Blessing question

[Team-Judgement]

Player 1 Has 31 cards left in his library, no cards and in hand and his graveyard are removed, he also has 1 gaes blessing back in his library

Player 2 Has gone infinite with worldgorger dragon and animate dead, he has a deep analysis, and a Laquatus Ambassadør in his graveyard, he hasnt stop his loop, so basicly he has infinite mana, but need to choose a number

So now he chooses the number 10000000000000000000000000000 0000000 So he got that many blue mana in his mana pool. Does he need to mill Player 1's library until blessing is the last card left and then use deep, or can a judge or player see that Player 1 is going to loose at one time

Well i once asked this question to a Jesper Sther(a danish lvl 3 judge)but he didnt give me an answer i could use for anything, he said that u couldnt because.... well it didnt work

What do you need to do to prove that Player 2 is going to win, if not in the time then in one of the extra turns. We discussed this alot and most players couldnt see how Player 2 could be accused for staling, because he does something active all the time

[Jebus]

I'll have to be honest.  I don't have a good answer for you.

I'll go ahead and say, you can't prove that you would be able to get their library into their graveyard with just blessing remaining within your activations of Laquatus.

So, you're kind of stuck.

But, how to resolve this?  I'll have to get back to you on that.  I'm going to have to confer with some others.

In the mean time, get some instant speed draw.  That will let you win.

[Ephraim]

You could probably figure out the probability of one or more Gaea's Blessings  being the last N cards in that player's library. Assuming you know exactly how many Gaea's Blessings are in the deck, this is possible. You could then declare a confidence interval of arbitrarily small size and mathematically determine the amount of mana necessary to achieve the desired result (Blessings on the bottom) within that confidence interval. I'm not saying that a judge would have to allow it, even in this situation, but I suppose that having rigourous mathematics that state that your opponent has one chance in a google of winning, if the mana is applied might be better than relying on intuitive probability alone.

[Razvan]

I think that Sheldon answered this like 1-2 years ago on SCG.

Basically, you can advance the game to any state with a limited ammount of repetitions, but only if every step can be safely predicted, and, more importantly, every aspect of that step as well. As Gaea's Blessing shuffles the deck, this cannot be done, as shuffling is random.

Technically and statistically, yes, there will be a state where the Gaea's Blessing will be the 31st card, and yes, this will happen, rather early as well (chances are, within 31 attempts). Milling the library 33333333333333333333333333333 33333 times with that mana pretty damn well guarantees that it will happen.

Alas, since you cannot predict, you are stuck either doing it about 31 times (people might frown), or finding another way to do this.

[Bram]

The number of mana he makes is obviously irrelevant as long as Blessing would be the exact last card. It being the second-to-last card just won't do, since the odds of burning yourself to death if you pass to a new phase are staggering.

Ephraim is right. It's all about confidence intervals, or rather expectance values.

In statistics and probability, an 'alpha' of 0,05 or 0,01 are often used (corresponding with a 'certainty' of 95% and 99% respectively).

So for starters, let's say you want to be 99% sure you get it right. There's no hypergeometric distribution involved in the probability calculations this time, because we're not drawing a card while not replacing it (as we would do for calculations concerning the likeliness of having something specific on hand on turn one or so). Rather, we simply want to know first of all: what is the probability that in a 31 card deck with 1 Blessing, the Blessing is on the bottom (or, rather, on any specified location) after shuffling the deck thouroughly. That's easy: the probability is 1/31. So what if I do it twice? Does it become 2/31? Um, nope. Because if it did, you'd only have to do it a maximum of 31 times for a 100% success ratio. And intuitively, we know that's impossible (since there will always be a slight chance you NEVER get it right).

Actually, when shuffling twice, you're using so-called 'complimentary' odds. The probability of the Blessing being in the right place (let's call this P(Y) for 'yes') is one minus the probability of it NOT being in the right place (P(N) for 'no'), to the power of two (the number of times you try it). In symbols:

P(Y) = 1 - P(N)^2

Now if we solve the following equation (subsituting 2 by X, because the bnumer of times we need to do it is what we really want to know), we find out how many times you need to shuffle the guys library to have had a 99% chance of having the Blessing in the correct posistion once.

Solving:

0.99 = 1 - (30/31)^x

produces X=140. This means that if you repeat the whole trick 140 times, there's a 99% chance you'll have had the Blessing as the bottom card at one point.

But 99% chance might be too rigorous. Let's say 95%.

