Having 1 leonin and 1 ghost quarter by turn 2 is a 23% chance, if you allow yourself to mulligan once for one of them. It is not THAT hyperbolic as you think, specially if you consider half way situatiosn like 1 leonin 1 quarters and 1 path by turn 3 ( not as crippling but effectively timewalking opponent by 2 turns.
Now if anyone want to niptick things. the hypergeometric calculated chance is 5.1% Not 4.3% Monte carlo simulations have a huge problem, they are done in computers that have lousy number generators. If you can settle for arbiter + 1 quarter +1 path as well the chance goes to a tiny bit over 17%
Quote from wagawagawali
I just won a game against jund yesterday with leonin and craking 2 ghost quarter turn 3.
Lost to jund nearly a weak ago on the Russian Modern Championship (finished 31 =( ) performing the same trick.
"I just got flooded, but You've fixed it" ,- said my opponent after the match.
I mean, performing such move w/o any information about enemy's hand is quite risky. One thing is certain: You will have minus 2 mana on a table. Other things are quite concealed.
I know. I'm one of the ones who doesn't (though it seems well-positioned, so that may have to change). I'm just saying that the option is out there. And if you don't have it, don't sell out on the land-hate plan that aggressively.
Stops Kiki-chord combo
Slows some aggressive decks down and gains life.
1 mana makes it early and easy to cast
One-sided
Not legendary
Hurts opponent lingering souls a bit
It might be better for soul sisters but still an exciting card!
Doesn't quite stop Kiki-chord as they can kiki-resto in the end step. It does slow them down however
Am I missing something? They have kiki in play, it's your end step, they flash in resto and make a million angels. They all enter tapped. you gain a million life. Now it's their turn. Untap all the angels and swing for 3 mil.
edit: I am missing something. Kiki enters tapped. Opps.
Now if anyone want to niptick things. the hypergeometric calculated chance is 5.1% Not 4.3% Monte carlo simulations have a huge problem, they are done in computers that have lousy number generators.
Actually, CharonsObol's 4.3% Monte Carlo estimate was quite accurate; the analytical solution using the multivariate hypergeometric distribution gives 2,455,606/56,858,241 (i.e approximately 0.0431882).
I'll throw the math in a spoiler for the curious. It's basically just an example similar to the examples cooked up in the post/article "How I Learned to Stop Worrying and Love the Hypergeometric Distribution" but specific to the Arbiter/GQ situation and with some properly typeset math (as much as I love that link, it kills me trying to follow that ascii math visually).
Assumptions:
A typical 60 card deck.
4x Arbiters in the deck.
4x GQ in the deck.
Card 9 is drawn on turn-3.
We are looking for the odds of drawing a certain subset of hands (a.k.a. the nutdraw, God hands, combo) that offer the potential for pulling off the double-wasteland trick on turn-3; to do this we'll want 1xArbiter (or more) and 2xGQ (or more).
We'll make the simplification that our deck only has three kinds of cards: Card_A (the Arbiters), Card_B (the GQs), and Card_X (the unspecified cards). The odds of drawing a certain number of each type of card from the deck is given by the following equation:
where NA is the number of Arbiters in the deck (4), NB is the number of Ghost Quarters in the deck (4), NX is the number of other cards in our deck (52), and ND is the size of our deck (60). The number nd is the total number of cards we've drawn (which is 9 cards by turn-3 for the example), and na and nb are the numbers of Arbiters and GQs we've drawn, and nx is the number of filler cards we've drawn. Tracking everything, na+nb+nx=nd should always be true, otherwise there has been a mistake.
Drawing 1xArbiter is a possibility that can satisfy the desired criteria. How many GQ must be drawn to satisfy the remaining criteria? 2xGQ or 3xGQ or 4xGQ are all fine. Adding those possibilities together (with the numbers plugged in for the variables) looks something like:
Drawing multiple Leonin Arbiters is perfectly acceptable too. Accounting for everything there are 12 possible outcomes; all combined the result is given by:
This is all still pure combinatorics with discrete integer inputs and the result is still purely analytical. Carrying out the algebra gives exactly P=2,455,606/56,858,241 which expressed as a decimal number is 0.043188216 to the first 8 digits.
tl;dr: 4.3% is legit.
For other multi-card combos (like drawing 1xVial 1xThalia 1xArbiter in your opening hand for example) the multivariate hypergeometric distribution can be expanded out for more and more complicated combinations. You just have to specify more "types" of cards and plug them in correctly according to something like this:
and then be very careful to track every allowed possibility.
Now if anyone want to niptick things. the hypergeometric calculated chance is 5.1% Not 4.3% Monte carlo simulations have a huge problem, they are done in computers that have lousy number generators.
Actually, CharonsObol's 4.3% Monte Carlo estimate was quite accurate; the analytical solution using the multivariate hypergeometric distribution gives 2,455,606/56,858,241 (i.e approximately 0.0431882).
I'll throw the math in a spoiler for the curious. It's basically just an example similar to the examples cooked up in the post/article "How I Learned to Stop Worrying and Love the Hypergeometric Distribution" but specific to the Arbiter/GQ situation and with some properly typeset math (as much as I love that link, it kills me trying to follow that ascii math visually).
Assumptions:
A typical 60 card deck.
4x Arbiters in the deck.
4x GQ in the deck.
Card 9 is drawn on turn-3.
We are looking for the odds of drawing a certain subset of hands (a.k.a. the nutdraw, God hands, combo) that offer the potential for pulling off the double-wasteland trick on turn-3; to do this we'll want 1xArbiter (or more) and 2xGQ (or more).
