.'  Sure it's intuative that if we each roll the same dice, we each have an equal chance to win.... but guess what, you need conditional probability (almost -exactly- like I post above) to -prove- that both players have an equal chance to win.  Infact you actually need an infinite geometric serise for the prove the 50:50 final outcome because - in theory there is a 1 in 6 chance that I will roll the same number as you, and there is no mathematically law that states we won't continue to roll the same number from now until the rapture.

No, you don't. Draw a 6x6 grid, label the axes "Me" and "You", and label each column and row 1 through 6. Now, for each of the 36 pairs, mark each box with who wins, or if there's a reroll on the 6 draws. If it helps, color one of the winners red and the other blue. That should make it obvious that there's an equal amount of situations where I win as you win. Since P(me) = P(you), we can than say that it's equally likely that either of us will win.

Also, when we flip a coin, it's actually completely IMPOSSIBLE to know if the coin is "fair."  There are entire divisions of mathematics that are devoted to proving signifigance.  Consider 'testing' a coin to try and decide if it's fair.  You flip it once and it comes up heads.  So did that prove the probability model 50:50?  100:0?  pi:1-pi?  ok how about flipping it twice? you get HH... what does that prove? 50:50? 100:0?  The point is, even if you flip it until the copper has worn off each face so you can't tell if its H or T... and even if that comes down to an exact 50:50 statistical distribution - you still haven't proven anything.

That's not true. You are trying to determine something in the realm of math using science. Science doesn't give us universal truths, just models that fit the data that we have.  

Ok one last example:  Ray is known for using Rock Lobster, Scissor Lizard, and Paper Tiger, to "play rock paper scissors for choice?"  and again, anyone who passes thier Probability 101 class will tell you that when the cards are chosen fairly and at random, the final case is 50:50 for either player to win. - now the counter arguement here is that his opponent can refuse to play the mini-game... and offer to roll a dice instead.  But I guess the question is: if Ray's opponent can refuse to play R-P-S, can Ray refuse to roll the dice on the grounds that he doesn't know if the outcome is 50:50?   Why is one method considered acceptable where the other is not?

If either player has an issue about the quality of the random (loaded dice, marked cards), they should call the judge. This is really a non-issue and it reaches out into the branch of math that deals with generating randomness. The long and short is that "having the properties of randomness" is usually an acceptable substitute for "truly random".

[Harlequin]

Ok, new hypothetical:  Lets say that the DCI tomorrow decides to change the floor rules to say: "Rolling for choice will be replaced with the following randomization techinque: On player rolls a D6, and if they get a 6 - they go first, if they don't the other player rolls to see if they get a 6, and if they do it's thier choice... this continues in a roll-off to see who rolls the first 6." 

There would be massive outcry, because anyone with a little common sense can see that this clearly favors the person who rolls first.  Now, I notice I didn't say "Everyone knows this is unfair."  I'll bet if you posed this "game" to 100 people and asked them if they considered it a fair game for both players you would get a half dozen that consider it fair.  According to the probability model - those people are wrong because it unfairly favors the player rolling first.

At the end of the day, this is EXACTLY what the DCI did.  They made a blanket ruling that unfairly over-values the card gaea's blessing and weakens the card Brainfreeze.   According to Anusien this ruling is "unpopular" - this is because it could be resolved, and DCI decided they would rather blanket rule the (non-)resolution of this stack.   But instead of 96 out of 100 people realizing it, it seems more like 1 out of 100.

If it helps, color one of the winners red and the other blue. That should make it obvious that there's an equal amount of situations where I win as you win. Since P(me) = P(you), we can than say that it's equally likely that either of us will win.

 
While, I agree this model can be used to illustrate the equality of the model, this doesn't hold water when it comes to proofs.  I would be willing to bet that less than 20% of judges could write a sufficent proof of the "roll for choice" model being 50:50.  And further more, I would be plesantly surprised if more than half could come up with an illustration of the point like TheAbyss has done.  My point here is that understanding the probability behind a rule or method is not a requisit for using it in a ruling.

The long and short is that "having the properties of randomness" is usually an acceptable substitute for "truly random".

