Brain Freeze and Gaea's Blessing

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Archived from groups: rec.games.trading-cards.magic.rules (More info?)

Brain Freeze
{1}{U}
Instant
Target player puts the top three cards of his or her library into his or
her graveyard.
Storm (When you play this spell, copy it for each spell played before it
this turn. You may choose new targets for the copies.)

Gaea's Blessing
{1}{G}
Sorcery
Target player shuffles up to three target cards from his or her
graveyard into his or her library.
Draw a card.
When Gaea's Blessing is put into your graveyard from your library,
shuffle your graveyard into your library.

Q:

Suppose I've been able to play one million spells (using some infinity
combo) and then I Brain Freeze my opponent, who has let's say 45 cards
left in his library.
But I'm not in luck and he has (at least one) Gaea's blessing in his
library...

Ok so I will not be able to deck him.
But, supposing no-one wants to interfere with the stack anymore,
how do we determine the state of his library and graveyard?

I mean : it's rather impractical to actually flip over 3 million cards,
and when appropriate reshuffling the library, because Gaea's Blessing
got dug up.

What do the rules say about this?

Any DCI tournament rulings about this?

Can anyone provide a practical solution that would be 'mathematically'
correct?

Thanks in advance.

 

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Archived from groups: rec.games.trading-cards.magic.rules (More info?)

Bowmore <mapsdump@hotmail.com> writes:
> Suppose I've been able to play one million spells (using some infinity
> combo) and then I Brain Freeze my opponent, who has let's say 45 cards
> left in his library.
> But I'm not in luck and he has (at least one) Gaea's blessing in his
> library...
>
> Ok so I will not be able to deck him.
> But, supposing no-one wants to interfere with the stack anymore,
> how do we determine the state of his library and graveyard?

Very Good Question.

This was discussed last month on the DCIJUDGE-L list.
<http://oracle.wizards.com/scripts/wa.exe?S2=dcijudge-l&s=1.5+Questions>
<http://oracle.wizards.com/scripts/wa.exe?A2=ind0406A&L=dcijudge-l&P=R2107>

People came up with some "approximations", but I don't recall anything
being a definite "do it this way" answer.

--
Peter C.
"During my service in the United States Congress, I took the
initiative in creating the Internet."
-- Al Gore, March 9, 1999, On CNN's Late Edition

 

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Archived from groups: rec.games.trading-cards.magic.rules (More info?)

Bowmore <mapsdump@hotmail.com> wrote:
>Brain Freeze 1U Instant
>Target player puts the top three cards of his or her library into his or
>her graveyard. / Storm (*)
>
>Gaea's Blessing 1G Sorcery
>Target player shuffles up to three target cards from his or her
>graveyard into his or her library. Draw a card. / When ~ is put into your
> graveyard from your library, shuffle your graveyard into your library.

If the Blessing is Milled during one of the Brain Freeze spell resolutions,
original or copy, the ability will trigger and will go on the stack after
-that resolution- is done. And will then reshuffle the graveyard (including
the GB itself) into the library before the next copy of Brain Freeze on the
stack gets to resolve at all.

>Suppose I've been able to play one million spells (using some infinity
>combo) and then I Brain Freeze my opponent, who has let's say 45 cards
>left in his library.
>But I'm not in luck and he has (at least one) Gaea's blessing in his
>library...

45 is divisible by three, so you absolutely will not be able to even get his
library empty this way.

>Ok so I will not be able to deck him.
>But, supposing no-one wants to interfere with the stack anymore,
>how do we determine the state of his library and graveyard?

Each time the Blessing shuffles them in, it starts again from a full library,
so in essence you have to determine a random number between 0 and 14 for how
many Brain Freeze copies have gone off since then in the -ending- state. If
there's more than one Blessing it complicates things. To simulate this:

shuffle the library
determine your random number from 0 to 14 (use a 20-sided die)
flip that many sets of three cards into his graveyard; if one of them has
a GB in it, reshuffle at that point and continue until you reach your number

will probably work as well as anything.

>What do the rules say about this?

They don't, actually; this is not an _unbounded_ loop.

>Can anyone provide a practical solution that would be 'mathematically'
>correct?

The above is probably not -quite- correct, but ought to suffice, since you
can't get to do the 15th set-of-three-cards flip (with 45 cards in the
library) without starting over.