We'll make the simplification that our deck only has three kinds of cards: Card_A (the Arbiters), Card_B (the GQs), and Card_X (the unspecified cards). The odds of drawing a certain number of each type of card from the deck is given by the following equation:
where NA is the number of Arbiters in the deck (4), NB is the number of Ghost Quarters in the deck (4), NX is the number of other cards in our deck (52), and ND is the size of our deck (60). The number nd is the total number of cards we've drawn (which is 9 cards by turn-3 for the example), and na and nb are the numbers of Arbiters and GQs we've drawn, and nx is the number of filler cards we've drawn. Tracking everything, na+nb+nx=nd should always be true, otherwise there has been a mistake.
Drawing 1xArbiter is a possibility that can satisfy the desired criteria. How many GQ must be drawn to satisfy the remaining criteria? 2xGQ or 3xGQ or 4xGQ are all fine. Adding those possibilities together (with the numbers plugged in for the variables) looks something like:
Drawing multiple Leonin Arbiters is perfectly acceptable too. Accounting for everything there are 12 possible outcomes; all combined the result is given by:
This is all still pure combinatorics with discrete integer inputs and the result is still purely analytical. Carrying out the algebra gives exactly P=2,455,606/56,858,241 which expressed as a decimal number is 0.043188216 to the first 8 digits.
tl;dr: 4.3% is legit.
For other multi-card combos (like drawing 1xVial 1xThalia 1xArbiter in your opening hand for example) the multivariate hypergeometric distribution can be expanded out for more and more complicated combinations. You just have to specify more "types" of cards and plug them in correctly according to something like this:
and then be very careful to track every allowed possibility.
Thank you for this post! I really wish I could upvote this twice. I'm sure it took forever to type up too, let alone get the analytical number. The LaTeX formatting looks great.
I'm glad that my simulation was accurate. The verification is really nice; my math aptitude isn't good enough for me to do it myself, unless I simplify the problem like I did here:
EDIT: **For the purposes of checking my program, I just ran a Monte Carlo simulation calculating the probability of finding at least one copy of a 4-of in your opening hand of 7 cards, with a 60-card deck. The analytical solution is 39.95%. My simulation returned 39.98%. The only other possible problem is that there is a bug in my code, but only for that particular case that tiago_oldman was concerned with.
From that case, I knew that a million trials wasn't enough to get the hundredths digit accurately, so I just shaved it from my ultimate answer of 4.3%.
For what it's worth, I just ran the same simulation with ten million trials, and the result was 4.31338%. In essence, moving up an order of magnitude in trials bought me an extra digit for my answer. There's clearly diminishing marginal returns on CPU time though, so as long as the Monte Carlo simulation returns a "good enough" answer, that's really all I can hope for.
The advantage of a Monte Carlo simulation rather than analytical solutions, is that it allows me to check complex probabilities involving Æther Vial. For example, let's say tiago_oldman wanted a more accurate number, where we actually needed the resources to put Arbiter into play by T3. That answer involves either finding a white mana source by turn 2 (the number of which varies from deck to deck) or an Æther Vial on T1. While it's not impossible to calculate that analytically, each extra dimension of complexity added makes it harder and harder to calculate. At some point, it just becomes easier to simulate.
Playing millions of cards every turn... Slowly and systematically obliterating any chance my opponent has of winning... Clicking the multitude of locking mechanisms into place... Not even trying to win myself until turn 10+ once I have nigh absolute control... Watching my opponent desperately trying to navigate the labyrinthine prison that I've constructed... Seeing the light of hope fade and ultimately extinguished in an excruciatingly slow manner... THAT'S fun Magic.
We have 2-3 users that are dramatically making this thread incomprehensible and non-productive for anyone else to possibly join in the discussion. This needs to change.
Every time I see [ktkenshinx] post in here, I get the impression of a stern dad walking in on a bunch of kids trying to do something dumb and just shaking his head in disappointment.
Near Mint: The same as Slightly Played, but we threw some Altoids in the box we stored it in to cover up the scent of dead mice. Slightly Played: The base condition for all MTG cards. This card looks OK, but there’s one minor annoying ding in it that will always irritate and distract you whenever you draw it. Moderately Played: This card looks like it survived the Tet Offensive tucked inside the waistband of GI underwear. It may smell like it, too. Heavily Played: This card looks like the remains of Mohammed Atta’s passport after 9/11. It may be playable if you double-sleeve it to stop the chunks from falling out. The condition formerly known as "Washing Machine Grade" Damaged: This card is the unfortunate victim of a Mirrorweave/March of the Machines/Chaos Confetti/Mindslaver combo.
[M]aking counterfeit cards is the absolute height of dishonesty. Ask yourself this question: Since most people...are totally cool with the use of proxies...what purpose do [high] quality counterfeit cards serve?
Recently thanks to the rotation of standard format, could pick up a playset of Collected Company and decided to build a D&T arround them. This is a W/G version some of you may believe is more a Hatebears deck but i try all the time to conserve the death and taxes most relevant cards.
Your list plays 4xFlickerwisp along with plenty of blink targets (Finks+Splicer), it seems fair to call your deck D&T and not Hatebears (even with the CoCo in there).
Without Noble Hierarch, your deck feels more like a mono-white list with a green micro-splash for CoCo, Gavony, and Witness. That is not necessarily a bad thing, just something to consider when you're tweaking your deck. Are you having any trouble with the 1GG cost of Witness?
Also, I usually hate parking my vials at 2 counters so I never really liked the idea of Epochrasite. Running Epochrasite in a list with CoCo is interesting, though, so +1 for that neat little idea.
The cost of the Eternal Witness is only a problem if your opponent is playing Blood Moon, hopefully in my LPS is not that common that a player uses a deck with several copies of it in the main, otherwise you will always or almost always have the vial to put her in play.
Epochrasite is an excelent card, i know is not the most powerful card but is a beater that can returns to play after a lost combat, so you can attack or block without fear of losing it. It can survive to Anger of the Gods and that is perfect because this card is becoming more popular with the valakut decks. I still thinking about what to do, do you think it will be good to change it for Thalia, Heretic Cathar, Loxodon Smiter, main Spellskite, Restoration Angel, Eldrazi Displacer, Brimaz, King of Oreskos or any other card?