..... Unless were talking about Laquatus or Brainfreeze - then you must avoid all properties of randomness - and any suggestion that such a short cut could be used is treason.  If you sugest it to a judge or opponent then at best: it's just voodoo or witchcraft, and at worst its considered on par with colution.

[BigBarn]

"Unless were talking about Laquatus or Brainfreeze - then you must avoid all properties of randomness - and any suggestion that such a short cut could be used is treason..."

Does the DCI let you use shortcuts for random situations?  I thought they only let you use shortcuts for repeated actions that have known outcomes.  The only thing close to a "shortcut for randomness" that I can think of is allowing a player to skip the shuffling between Mind's Desire's copies to save time (again, if both players agree).  And I don't know if that's even an official ruling, or just good judging trying to speed up the games.

[Anusien]

At the end of the day, this is EXACTLY what the DCI did.  They made a blanket ruling that unfairly over-values the card gaea's blessing and weakens the card Brainfreeze.   According to Anusien this ruling is "unpopular" - this is because it could be resolved, and DCI decided they would rather blanket rule the (non-)resolution of this stack.   But instead of 96 out of 100 people realizing it, it seems more like 1 out of 100.

I never said the ruling was unpopular.  In fact it makes things much easier for EVERYONE ELSE in the tournament.

Anyway, no one is forcing you to play Brain Freeze and an infinite combo.  There's no great injustice here.

Let's say that you have a probability of .9999.. with 10^100 nines, as you suggest. Let's assume, for the sake of argument, that it takes a storm count of 1,000,050 to get that probability. What does the judge say if you have a storm of 1000? What about a storm of 100,000? What about a storm of 1,000,000? In the last case, we are back to where we start, except that now, instead of one policy, there's two. And a number to remember. Now, let's assume that instead of something easy, like 1 million + 50, it's something such as 487,754,549,875. How does a judge remember that? Or do they look it up? And where would that ruling go? The card FAQs? The Magic Floor Rules? The Universal Tournament Rules? The Magic rulebook?

Anyway, remember that you can win this discussion and still be wrong in the eyes of the way the cards interact in a tournament session.  Feel free to spend 3 hours resolving Brain Freezes in your own home.

[oneofchaos]

Well I never assumed I had a recall in hand to deck the opponent.  Well regardless, say I now have a recall in hand and aim to brain freeze and deck the opponent.  If a billion brain freezes are going off, I feel you shouldn't be forced to play out each one until you hit the result you seek, provided you have a response.  Example is you can't set storm = to 1,000 and have on the 1,000th storm the order be your choosing.  I do think that if you have a triggered ability/activated ability or an instant, you should be able to play it out as you choose and respond because the order will eventually have to be said order.  You don't know when that order will be that order, but your not ending on that order.  Your pausing temporarily to observe a mathematically sound arrangement that could occur on storm 11230 of 100000 storm and you have more brain freeze copies resolving after it.  I would think a sensible end all on the situation would be, provided you have a response, you can manipulate the deck to your advantage since this is occurring on a random storm copy, and it doesn't have to be accounted for (which number it is).  The important facet is that if you wanted to deck an opponent by making blessing the last card, then you would need to figure out the math on the probability that would occur on the last copy, which is highly unlikely.  However an order of your choosing is likely to occur during some part of this interaction.  Also I wouldn't foresee this as stalling, as you would know directly what you want to achieve and based on the mathematical soundness and your skipping iterations of the combo as you do in any infinite combo.  This seems like the diving by 0 point of magic.