0.95 = 1 - (30/31)^x gives X=91.

You can do this for any number really. Concluding, some results:

140 shuffles give you a 99% expectance of winning
91 shuffles give you a 95% expectance of winning
49 shuffles give you a 80% expectance of winning
21 shuffles give you a 50% expectance of winning

In the end, it's all up to the judge to disregard the statistics of it all or not. If the judge says 'I'll give you time for 10 attempts', your odds of winning drop to 28%.

A judge can either rule:
1. allright, so if I gave you, like, 90 or thereabouts attempts you'd win this, so I declare you the winner, or
2. it'd take too long to actually do that and there was ALWAYS be a chance you'd never win it at all, so I'll give you X attempts (or the remainder of the time on clock) to try your luck.

I highly doubt he can get you for stalling, since you're not doing that at all. At worst, he can take option 2 and make you sweat for the remainder of the time. At least now you'll now your chances :-)


[edit] @Razvan: chances of it happening after 31 tries are some 64%.

[leviat]

Personally I think that the Dragon player should not be allowed to win in this case. Why? Because typically, the point to having a Blessing is to prevent yourself from being decked. To play around it should require skill on behalf of the person playing the Dragon deck. Since they do not have instant speed draw or instant speed GY removal, they have not sufficiently played around the protection and therefor the opponent should not be decked.

I would argue that continueing to deck the opponent over and over is to rely solely on dumb luck and results in delay of game.

[Bram]

That's kind of weird. It's not dumb luck, it's probability. I can't see why a judge would not let the dragon player try to combo out. If he makes it in time, he wins. If he doesn't, he loses.

The other player always has the option of conceding...

[Ephraim]

The other player should certainly not concede if you decide to try to play it out. That guarantees a loss on his part when, in fact, if he were to continue playing, he might be able to eck out a draw, or even a win, if he can somehow find a way to force the game into the next phase, inducing mana burn.

[ProZachar]

How many other competitive events/sports allow a game- or tournament official to say "Well, we've determined that player/team A has a 99% chance of beating player/team B if we play this out, so we're going to stop play and give player/team A the win"?

I've thought about it for the last 5 minutes, and the only types of "game" I can come up with are contact fighting events.  But that's because "we've determined player A has a 99% chance of winning if we play this out" often means "player B has an unacceptably high chance of leaving this place with serious and/or permanent injuries, including death, if we play this out".

[Ephraim]

This isn't a real system, though. You can generate enough mana such that the probability of your opponent winning is about as small as the probability that you'll spontaneously quantum tunnel through the floor of the tournament hall.

[brianb]

We worked this question over in a previous thread.

It is a statistical certainty that if you had enough time, you could win the game in this scenario.  You do not have infinite time, though, and there is no rule explicitly forcing your opponent to concede to an arbitrarily overwhelming probability of defeat.  So if you are ahead 1-0 in games, feel free to mill them to your heart's content.  Either you will win the game or time (and any overtime the judge wants to allow) will expire.  You win the match 1-0 (or 2-0 if you get lucky).  This could not be contrued as stalling, since you are following an algorithm which would certainly lead to victory, given enough time.  If you are behind 1-0 in games, you may want to consider some other strategy if the remaining time is unlikely to yield you the result you desire.  With a full clock, you could try a bunch of shuffles, and if your opponent doesn't slow-shuffle, have a decent chance of success.  You may at some point have to settle for something less than the optimal solution, pumping all the mana into the ambassador and letting the chips fall where they may.  If you are at 0-0 or 1-1, it will be a strategic decision how long you want to keep milling.  In the 0-0 case, it's up to your opponent how long they want to let you go before conceding.  Depending on the tournament situation, the two of you might just let it end as a draw.

[Machinus]

The rules explcitly state that a match cannot be determined by random methods.

Therefore, there are two scenarios that a judge should take: limiting the dragon player on time, or limiting him on attempts.

Clearly if the round has ended, the players are in extra turns, and the dragon player is generating mana and sinking it and the oath player (what else runs blessing?) is shuffling, they are not stalling. There are no provisions in the rules for this kind of thing, so I would say that if you want to do it as fairly as possible, you should limit it by attempts.

So, clearly the more attempts that are allowed, the better it is for the dragon player. How many attempts should be allowed? Bram's formula is correct, and so all that we want to do is determine the fairest and most equal solution to both players. The dragon player has already committed himself to a game of chance in order to win, and so I don't think he gets any special consideration in terms of probability. The oath player has the necessary tools in his deck to fight the game of chance, and so he also has committed himself against this game. There is no other way to determine the outcome than by the following calculations:

50% chance of winning to both players

0.50 = 1-(.967741...)^X

X = 21.139... attempts

Rounding gives 21 attempts to the dragon player to find the blessing last.