Stops Kiki-chord combo
Slows some aggressive decks down and gains life.
1 mana makes it early and easy to cast
One-sided
Not legendary
Hurts opponent lingering souls a bit
It might be better for soul sisters but still an exciting card!
It's interesting for sure, but we just got Thalia, heretic cathar so I can't imagine wanting to run that MD over her and feel like there have to be better SB options.
Thank you for this post! [...] I'm glad that my simulation was accurate.
The advantage of a Monte Carlo simulation rather than analytical solutions, is that it allows me to check complex probabilities...
Yeah, no problem man. This specific example was right at the edge of doable by hand for me, so I'd rather you not feel shaky on your (good) MC code in case a new question gets kicked up further down the road. Conditional decision trees and/or stuff with more than two named cards is just not something I want to attempt by hand. Ever. lol
I just tried a build of WU Death and Tempo with a GY subtheme in a modern friendly league and went 4-1, losing only to burn (0-2
0 and beating a nivmagus elemental deck, infect, mill, and jeskai nahri kiki combo deck.
I had some anti burn stuff in the board, but I may have to change it up a bit. The biggest problem I noticed was that I had no idea how to sideboard with it. This is the current list:
I can't really say how well JVP performed because he was prioritized by my opponents over almost everything else. The only game I used him at all was against mill in which he flipped after 1 use. I did play a game before the tournament in the practice rooms against Junk where he was really good. I dropped him when we had ground down to nothing and he just pulled me ahead.
Every time I used Skaab, it was pretty nuts. it's a only a beater, but it hits haaard and can block any fatty your opponent has. Path kills it well, but burn or kill spells have a hard time since it has recursion and just huge toughness. The rest of the deck played very tempo-y. I think this version has a pretty good MU vs infect since you have added disruption in the form of bounce and also spell queller can stop them from protecting their dudes/ buffing them while also being a relevant air blocker for inkmoth.
Not all of the MUs were top tier, but it felt pretty good against nihiri too. The idea of having vial up to reflector mage their Emrakul, the aeons torn is just dirty.
For burn, I'm wondering if I just had some bad luck. If I keep having problems against them, I'll add another kor firewalker to the board.
My thought behind 3 arbiter is that JVP helps consistency. I know you usually want arbiter early, but with the mindcensors too, it felt like enough. I didn't want to load on up 2 drops too much. Do you think cutting the 4th one was a mistake?
The flooded strands help to reduce merfolks inherent lead over you as well as buff your yard for JVP ideally. The mana base felt pretty decent and as always moorland haunt is a powerhouse.
Thank you for this post! [...] I'm glad that my simulation was accurate.
The advantage of a Monte Carlo simulation rather than analytical solutions, is that it allows me to check complex probabilities...
Yeah, no problem man. This specific example was right at the edge of doable by hand for me, so I'd rather you not feel shaky on your (good) MC code in case a new question gets kicked up further down the road. Conditional decision trees and/or stuff with more than two named cards is just not something I want to attempt by hand. Ever. lol
I originally built the MC code because I'm currently playing WG D&T, and I wanted to know how often I would get an opening hand with a T2 land-destruction play involving Hierarch, Arbiter, Ghost Quarter, and a green mana source. Not surprisingly, the odds are pretty low. But at least I can have a little more confidence in that answer now.
I just tried a build of WU Death and Tempo with a GY subtheme in a modern friendly league and went 4-1, losing only to burn (0-2
0 and beating a nivmagus elemental deck, infect, mill, and jeskai nahri kiki combo deck.
I had some anti burn stuff in the board, but I may have to change it up a bit. The biggest problem I noticed was that I had no idea how to sideboard with it. This is the current list:
I can't really say how well JVP performed because he was prioritized by my opponents over almost everything else. The only game I used him at all was against mill in which he flipped after 1 use. I did play a game before the tournament in the practice rooms against Junk where he was really good. I dropped him when we had ground down to nothing and he just pulled me ahead.
Every time I used Skaab, it was pretty nuts. it's a only a beater, but it hits haaard and can block any fatty your opponent has. Path kills it well, but burn or kill spells have a hard time since it has recursion and just huge toughness. The rest of the deck played very tempo-y. I think this version has a pretty good MU vs infect since you have added disruption in the form of bounce and also spell queller can stop them from protecting their dudes/ buffing them while also being a relevant air blocker for inkmoth.
Not all of the MUs were top tier, but it felt pretty good against nihiri too. The idea of having vial up to reflector mage their Emrakul, the aeons torn is just dirty.
For burn, I'm wondering if I just had some bad luck. If I keep having problems against them, I'll add another kor firewalker to the board.
My thought behind 3 arbiter is that JVP helps consistency. I know you usually want arbiter early, but with the mindcensors too, it felt like enough. I didn't want to load on up 2 drops too much. Do you think cutting the 4th one was a mistake?
The flooded strands help to reduce merfolks inherent lead over you as well as buff your yard for JVP ideally. The mana base felt pretty decent and as always moorland haunt is a powerhouse.
I love the list.
It's pretty hard for me to comment on the 4th JVP, because I've never tested it in this deck before. I've been having a lot of success with Selfless Spirit though, so I'd consider running a few more of those (even though you didn't want to load up on 2 drops). They swing for damage while protecting your taxers and Spell Quellers; I've had a few games now where double Selfless Spirit basically locks my opponent out of the game, especially if it's protecting a Thalia or Arbiter.
I'm glad that Ruinator is doing some work for you. That card is pretty underrated in the blue splash, and it must feel awesome to pitch that to JVP.
Playing millions of cards every turn... Slowly and systematically obliterating any chance my opponent has of winning... Clicking the multitude of locking mechanisms into place... Not even trying to win myself until turn 10+ once I have nigh absolute control... Watching my opponent desperately trying to navigate the labyrinthine prison that I've constructed... Seeing the light of hope fade and ultimately extinguished in an excruciatingly slow manner... THAT'S fun Magic.