[Anusien]

Well I never assumed I had a recall in hand to deck the opponent.  Well regardless, say I now have a recall in hand and aim to brain freeze and deck the opponent.  If a billion brain freezes are going off, I feel you shouldn't be forced to play out each one until you hit the result you seek, provided you have a response.  Example is you can't set storm = to 1,000 and have on the 1,000th storm the order be your choosing.  I do think that if you have a triggered ability/activated ability or an instant, you should be able to play it out as you choose and respond because the order will eventually have to be said order.  You don't know when that order will be that order, but your not ending on that order.  Your pausing temporarily to observe a mathematically sound arrangement that could occur on storm 11230 of 100000 storm and you have more brain freeze copies resolving after it.  I would think a sensible end all on the situation would be, provided you have a response, you can manipulate the deck to your advantage since this is occurring on a random storm copy, and it doesn't have to be accounted for (which number it is).  The important facet is that if you wanted to deck an opponent by making blessing the last card, then you would need to figure out the math on the probability that would occur on the last copy, which is highly unlikely.  However an order of your choosing is likely to occur during some part of this interaction.  Also I wouldn't foresee this as stalling, as you would know directly what you want to achieve and based on the mathematical soundness and your skipping iterations of the combo as you do in any infinite combo.  This seems like the diving by 0 point of magic.

It's nice you feel that way, but you're wrong.  Please read what I said above about official policy.

Quote from Andy Heckt, previous Judge Manager and now Manager to the Judge Manager:

> > Can a player use a statistical model to effectively stack=20
> > their opponent's deck?
No. This was discussed with Gaea and Sensei and "no" is still the
official ruling. 100% or not a loop.

Every try to get around this has a nonzero chance of never hitting what you want for any finite number of copies of Brain Freeze or activations of Laquatus.

[ELD]

@Anusien - I don't think anyone here is arguing about what the official DCI policy is.  I believe the discussion here reflects the fact that people feel that policy is inadequate, as well as a desire to discuss better ways to handle these situations.  This is reflected in requesting input from mathematicians, statisticians, and Tournement Judges.  If this was just an exercise in looking up DCI policy, Jeff would not have spent the thought, time and energy that he did in looking at this problem. 

One large problem with the theoretical discussions about interactions is they assume perfect information.  The library, as well as players hands, not being public information creates some issues.  Does the player have one or two Blessings?  Do they have relevant plays in hand?  Are there flashback cards or other interactions that might come up?  These questions impact the situation greatly.  Both players do not necessarily have all the info, so a judge would certainly have to be involved.  This does not mean these issues could not be overcome with a judges discretion, but it does complicate things. 

I would like to discuss the possibility of seeing shortcuts to the endgame of the problems.  Dice could easily simulate game actions much more quickly.  In the example of an infinite mana'd Laquatus vs Blessings, the odds of blessing not ending up in the bottom 1, 2 or 3 cards could be determined to be of a certain value, like say much higher than 1,000,000,000,000 to one.  In this case, I would like to see 13 D10 rolled, and unless they are all 10s, the results hold up.  Even though this result would be more likely to fail than actually doing it out, it would allow players to fast forward and continue the game.  Other shortcuts like these could be reasonable ways to resolve these issues. 

One step forward would be to create a rule regarding arbitrarily large numbers.  With rules regarding a certain upper limit in place, this would allow people to proceed with predictable results.  People would know if they go with X= 1,000,000,000,000 instead of X=1000, they would be dealing with these new rules, and should make their choices accordingly.  If the DCI would create certain judge rulings on given situations where the variable is said to be of a minimum size, we could eventually handle many of the plausible tournament situations in a way that would reflect the outcome if cards actually played out. 

In the instance of Brainfreeze with Ancestral vs Gaea's Blessing, I propose the following.  Continue the loop until there is no graveyard, with the entire library shuffled up.  With the multiple Brainfreezes still on the stack, roll dice to determine where in the deck the Gaea's Blessing is.  This could be done with 2d10 and rerolling numbers higher than the number of cards in the deck.  A 1 means the top card, 2 the second an so on.  Eventually, there will be an instance where the Blessing is in the bottom few cards.  Players can then proceed from that point once the correct roll comes up.  The judge would roll, and keep the results to himself, so the players would not know where in the bottom cards the Blessing is. 

I believe all these situations could be handled in a similar fashion.  It is messy, but it seems better than the current system. 