(Bram already did this calculation, but I wanted to show why it is important.)

[brianb]

There's no need to limit the attempts.  The dragon player can try as many times as he pleases.  Eventually, the judge has to declare that the time has expired.  Since the 5 turns will not complete, he will have to exercise his perrogative to limit the overtime.  He declares that the match ends in 5 (or 10 or whatever) minutes.  At the end of that time, the match is a draw if nobody has won.

[Machinus]

A judge can't just arbitratily set a time limit on the games. That just causes too many problems within the preestablished rules. Extra turns was implemented in order to make time a NON issue, so that stalling and things like that could be avoided. It poses too many problems and fairness issues to say that for a certiain deck in a certian scenario, you get extra time. The round ends when it ends for everyone, and so there has to be some additional discrete limitation on the game, some kind of definite restriction. The player is going infinite within the space of a single turn, so the established means are clearly insufficient to address the problem. This is a unique and unaddressed issue, but since it is relatively obscure, of course a judge is allowed to do whatever he/she wants, or thinks is fair or best. But the whole reason for this thread is that no solution has been good enough so far. And limiting time is, I think, not good enough.

[brianb]

I don't see overtime time limits in the rules, but I've seen them enforced at the PT level--specifically at PT Rome when high tide and academy were running around extended.  So many minutes after the regular time ended, the game was cut off.  This is a practical necessity when you have a lot of combodecks that can take very, very long turns.  In this case, it is an absolute necessity, since there is nothing else that can reasonably stop the dragon player from going on all day.

[Team-Judgement]

So you get to mill the rest of the time + f.x 5-10 minutes or what the judge decide, and then its all about luck.... But i suppose this should be different from judge to judge, and against who you play against. On the other side it seems unfair that a judge can simply stop the game if he when he likes it, since the dragon player with infinite time will win, and everybody know this, it would be quite fair if he was going to win.... i think  :shock:

But wont the most players conceede if this scenario happens....

[Limbo]

Shouldn't we adres wizards to make a ruling for this scenario? Using mathematics you can calculate how much mana you need to create to make the chance of your opponent surviving like 1/googol. I'd say having a chance of 1/googol of surviving a loop is sufficient to make a player just flat out lose.

It's the same with an Isochron sceptered final fortune in combination with a platinum angel and a previously active but now disabled infinite life loop for the opponent. The opponent will die as well, but officially it will take infinite time to do so.

I'd say as long as there is no ruling about this it is all about the sportsmanship of the player at the receiving end of the beating...

[Dante]

If the match was 1-1 or the non-dragon player was up 1-0, why would that player concede?  No way would they concede, they would make the other player actually have to kill them - between the shuffling and cutting, no way the dragon player would win unless they got lucky.  Furthermore,  no judge in their right mind would or should give you the win because you can mathematically prove you statistically will get the blessing at the bottom...you need to actually win.

Bill

[Bram]

OK, so I contacted a level 4 (count 'em...FOUR judge about this scenario. He told me there were no absolutely clear rules on this scenario and that it's mostly a judgement call (note however that a judge can still make a wrong, basically illegal decision in this case). He stated that:

1. It is not stalling by any means if the player isn't playing slow. He's actually trying very hard to win, and should be allowed to do so.
2. There will be no automatic wins or losses declared because the outcome isn't certain.
3. the dragon player WILL be allowed to spend the rest of the match trying to go off. The judge, however, will be watching closely, keeping an eye out for intentional slow play on either side. Both players will be asked to find and implement an acceptable 'shortcut'. In this case it means the whole 'milling' process can be skipped after it becomes apparent (after one complete mill or so) that nothing ELSE can happen. The other player will be asked to shuffle his deck and reveal the bottom card as many times as the Dragon player wants, since this is basically what it comes down to. If the Blessing hits the bottom slot eventually, the Dragon player must finish the game and win. If it doesnt come up during the duration of the match, it's a draw (unless the dragon player makes the mistake of going to the next phase

And that's the end of it, boys'n'gals.

[Limbo]

Hmm, this is quite an unsatisfying solution, but at least better then a judge setting a time the dragon player gets for trying to win.