We have 2-3 users that are dramatically making this thread incomprehensible and non-productive for anyone else to possibly join in the discussion. This needs to change.
Every time I see [ktkenshinx] post in here, I get the impression of a stern dad walking in on a bunch of kids trying to do something dumb and just shaking his head in disappointment.
Near Mint: The same as Slightly Played, but we threw some Altoids in the box we stored it in to cover up the scent of dead mice. Slightly Played: The base condition for all MTG cards. This card looks OK, but there’s one minor annoying ding in it that will always irritate and distract you whenever you draw it. Moderately Played: This card looks like it survived the Tet Offensive tucked inside the waistband of GI underwear. It may smell like it, too. Heavily Played: This card looks like the remains of Mohammed Atta’s passport after 9/11. It may be playable if you double-sleeve it to stop the chunks from falling out. The condition formerly known as "Washing Machine Grade" Damaged: This card is the unfortunate victim of a Mirrorweave/March of the Machines/Chaos Confetti/Mindslaver combo.
[M]aking counterfeit cards is the absolute height of dishonesty. Ask yourself this question: Since most people...are totally cool with the use of proxies...what purpose do [high] quality counterfeit cards serve?
I just tried a build of WU Death and Tempo with a GY subtheme in a modern friendly league and went 4-1, losing only to burn (0-2
0 and beating a nivmagus elemental deck, infect, mill, and jeskai nahri kiki combo deck.
I had some anti burn stuff in the board, but I may have to change it up a bit. The biggest problem I noticed was that I had no idea how to sideboard with it. This is the current list:
I can't really say how well JVP performed because he was prioritized by my opponents over almost everything else. The only game I used him at all was against mill in which he flipped after 1 use. I did play a game before the tournament in the practice rooms against Junk where he was really good. I dropped him when we had ground down to nothing and he just pulled me ahead.
Every time I used Skaab, it was pretty nuts. it's a only a beater, but it hits haaard and can block any fatty your opponent has. Path kills it well, but burn or kill spells have a hard time since it has recursion and just huge toughness. The rest of the deck played very tempo-y. I think this version has a pretty good MU vs infect since you have added disruption in the form of bounce and also spell queller can stop them from protecting their dudes/ buffing them while also being a relevant air blocker for inkmoth.
Not all of the MUs were top tier, but it felt pretty good against nihiri too. The idea of having vial up to reflector mage their Emrakul, the aeons torn is just dirty.
For burn, I'm wondering if I just had some bad luck. If I keep having problems against them, I'll add another kor firewalker to the board.
My thought behind 3 arbiter is that JVP helps consistency. I know you usually want arbiter early, but with the mindcensors too, it felt like enough. I didn't want to load on up 2 drops too much. Do you think cutting the 4th one was a mistake?
The flooded strands help to reduce merfolks inherent lead over you as well as buff your yard for JVP ideally. The mana base felt pretty decent and as always moorland haunt is a powerhouse.
This looks a lot like the build I'm currently piecing together as a combination of my Spirits deck and a D&T shell. May I suggest Geist of Saint Traft to go with Worship in Burn matchups? I did that against a burn deck last FNM and it worked super well (and would have won me the game had I not gotten greedy and misplayed and lost it to a block). There's just not much they can do to get around a creature they can't bolt away-- your life won't drop past 1.
I just tried a build of WU Death and Tempo with a GY subtheme in a modern friendly league and went 4-1, losing only to burn (0-2
0 and beating a nivmagus elemental deck, infect, mill, and jeskai nahri kiki combo deck.
I had some anti burn stuff in the board, but I may have to change it up a bit. The biggest problem I noticed was that I had no idea how to sideboard with it. This is the current list:
I can't really say how well JVP performed because he was prioritized by my opponents over almost everything else. The only game I used him at all was against mill in which he flipped after 1 use. I did play a game before the tournament in the practice rooms against Junk where he was really good. I dropped him when we had ground down to nothing and he just pulled me ahead.
Every time I used Skaab, it was pretty nuts. it's a only a beater, but it hits haaard and can block any fatty your opponent has. Path kills it well, but burn or kill spells have a hard time since it has recursion and just huge toughness. The rest of the deck played very tempo-y. I think this version has a pretty good MU vs infect since you have added disruption in the form of bounce and also spell queller can stop them from protecting their dudes/ buffing them while also being a relevant air blocker for inkmoth.
Not all of the MUs were top tier, but it felt pretty good against nihiri too. The idea of having vial up to reflector mage their Emrakul, the aeons torn is just dirty.
For burn, I'm wondering if I just had some bad luck. If I keep having problems against them, I'll add another kor firewalker to the board.
My thought behind 3 arbiter is that JVP helps consistency. I know you usually want arbiter early, but with the mindcensors too, it felt like enough. I didn't want to load on up 2 drops too much. Do you think cutting the 4th one was a mistake?
The flooded strands help to reduce merfolks inherent lead over you as well as buff your yard for JVP ideally. The mana base felt pretty decent and as always moorland haunt is a powerhouse.
I love the list.
It's pretty hard for me to comment on the 4th JVP, because I've never tested it in this deck before. I've been having a lot of success with Selfless Spirit though, so I'd consider running a few more of those (even though you didn't want to load up on 2 drops). They swing for damage while protecting your taxers and Spell Quellers; I've had a few games now where double Selfless Spirit basically locks my opponent out of the game, especially if it's protecting a Thalia or Arbiter.
I'm glad that Ruinator is doing some work for you. That card is pretty underrated in the blue splash, and it must feel awesome to pitch that to JVP.
Thanks!I was pleasantly surprised at how well it seemed to go together on my first test run of it period. I think 3 JVP is probably fine for the moment. I originally had 2 selfless spirit in, but I ended up cutting one. What do you think I should cut for 1? I don't think I need as many as 3.
skaab ruinator might be the U beater. It doesn't have hexproof like geist of saint traft does, but it can block too while only coming in for 1 less damage and gains recursions plus the added ability of pitching it to JVP as you mentioned. It really Ruined some of my opponents days already. Eh? eh?