Dave
--
\/David DeLaney posting from dbd@vic.com "It's not the pot that grows the flower
It's not the clock that slows the hour The definition's plain for anyone to see
Love is all it takes to make a family" - R&P. VISUALIZE HAPPYNET VRbeable<BLINK>
http://www.vic.com/~dbd/ - net.legends FAQ & Magic / I WUV you in all CAPS! --K.

 

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Archived from groups: rec.games.trading-cards.magic.rules (More info?)

Peter Cooper Jr. wrote:
> Bowmore <mapsdump@hotmail.com> writes:
>
>>Suppose I've been able to play one million spells (using some infinity
>>combo) and then I Brain Freeze my opponent, who has let's say 45 cards
>>left in his library.
>>But I'm not in luck and he has (at least one) Gaea's blessing in his
>>library...
>>
>>Ok so I will not be able to deck him.
>>But, supposing no-one wants to interfere with the stack anymore,
>>how do we determine the state of his library and graveyard?
>
>
> Very Good Question.
>
> This was discussed last month on the DCIJUDGE-L list.
> <http://oracle.wizards.com/scripts/wa.exe?S2=dcijudge-l&s=1.5+Questions>
> <http://oracle.wizards.com/scripts/wa.exe?A2=ind0406A&L=dcijudge-l&P=R2107>
>
> People came up with some "approximations", but I don't recall anything
> being a definite "do it this way" answer.
>

Makes for some interesting reading.
And pondering the problem a bit further I came upon another issue
with this simulation (which will definitely fall in the far-fetched
category)

So:

Assume we have a simulation (mathematically correct or not) that both
players accept.

Player 2 (whose library is being milled a lot) may have 1 to 4 copies of
Gaea's Blessing in his library.
Suppose that all copies are in the players library.

Player one can see at most three of them at the same time (during one
resolution of a BF copy), after which they all get shuffled back
in the library (upon resolving the triggered effect of the last of those
GB's that got milled).

Now how to determine what information player 1 got about the actual
number of GB's in player 2's library?

He saw at least one.
He definitelty did not see four.
What are the odds he saw two?
What are the odds he saw three?

And then even wackier :

It is theoretically possible that player 1 did not see all cards of
player 2's library.
What are the odds of a card that occurs n times in the library, not
being revealed to player 1 after x resolutions of BF?


Finally I'd like to stress that I am aware of how far-fetched this is,
it's just fun to explore the complexity of the game of magic.

Thanks in advance.

 

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Archived from groups: rec.games.trading-cards.magic.rules (More info?)

Bowmore sez:

<<
>Brain Freeze
>{1}{U}
>Instant
>Target player puts the top three cards of his or her library into his or
>her graveyard.
>Storm (When you play this spell, copy it for each spell played before it
>this turn. You may choose new targets for the copies.)
>
>Gaea's Blessing
>{1}{G}
>Sorcery
>Target player shuffles up to three target cards from his or her
>graveyard into his or her library.
>Draw a card.
>When Gaea's Blessing is put into your graveyard from your library,
>shuffle your graveyard into your library.
>
>Q:
>
>Suppose I've been able to play one million spells (using some infinity
>combo) and then I Brain Freeze my opponent, who has let's say 45 cards
>left in his library.
>But I'm not in luck and he has (at least one) Gaea's blessing in his
>library...
>
>Ok so I will not be able to deck him.
>But, supposing no-one wants to interfere with the stack anymore,
>how do we determine the state of his library and graveyard?
>
>I mean : it's rather impractical to actually flip over 3 million cards,
>and when appropriate reshuffling the library, because Gaea's Blessing
>got dug up.
>
>What do the rules say about this?

>>

Well, this works like any other triggered ability. After the copy of the
Blessing hits the graveyard, you finish the resolution of the Freeze copy
you're in, then he shuffles his library, and you do it again. This is
important in game terms, because you don't know when the Blessing's going to
show up. So he could end up with all of his cards in his library, or just the
Blessing.

What I would do (since the rules don't really cover it), is give an
approximation as to how many times the Blessing will show up. I'd say in 1
million Brain Freezes, on average, a library with 1 Blessing in it will show up
about 60,000 times. About 1 in 15. So I'd cut to the last 30 or so iterations
of the Brain Freeze and just go from there...