One thing I am unclear about in these examples is who is actually "slow playing?"  To me, the only player who is taking any actions is the player targeted by Brainfreeze and controling the Gaea's Blessing triggers.  The Brainfreeze player made plays that are commonly seen, without any penalty or consideration, in every Type 1 event.  The player who is being targeted is the one doing all the shuffling and milling, while the controller of the Brainfreeze is powerless to do anything but sit and watch.  It's not like the player controlling the Brainfreeze copies is able to do anything, and there are no rules against how high the storm can get, nor should there be. 

[Englishman_in_NH]

I'm not going to get involved in the discussion on the DCI policy, because as policy it can only be changed by the DCI, so what I think here is of no consequence.

However, if I had a player resolving copies of Brain Freeze or Laquatus triggers in a timely manner, regardless of the number of 'storm' copies, I don't know if as a judge I could call either player for slow playing or stalling. Yes the match will probably go to time and then take a while to complete, but unless the players can agree on an outcome to the game via one players concession, I don't see how it is fair for a TO or judge to interfere when they are playing at an adequate pace.

Before everyone tries to crucify me, I understand that this is not feasable in a real tournament setting, as it would cause havoc to the event, however, is this not something that the DCI should have looked at before making such a ruling?

Both players have the option to concede at any time. If the player with the Blessing realises that there is no way that this game is not going to go to time, then if he is up a game he will play it out, if he thinks he can take a draw. If he is down a game, if he thinks he cannot win in 3 turns, then he may as well scoop it up as that is all he will have after time is called. If it is game one, I guess it depends on if he needs a draw or has to go for a win.

Similar thought occurs for the player with the Brain Freeze, however, it would be nice if one could shortcut to the final few copies to see where in the deck the Blessing hit.

First of all, I'm not really trying to change to offical DCI ruling.  Personally, I only play unsactioned vintage.  So when it comes down to brass tacks - I honestly do not care what the DCI ruling is.  This occured at the last Myriad Game tournement. Dan rule that the Gaea's blessing would be shuffled into a clean library and the GY would be empty, and the stack would be empty.  Honestly, that answer is more statifing to me than "Silly player, why did you make so much storm? I have to punish you now..."  Even if Dan gave Jer a warning for "Failure to keep storm reasonable" and told him that if he makes that much storm again he would be punished.  That would be more acceptable to me as well.

Dan SAYS he runs his tournaments as if they would be sanctioned, only they're not.
(A Warning for "Failure to Keep Storm Reasonable" seems ridiculous, but it's not the only thing I've heard of Dan doing that flies in the face of DCI policy.  That's neither here nor there.)
In order to do that, he has to go with this policy.  If you only care about unsanctioned Vintage, your TO can do whatever they want and set whatever policy about it they want.  But even in an unsanctioned tournament, I would recommend sticking with DCI policy.

I don't want to get into a war of words, however, I do want to point out that what Jeff said was quantified by if. This is not what Dan did, just an example in his eyes of what would be more reasonable to him than the current ruling. (Jeff, please correct me if I'm wrong)

As an aside, I would be interested to hear via pm what else you felt Dan has done that flies in the face of DCI policy, as, as far as I know Dan and Myriad run a tight ship and try to keep there events very professional.

Oli

[Moxlotus]

One thing I am unclear about in these examples is who is actually "slow playing?"  To me, the only player who is taking any actions is the player targeted by Brainfreeze and controling the Gaea's Blessing triggers.  The Brainfreeze player made plays that are commonly seen, without any penalty or consideration, in every Type 1 event.  The player who is being targeted is the one doing all the shuffling and milling, while the controller of the Brainfreeze is powerless to do anything but sit and watch.  It's not like the player controlling the Brainfreeze copies is able to do anything, and there are no rules against how high the storm can get, nor should there be. 

I am also confused.  The storm player unknowingly created a bad situation so i don't understand why he would ge the slow play penalty.  The player targeted by Brainfreeze is only doing the repeated motions that the opponent told him to (and the player target w/ BF would clearly rather not do).  Who is getting the slow play penalty?

[Anusien]

If you don't agree with Slow Play, how else will you resolve the situation in a way that is fair to both players and to everyone else in the tournament.

P.S., discussion of what policy changes you want should probably go to Customer Service that I posted above, but it's extremely unlikely to change.  Just saying.