I'm not convinced on that 1 vapor snag yet, but if I cut it, it'd probably just become another reflector mage.
Something to note with this list if anyone wants to try it; consider holding lands to pitch to JVP if you have enough mana to do what you need to. LD takes precedent, but this deck has a low curve (no 4 drops) and we don't usually need 7 mana up with a vial.
DnT! I'm a power-load
DnT! Watch me Explode
Lost to jund nearly a weak ago on the Russian Modern Championship (finished 31 =( ) performing the same trick.
"I just got flooded, but You've fixed it" ,- said my opponent after the match.
I mean, performing such move w/o any information about enemy's hand is quite risky. One thing is certain: You will have minus 2 mana on a table. Other things are quite concealed.
DnT! I'm a power-load
DnT! Watch me Explode
Legacy: Merfolk U; Shadow UB; Eldrazi Stompy C
Pauper: Delver U
Vintage: Merfolk U
Primers:
DnT! I'm a power-load
DnT! Watch me Explode
Legacy: Merfolk U; Shadow UB; Eldrazi Stompy C
Pauper: Delver U
Vintage: Merfolk U
Primers:
Doesn't quite stop Kiki-chord as they can kiki-resto in the end step. It does slow them down however
UBR Grixis Death's shadow
edit: I am missing something. Kiki enters tapped. Opps.
UBR Grixis Death's shadow
I'll throw the math in a spoiler for the curious. It's basically just an example similar to the examples cooked up in the post/article "How I Learned to Stop Worrying and Love the Hypergeometric Distribution" but specific to the Arbiter/GQ situation and with some properly typeset math (as much as I love that link, it kills me trying to follow that ascii math visually).
Assumptions:
We are looking for the odds of drawing a certain subset of hands (a.k.a. the nutdraw, God hands, combo) that offer the potential for pulling off the double-wasteland trick on turn-3; to do this we'll want 1xArbiter (or more) and 2xGQ (or more).
We'll make the simplification that our deck only has three kinds of cards: Card_A (the Arbiters), Card_B (the GQs), and Card_X (the unspecified cards). The odds of drawing a certain number of each type of card from the deck is given by the following equation:
where NA is the number of Arbiters in the deck (4), NB is the number of Ghost Quarters in the deck (4), NX is the number of other cards in our deck (52), and ND is the size of our deck (60). The number nd is the total number of cards we've drawn (which is 9 cards by turn-3 for the example), and na and nb are the numbers of Arbiters and GQs we've drawn, and nx is the number of filler cards we've drawn. Tracking everything, na+nb+nx=nd should always be true, otherwise there has been a mistake.
Drawing 1xArbiter is a possibility that can satisfy the desired criteria. How many GQ must be drawn to satisfy the remaining criteria? 2xGQ or 3xGQ or 4xGQ are all fine. Adding those possibilities together (with the numbers plugged in for the variables) looks something like:
Drawing multiple Leonin Arbiters is perfectly acceptable too. Accounting for everything there are 12 possible outcomes; all combined the result is given by:
This is all still pure combinatorics with discrete integer inputs and the result is still purely analytical. Carrying out the algebra gives exactly P=2,455,606/56,858,241 which expressed as a decimal number is 0.043188216 to the first 8 digits.
tl;dr: 4.3% is legit.
For other multi-card combos (like drawing 1xVial 1xThalia 1xArbiter in your opening hand for example) the multivariate hypergeometric distribution can be expanded out for more and more complicated combinations. You just have to specify more "types" of cards and plug them in correctly according to something like this:
and then be very careful to track every allowed possibility.
I'm glad that my simulation was accurate. The verification is really nice; my math aptitude isn't good enough for me to do it myself, unless I simplify the problem like I did here:
From that case, I knew that a million trials wasn't enough to get the hundredths digit accurately, so I just shaved it from my ultimate answer of 4.3%.
For what it's worth, I just ran the same simulation with ten million trials, and the result was 4.31338%. In essence, moving up an order of magnitude in trials bought me an extra digit for my answer. There's clearly diminishing marginal returns on CPU time though, so as long as the Monte Carlo simulation returns a "good enough" answer, that's really all I can hope for.
The advantage of a Monte Carlo simulation rather than analytical solutions, is that it allows me to check complex probabilities involving Æther Vial. For example, let's say tiago_oldman wanted a more accurate number, where we actually needed the resources to put Arbiter into play by T3. That answer involves either finding a white mana source by turn 2 (the number of which varies from deck to deck) or an Æther Vial on T1. While it's not impossible to calculate that analytically, each extra dimension of complexity added makes it harder and harder to calculate. At some point, it just becomes easier to simulate.
WUDeath&TaxesWG
Legacy
UBRGDredgeUBRG
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I LOVE that thread.
DnT! I'm a power-load
DnT! Watch me Explode
The cost of the Eternal Witness is only a problem if your opponent is playing Blood Moon, hopefully in my LPS is not that common that a player uses a deck with several copies of it in the main, otherwise you will always or almost always have the vial to put her in play.
Epochrasite is an excelent card, i know is not the most powerful card but is a beater that can returns to play after a lost combat, so you can attack or block without fear of losing it. It can survive to Anger of the Gods and that is perfect because this card is becoming more popular with the valakut decks. I still thinking about what to do, do you think it will be good to change it for Thalia, Heretic Cathar, Loxodon Smiter, main Spellskite, Restoration Angel, Eldrazi Displacer, Brimaz, King of Oreskos or any other card?
It's interesting for sure, but we just got Thalia, heretic cathar so I can't imagine wanting to run that MD over her and feel like there have to be better SB options.