----
"I feel like 'Cactus Gavvy' Cravath. Do you know who that is? Right. Nobody
does. He's the guy who had the home run record before Babe Ruth came along."
--Tom Walsh, whom Ken Jennings passed to become winningest ever Jeopardy!
champion

 

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Archived from groups: rec.games.trading-cards.magic.rules (More info?)

dbd@gatekeeper.vic.com (David DeLaney) wrote in
news:slrncedrfv.a8i.dbd@gatekeeper.vic.com:

> Bowmore <mapsdump@hotmail.com> wrote:
>>Brain Freeze 1U Instant
>>Target player puts the top three cards of his or her library into his
>>or her graveyard. / Storm (*)
>>
>>Gaea's Blessing 1G Sorcery
>>Target player shuffles up to three target cards from his or her
>>graveyard into his or her library. Draw a card. / When ~ is put into
>>your
>> graveyard from your library, shuffle your graveyard into your
>> library.
>
> If the Blessing is Milled during one of the Brain Freeze spell
> resolutions, original or copy, the ability will trigger and will go on
> the stack after -that resolution- is done. And will then reshuffle the
> graveyard (including the GB itself) into the library before the next
> copy of Brain Freeze on the stack gets to resolve at all.
>
>>Suppose I've been able to play one million spells (using some infinity
>>combo) and then I Brain Freeze my opponent, who has let's say 45 cards
>>left in his library.
>>But I'm not in luck and he has (at least one) Gaea's blessing in his
>>library...
>
> 45 is divisible by three, so you absolutely will not be able to even
> get his library empty this way.
>
>>Ok so I will not be able to deck him.
>>But, supposing no-one wants to interfere with the stack anymore,
>>how do we determine the state of his library and graveyard?
>
> Each time the Blessing shuffles them in, it starts again from a full
> library, so in essence you have to determine a random number between 0
> and 14 for how many Brain Freeze copies have gone off since then in
> the -ending- state. If there's more than one Blessing it complicates
> things. To simulate this:

This is only right if there is no cards in the graveyard...

After the first GB resolves, the cards that were also in the graveyard
will be put back into the deck. The deck will be back to X cards (where
X => number of cards initially in the library less the cards in play and
in hand of the GB player).

> shuffle the library
> determine your random number from 0 to 14 (use a 20-sided die)
> flip that many sets of three cards into his graveyard; if one of them
> has
> a GB in it, reshuffle at that point and continue until you reach your
> number
>
> will probably work as well as anything.
>
>>What do the rules say about this?
>
> They don't, actually; this is not an _unbounded_ loop.
>
>>Can anyone provide a practical solution that would be 'mathematically'
>>correct?

I don't know about practical solution (I think the BF player should just
scoop! he picked the wrong guy to try to combo out) but as far as a
'mathematically' correct (what's with the quotes?) solution goes...

I have constructed a spreadsheet to work out the various probabilities.
(http://members.optusnet.com.au/massm1/magic.xls). It was something I
constructed quickly so if anyone has obtained similar results I wouldn't
mind knowing (it is ego boosting to know it is correct).

For any number of Brain Freezes cast (and any number of cards in the
library/not removed from the game) it is possible to look up the chances
of how many cards ultimately get taken out by the Brain Freezes.

The problem is generating the appropriate probabilities in a match. I
leave it as an exercise to try to work out how to generate those
probabilities in a tourney...

Dave's method tends to short change the GB player quite a bit...
(e.g. the chance that the max # of cards are taken out, 42, is 1/15 =
6.7% as compared with the true probability of 0.83%) but it might be the
best available with only dice and no computers...

Kelly
(beware the analyst with a lot of time on his hands!)

 

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Archived from groups: rec.games.trading-cards.magic.rules (More info?)

yeah these things get quite anoying, and while the chances of not
seeing certain cards is low, alot of people don't bother with 1000000
iterations, they just pick say 1000 or even 100, i mean both are
numbers more than high enough to kill and anything higher can just get
anoying.