What about the infinite damage loop with final fortune / platinum angel? In that scenario the "winning" player can get a draw at maximum?

[Jebus]

What about the infinite damage loop with final fortune / platinum angel? In that scenario the "winning" player can get a draw at maximum?

Can you expand on this a bit.  I believe I know what you are referring to, but I want to make sure as this can possibly end up quite different.

I don't know which Level 4 Bram contacted...but I agree with that judge's assessment.

[Bram]

Jaap Brouwer. I could also ask Gis and make it a level 5 call if you like

[Jebus]

Jaap Brouwer. I could also ask Gis and make it a level 5 call if you like

I said I agreed with him.  

I was going to go the same route yesterday, but I unfortuantely did not have the time.

[Bram]

I know. I read your post. I wasn't being sarcastic

Good. You'll make a fine lvl 4 one day!

[Gandalf_The_White_1]

OK, so I contacted a level 4 (count 'em...FOUR judge about this scenario. He told me there were no absolutely clear rules on this scenario and that it's mostly a judgement call (note however that a judge can still make a wrong, basically illegal decision in this case). He stated that:

1. It is not stalling by any means if the player isn't playing slow. He's actually trying very hard to win, and should be allowed to do so.
2. There will be no automatic wins or losses declared because the outcome isn't certain.
3. the dragon player WILL be allowed to spend the rest of the match trying to go off. The judge, however, will be watching closely, keeping an eye out for intentional slow play on either side. Both players will be asked to find and implement an acceptable 'shortcut'. In this case it means the whole 'milling' process can be skipped after it becomes apparent (after one complete mill or so) that nothing ELSE can happen. The other player will be asked to shuffle his deck and reveal the bottom card as many times as the Dragon player wants, since this is basically what it comes down to. If the Blessing hits the bottom slot eventually, the Dragon player must finish the game and win. If it doesnt come up during the duration of the match, it's a draw (unless the dragon player makes the mistake of going to the next phase

And that's the end of it, boys'n'gals.

I don't see how this solves the time problem.  Theoretically, even with the shortcut, the game could end up lasting a week as the dragon player keeps trying and the bottom card doesn't appear (or even 50 years).  Is a draw/concession on the part of the players the only way to end that thing?

Also, wow finally an actual good rules question.

[Jebus]

Extra turns don't really have a time limit, but they can't last forever.

You won't be able to keep playing for ever.  Eventually the judge will have to intervene in that case.

[Gandalf_The_White_1]

Extra turns don't really have a time limit, but they can't last forever.

You won't be able to keep playing for ever.  Eventually the judge will have to intervene in that case.

Well, you will die eventually . (Edit: literally, not in the game)

So, then I suppose it's up to the judge's discretion and he/she can stop you after a couple of hours or w/e if it's getting out of hand.  (Man, this would really suck if it happened at a tourney and the round was delayed for like 2 hours... attention all dragon players: COMPULSION > BAZAAR)

[Jebus]

It would never be delayed for hours.  Extra turns should not last more than a few minutes.

[Limbo]

What is quite weird is, that the outcome of this is dependant of the round. Suppose this is in the T8 (lets say the finals), then time limit does not apply, so the dragon player has all the time to do his stuff in the one fase, untill he wins. In this case, it is quite easy to use the arguments stated above to mathematically prove that you will win, and thereby prevent flipping the bottom card an X number of times untill blessing is last call, so that game ends then and there, without taking like 1-30 minutes to prove he is right.

If this is in like swiss, and you have the exact same situation, and again you don't leave the fase untill you win, then you could end up with a draw.

It makes no sense that when there is no time limit, you are actually done quicker...

[sidenote]As for the platinum angel situation:
Player A: Platinum Angel in play
Isochron scepter in play (Final Fortune imprinted)
Mana sources to activate the scepter

Player B: Confirmed no solution to the angel or the scepter (lets suppose tapped out, and no cards in hand)
No blockers for the angel.

If player B is at infinite life because of a previous active loop (lets say zuran orb, fast bond, crucible of worlds) but no longer is able to use that loop, will player B lose or not within the time limit? I'd say it is the same situation as the blessing / ambassador thing. You can prove you will win, but you need time to do so.

[Ephraim]

I'd say that player A wins in that situation. In the Dragon situation, the only way the probability of player B winning goes to zero is given infinite time. Since somebody who's executed an "infinite life" combo isn't actually at infinite life, but at an arbitrarily large finite amount of life, the probability of that player winning goes to zero in finite time, so player A should take the game.