4 tectonic edge
4 ghost quarter
2 sea gate wreckage
2 horizon canopy
1 Gemstone Caverns
1 Eiganjo Castle
9 Plains
8 non creature spells
4 Aether Vial
4 Path to Exile
4 Leonin Arbiter
4 Thalia, Guardian of Thraben
3 Selfless Spirit
2 Spellskite
1 Phyrexian Revoker
3 blade splicer
3 Eldrazi Displacer
2 Fiend Hunter
4 Flickerwisp
3 Restoration Angel
2 Blessed Alliance
2 Rest in Peace
2 Stony Silence
2 Ghostly Prison
1 Worship
1 Gideon, Ally of Zendikar
2 Surgical Extraction
1 Sundering Growth
2 Plains
1 Forest
2 Razorverge Thicket
1 Temple Garden
2 Brushland
3 Horizon Canopy
4 Ghost Quarter
2 stirring wildwood
2 Gavony Township
1 tectonic edge
1 gemstone caverns
10 noncreature spells
4 Path to Exile
4 Aether Vial
2 Collected Company
28 creatures
4 Noble Hierarch
4 Leonin Arbiter
3 Thalia, Guardian of Thraben
2 Scavenging Ooze
2 Spellskite
1 Selfless Spirit
4 Flickerwisp
2 Thalia, Heretic Cathar
2 Courser of Kruphix
1 Eternal Witness
1 Eldrazi Displacer
2 Restoration Angel
2 Stony Silence
2 Rest in Peace
2 Surgical Extraction
2 Burrenton Forge-Tender
2 Blessed Alliance
2 Ghostly Prison
1 Worship
1 Gideon, Ally of Zendikar
4 Caves of Koilos
4 Concealed Courtyard
2 Godless Shrine
1 Shambling Vent
4 Ghost Quarter
4 Eldrazi Temple
1 Vault of the Archangel
2 Plains
1 Gemstone Caverns
8 Noncreature Spells
4 Aether Vial
4 Path to Exile
4 Tidehollow Sculler
4 Leonin Arbiter
3 Thalia, Guardian of Thraben
4 Flickerwisp
4 Eldrazi Displacer
2 Spellskite
2 Selfless Spirit
3 Wasteland Strangler
4 Thought-Knot Seer
2 Surgical Extraction
2 Rest in Peace
2 Gideon, Ally of Zendikar
2 Sin Collector
2 Orzhov Pontiff
2 Blessed Alliance
2 Burrenton Forge-Tender
1 Worship
3 Brushland
3 Eldrazi Temple
1 Forest
2 Gavony Township
1 Gemstone Caverns
4 Ghost Quarter
2 Plains
3 Razorverge Thicket
2 Stirring Wildwood
1 Temple Garden
10 noncreature spells
4 Aether Vial
2 Ancient Stirrings
4 Path to exile
4 Noble Hierarch
3 Thalia, Guardian of Thraben
3 Leonin Arbiter
1 Aven Mindcensor
1 Thalia, Heretic Cathar
1 Spellskite
1 Scavenging Ooze
3 Eldrazi Displacer
4 Flickerwisp
1 Eternal Witness
4 Thought-knot seer
2 Reality Smasher
1 Reclamation Sage
2 Stony Silence
2 Rest in Peace
2 Surgical Extraction
2 Burrenton Forge-Tender
2 Blessed Alliance
1 Worship
1 Spellskite
2 Gideon, Ally of Zendikar
4 Ghost Quarter
1 Hallowed Fountain
4 Seachrome Coast
1 Eiganjo Castle
2 Tectonic Edge
1 Moorland Haunt
2 Mutavault
1 Island
2 Plains
2 Horizon Canopy
1 adarkar wastes
1 flooded strand
9 noncreature spells
4 Aether Vial
4 Path to Exile
1 detention sphere
28 creatures
3 Spell Queller
3 Selfless Spirit
3 Thalia, Guardian of Thraben
3 eldrazi displacer
3 Reflector Mage
4 Flickerwisp
2 Phyrexian Revoker
3 leonin arbiter
2 Venser, Shaper Savant
2 spellskite
2 Rest in Peace
2 stony silence
1 Engineered Explosives
1 Gideon, Ally of Zendikar
2 ghostly prison
2 burrenton forge-tender
2 Surgical Extraction
1 kira, great glass-spinner
1 blessed alliance
0 and beating a nivmagus elemental deck, infect, mill, and jeskai nahri kiki combo deck.
I had some anti burn stuff in the board, but I may have to change it up a bit. The biggest problem I noticed was that I had no idea how to sideboard with it. This is the current list:
4 Path to Exile
1 Vapor Snag
4 Spell Queller
1 Selfless Spirit
1 Vendilion Clique
3 Thalia, Guardian of Thraben
3 Leonin Arbiter
2 Aven Mindcensor
3 Reflector Mage
4 Flickerwisp
2 Skaab Ruinator
2 Thalia, Heretic Cathar
3 Jace, Vryn's Prodigy
4 Ghost Quarter
2 Hallowed Fountain
4 Seachrome Coast
1 Eiganjo Castle
2 Tectonic Edge
2 Moorland Haunt
1 Minamo, School at Water's Edge
1 Island
2 Snow-Covered Plains
2 Flooded Strand
1 Echoing Truth
1 Hibernation
2 Surgical Extraction
3 Kataki, War's Wage
1 Engineered Explosives
2 Spellskite
1 Worship
2 Kor Firewalker
2 Phyrexian Revoker
I can't really say how well JVP performed because he was prioritized by my opponents over almost everything else. The only game I used him at all was against mill in which he flipped after 1 use. I did play a game before the tournament in the practice rooms against Junk where he was really good. I dropped him when we had ground down to nothing and he just pulled me ahead.
Every time I used Skaab, it was pretty nuts. it's a only a beater, but it hits haaard and can block any fatty your opponent has. Path kills it well, but burn or kill spells have a hard time since it has recursion and just huge toughness. The rest of the deck played very tempo-y. I think this version has a pretty good MU vs infect since you have added disruption in the form of bounce and also spell queller can stop them from protecting their dudes/ buffing them while also being a relevant air blocker for inkmoth.