On Sat, 03 Jul 2004 21:36:25 +0200, Bowmore <mapsdump@hotmail.com>
wrote:

>Peter Cooper Jr. wrote:
>> Bowmore <mapsdump@hotmail.com> writes:
>>
>>>Suppose I've been able to play one million spells (using some infinity
>>>combo) and then I Brain Freeze my opponent, who has let's say 45 cards
>>>left in his library.
>>>But I'm not in luck and he has (at least one) Gaea's blessing in his
>>>library...
>>>
>>>Ok so I will not be able to deck him.
>>>But, supposing no-one wants to interfere with the stack anymore,
>>>how do we determine the state of his library and graveyard?
>>
>>
>> Very Good Question.
>>
>> This was discussed last month on the DCIJUDGE-L list.
>> <http://oracle.wizards.com/scripts/wa.exe?S2=dcijudge-l&s=1.5+Questions>
>> <http://oracle.wizards.com/scripts/wa.exe?A2=ind0406A&L=dcijudge-l&P=R2107>
>>
>> People came up with some "approximations", but I don't recall anything
>> being a definite "do it this way" answer.
>>
>
>Makes for some interesting reading.
>And pondering the problem a bit further I came upon another issue
>with this simulation (which will definitely fall in the far-fetched
>category)
>
>So:
>
>Assume we have a simulation (mathematically correct or not) that both
>players accept.
>
>Player 2 (whose library is being milled a lot) may have 1 to 4 copies of
>Gaea's Blessing in his library.
>Suppose that all copies are in the players library.
>
>Player one can see at most three of them at the same time (during one
>resolution of a BF copy), after which they all get shuffled back
>in the library (upon resolving the triggered effect of the last of those
>GB's that got milled).
>
>Now how to determine what information player 1 got about the actual
>number of GB's in player 2's library?
>
>He saw at least one.
>He definitelty did not see four.
>What are the odds he saw two?
>What are the odds he saw three?
>
>And then even wackier :
>
>It is theoretically possible that player 1 did not see all cards of
>player 2's library.
>What are the odds of a card that occurs n times in the library, not
>being revealed to player 1 after x resolutions of BF?
>
>
>Finally I'd like to stress that I am aware of how far-fetched this is,
>it's just fun to explore the complexity of the game of magic.
>
>Thanks in advance.

 

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Archived from groups: rec.games.trading-cards.magic.rules (More info?)

Kelly Trinh wrote:
>>>Can anyone provide a practical solution that would be 'mathematically'
>>>correct?
>
>
> I don't know about practical solution (I think the BF player should just
> scoop! he picked the wrong guy to try to combo out) but as far as a
> 'mathematically' correct (what's with the quotes?) solution goes...
>

Actually I was the guy with the BF... I didn't scoop because I had other
win conditions up my sleeve.
(I chose to play 1 million spells because that just seemed arbitrarily
large enough... If I'd known he had GB's in his deck, I wouldn't even
have bothered with the BF of course)

What's with the quotes? I had hesitated to use 'logically' instead.
In hindsight, I'd opt for 'statistically'.
I was just unsure in which field a good answer could lie.

> I have constructed a spreadsheet to work out the various probabilities.
> (http://members.optusnet.com.au/massm1/magic.xls). It was something I
> constructed quickly so if anyone has obtained similar results I wouldn't
> mind knowing (it is ego boosting to know it is correct).
>
> For any number of Brain Freezes cast (and any number of cards in the
> library/not removed from the game) it is possible to look up the chances
> of how many cards ultimately get taken out by the Brain Freezes.
>
> The problem is generating the appropriate probabilities in a match. I
> leave it as an exercise to try to work out how to generate those
> probabilities in a tourney...
>

I have been pondering the problem a bit longer and found that the state
of the library and graveyard are just one piece of the puzzle.
Additional problems are :

How many of the total GB's got revealed to the BF player? (minimum 1,
maximum 3, even that depends on how many there are in the
library/graveyard to begin with)
How to determine the odds (that are definitely influenced by the number
of GB's) without revealing this number to the BF player, and still have
him accept a simulation?
How to determine which cards got revealed and which didn't, through
simulation? (this is influenced both by the number of GB's and by the
number of that particular card in the deck)

> Dave's method tends to short change the GB player quite a bit...
> (e.g. the chance that the max # of cards are taken out, 42, is 1/15 =
> 6.7% as compared with the true probability of 0.83%) but it might be the
> best available with only dice and no computers...
>
> Kelly
> (beware the analyst with a lot of time on his hands!)

Do you have a lot of time on your hands? Perhaps you might give the
three additional questions I posed above a try...

Thanks for the input, I'll certainly have a closer look at that
spreadsheet of yours.

Greetz,

Bowmore