Not all of the MUs were top tier, but it felt pretty good against nihiri too. The idea of having vial up to reflector mage their Emrakul, the aeons torn is just dirty.
For burn, I'm wondering if I just had some bad luck. If I keep having problems against them, I'll add another kor firewalker to the board.
My thought behind 3 arbiter is that JVP helps consistency. I know you usually want arbiter early, but with the mindcensors too, it felt like enough. I didn't want to load on up 2 drops too much. Do you think cutting the 4th one was a mistake?
The flooded strands help to reduce merfolks inherent lead over you as well as buff your yard for JVP ideally. The mana base felt pretty decent and as always moorland haunt is a powerhouse.
4 tectonic edge
4 ghost quarter
2 sea gate wreckage
2 horizon canopy
1 Gemstone Caverns
1 Eiganjo Castle
9 Plains
8 non creature spells
4 Aether Vial
4 Path to Exile
4 Leonin Arbiter
4 Thalia, Guardian of Thraben
3 Selfless Spirit
2 Spellskite
1 Phyrexian Revoker
3 blade splicer
3 Eldrazi Displacer
2 Fiend Hunter
4 Flickerwisp
3 Restoration Angel
2 Blessed Alliance
2 Rest in Peace
2 Stony Silence
2 Ghostly Prison
1 Worship
1 Gideon, Ally of Zendikar
2 Surgical Extraction
1 Sundering Growth
2 Plains
1 Forest
2 Razorverge Thicket
1 Temple Garden
2 Brushland
3 Horizon Canopy
4 Ghost Quarter
2 stirring wildwood
2 Gavony Township
1 tectonic edge
1 gemstone caverns
10 noncreature spells
4 Path to Exile
4 Aether Vial
2 Collected Company
28 creatures
4 Noble Hierarch
4 Leonin Arbiter
3 Thalia, Guardian of Thraben
2 Scavenging Ooze
2 Spellskite
1 Selfless Spirit
4 Flickerwisp
2 Thalia, Heretic Cathar
2 Courser of Kruphix
1 Eternal Witness
1 Eldrazi Displacer
2 Restoration Angel
2 Stony Silence
2 Rest in Peace
2 Surgical Extraction
2 Burrenton Forge-Tender
2 Blessed Alliance
2 Ghostly Prison
1 Worship
1 Gideon, Ally of Zendikar
4 Caves of Koilos
4 Concealed Courtyard
2 Godless Shrine
1 Shambling Vent
4 Ghost Quarter
4 Eldrazi Temple
1 Vault of the Archangel
2 Plains
1 Gemstone Caverns
8 Noncreature Spells
4 Aether Vial
4 Path to Exile
4 Tidehollow Sculler
4 Leonin Arbiter
3 Thalia, Guardian of Thraben
4 Flickerwisp
4 Eldrazi Displacer
2 Spellskite
2 Selfless Spirit
3 Wasteland Strangler
4 Thought-Knot Seer
2 Surgical Extraction
2 Rest in Peace
2 Gideon, Ally of Zendikar
2 Sin Collector
2 Orzhov Pontiff
2 Blessed Alliance
2 Burrenton Forge-Tender
1 Worship
3 Brushland
3 Eldrazi Temple
1 Forest
2 Gavony Township
1 Gemstone Caverns
4 Ghost Quarter
2 Plains
3 Razorverge Thicket
2 Stirring Wildwood
1 Temple Garden
10 noncreature spells
4 Aether Vial
2 Ancient Stirrings
4 Path to exile
4 Noble Hierarch
3 Thalia, Guardian of Thraben
3 Leonin Arbiter
1 Aven Mindcensor
1 Thalia, Heretic Cathar
1 Spellskite
1 Scavenging Ooze
3 Eldrazi Displacer
4 Flickerwisp
1 Eternal Witness
4 Thought-knot seer
2 Reality Smasher
1 Reclamation Sage
2 Stony Silence
2 Rest in Peace
2 Surgical Extraction
2 Burrenton Forge-Tender
2 Blessed Alliance
1 Worship
1 Spellskite
2 Gideon, Ally of Zendikar
4 Ghost Quarter
1 Hallowed Fountain
4 Seachrome Coast
1 Eiganjo Castle
2 Tectonic Edge
1 Moorland Haunt
2 Mutavault
1 Island
2 Plains
2 Horizon Canopy
1 adarkar wastes
1 flooded strand
9 noncreature spells
4 Aether Vial
4 Path to Exile
1 detention sphere
28 creatures
3 Spell Queller
3 Selfless Spirit
3 Thalia, Guardian of Thraben
3 eldrazi displacer
3 Reflector Mage
4 Flickerwisp
2 Phyrexian Revoker
3 leonin arbiter
2 Venser, Shaper Savant
2 spellskite
2 Rest in Peace
2 stony silence
1 Engineered Explosives
1 Gideon, Ally of Zendikar
2 ghostly prison
2 burrenton forge-tender
2 Surgical Extraction
1 kira, great glass-spinner
1 blessed alliance
I love the list.
It's pretty hard for me to comment on the 4th JVP, because I've never tested it in this deck before. I've been having a lot of success with Selfless Spirit though, so I'd consider running a few more of those (even though you didn't want to load up on 2 drops). They swing for damage while protecting your taxers and Spell Quellers; I've had a few games now where double Selfless Spirit basically locks my opponent out of the game, especially if it's protecting a Thalia or Arbiter.
I'm glad that Ruinator is doing some work for you. That card is pretty underrated in the blue splash, and it must feel awesome to pitch that to JVP.
WUDeath&TaxesWG
Legacy
UBRGDredgeUBRG
UHigh TideU
URGLandsURG
WR Card Choice List
WUR American D&T
WUB Esper D&T
The Reserved List
Heat Maps
This looks a lot like the build I'm currently piecing together as a combination of my Spirits deck and a D&T shell. May I suggest Geist of Saint Traft to go with Worship in Burn matchups? I did that against a burn deck last FNM and it worked super well (and would have won me the game had I not gotten greedy and misplayed and lost it to a block). There's just not much they can do to get around a creature they can't bolt away-- your life won't drop past 1.
(...well, that or Leyline of Sanctity works.)
WB Ayli, Eternal Pilgrim | WBR Queen Marchesa | WUBR Breya, Etherium Shaper
Modern:
/ Death and Taxes | W/ Soul Sisters | Spirits | U Faeries | Tempered Steel Affinity
Thanks!I was pleasantly surprised at how well it seemed to go together on my first test run of it period. I think 3 JVP is probably fine for the moment. I originally had 2 selfless spirit in, but I ended up cutting one. What do you think I should cut for 1? I don't think I need as many as 3.
skaab ruinator might be the U beater. It doesn't have hexproof like geist of saint traft does, but it can block too while only coming in for 1 less damage and gains recursions plus the added ability of pitching it to JVP as you mentioned. It really Ruined some of my opponents days already. Eh? eh?
I'm not convinced on that 1 vapor snag yet, but if I cut it, it'd probably just become another reflector mage.
Something to note with this list if anyone wants to try it; consider holding lands to pitch to JVP if you have enough mana to do what you need to. LD takes precedent, but this deck has a low curve (no 4 drops) and we don't usually need 7 mana up with a vial.
4 tectonic edge
4 ghost quarter
2 sea gate wreckage
2 horizon canopy
1 Gemstone Caverns
1 Eiganjo Castle
9 Plains
8 non creature spells
4 Aether Vial
4 Path to Exile
4 Leonin Arbiter
4 Thalia, Guardian of Thraben
3 Selfless Spirit
2 Spellskite
1 Phyrexian Revoker
3 blade splicer
3 Eldrazi Displacer
2 Fiend Hunter
4 Flickerwisp
3 Restoration Angel
2 Blessed Alliance
2 Rest in Peace
2 Stony Silence
2 Ghostly Prison
1 Worship
1 Gideon, Ally of Zendikar
2 Surgical Extraction
1 Sundering Growth
2 Plains
1 Forest
2 Razorverge Thicket
1 Temple Garden
2 Brushland
3 Horizon Canopy
4 Ghost Quarter
2 stirring wildwood
2 Gavony Township
1 tectonic edge
1 gemstone caverns
10 noncreature spells
4 Path to Exile
4 Aether Vial
2 Collected Company
28 creatures
4 Noble Hierarch
4 Leonin Arbiter
3 Thalia, Guardian of Thraben
2 Scavenging Ooze
2 Spellskite
1 Selfless Spirit
4 Flickerwisp
2 Thalia, Heretic Cathar
2 Courser of Kruphix
1 Eternal Witness
1 Eldrazi Displacer
2 Restoration Angel
2 Stony Silence
2 Rest in Peace
2 Surgical Extraction
2 Burrenton Forge-Tender
2 Blessed Alliance
2 Ghostly Prison
1 Worship
1 Gideon, Ally of Zendikar
4 Caves of Koilos
4 Concealed Courtyard
2 Godless Shrine
1 Shambling Vent
4 Ghost Quarter
4 Eldrazi Temple
1 Vault of the Archangel
2 Plains
1 Gemstone Caverns
8 Noncreature Spells
4 Aether Vial
4 Path to Exile
4 Tidehollow Sculler
4 Leonin Arbiter
3 Thalia, Guardian of Thraben
4 Flickerwisp
4 Eldrazi Displacer
2 Spellskite
2 Selfless Spirit
3 Wasteland Strangler
4 Thought-Knot Seer
2 Surgical Extraction
2 Rest in Peace
2 Gideon, Ally of Zendikar
2 Sin Collector
2 Orzhov Pontiff
2 Blessed Alliance
2 Burrenton Forge-Tender
1 Worship
3 Brushland
3 Eldrazi Temple
1 Forest
2 Gavony Township
1 Gemstone Caverns
4 Ghost Quarter
2 Plains
3 Razorverge Thicket
2 Stirring Wildwood
1 Temple Garden
10 noncreature spells
4 Aether Vial
2 Ancient Stirrings
4 Path to exile
4 Noble Hierarch
3 Thalia, Guardian of Thraben
3 Leonin Arbiter
1 Aven Mindcensor
1 Thalia, Heretic Cathar
1 Spellskite
1 Scavenging Ooze
3 Eldrazi Displacer
4 Flickerwisp
1 Eternal Witness
4 Thought-knot seer
2 Reality Smasher
1 Reclamation Sage
2 Stony Silence
2 Rest in Peace
2 Surgical Extraction
2 Burrenton Forge-Tender
2 Blessed Alliance
1 Worship
1 Spellskite
2 Gideon, Ally of Zendikar
4 Ghost Quarter
1 Hallowed Fountain
4 Seachrome Coast
1 Eiganjo Castle
2 Tectonic Edge
1 Moorland Haunt
2 Mutavault
1 Island
2 Plains
2 Horizon Canopy
1 adarkar wastes
1 flooded strand
9 noncreature spells
4 Aether Vial
4 Path to Exile
1 detention sphere
28 creatures
3 Spell Queller
3 Selfless Spirit
3 Thalia, Guardian of Thraben
3 eldrazi displacer
3 Reflector Mage
4 Flickerwisp
2 Phyrexian Revoker
3 leonin arbiter
2 Venser, Shaper Savant
2 spellskite
2 Rest in Peace
2 stony silence
1 Engineered Explosives
1 Gideon, Ally of Zendikar
2 ghostly prison
2 burrenton forge-tender
2 Surgical Extraction
1 kira, great glass-spinner
1 blessed alliance