Hi guys, I'm new to this thread and forum. What do you guys think aboutspark elemental? IMO it's just like another burn spell with cmc 1. I noticed that in late game it can be a dead card due to the opponent's blockers but i think it could still do good.
A lot of people like Hellspark in the slot if there is one for the extra creature. This gives consistency and reliability. Personally, I think it depends on your build overall. Coming in the extra turn early is nice, but later when your top decks threaten to lose you the game, Unearthing a Hellspark can be clutch. I've used both in test lists before, but I can't give solid results one way or the other.
RUG Delver
G1 Raced eachother and he got there first
G2 I won the race by far, I think he took a greedy hand and didnt see more than two lands.
G3 I had him down to 1 life with no more burn in my hand. All of my top deck got countered until he killed me. All I needed to draw was a Volcanic Fallout to win.
0-1
G/w/r Human/werewolf Tribal. Pretty much a standard deck.
G1&2 were real quick, dont remember the details but I killed him real quick.
1-1
B/g/w Homebrew.
G1 He stableized at 3 life for a couple turns while I drew lands, but eventually I drew a Bolt and won.
G2 His Bobs did a lot of work for me, but it was still a close game with me staring down a sworded up Oblitorator at the end.
2-1
5 Color control
G1&2 he was so slow he didnt even really anything while I won in four turns both games.
3-1
Cut to top 8.
Aggro Loam
G1 His discard slows me down a lot but I get there eventually
G2 His deck works as planned while I draw mountains and i lose.
G3 Repeat of G1.
4-1
Top 4
Burn! He splashed Black
G1&2 re gets nuts draws both games and I am slightly slower.
4-2
The R/b Burn player played against Affinity for 1st and 2nd. I believe the Affinity player went 2-1 that match. It seemed like the Burn player had really no sideboard against Affinity, which was strange.
Thanks for everyone's comments. I won a Mutavault and a Chalice of the Void for 4th place, so not too bad for a cheap deck. My LGS is planning to play Modern every month or so so I am planning to get the Fetches to splash for Black definitely, and maybe even white for better sideboard options.
LordOwlington had something correct which I didn't earlier, and I've figured out all my mistakes and fixed my sheet. There are only a few of us so far that seem to think TW is worth running. I'm not trying to prove anything necessarily, but I've gone through the process of getting the numbers and enjoyed doing it. I'll share my final values and the corrected version of the graph I posted earlier, as this is valid for any miracle calculation anyway. Maybe someone will find it useful. I also want to post a list including TW, and I would like for the people who think it's bad to tell me what serves the slots better. That would also make the discussion more level.
So these numbers will assume you are on the play, and get to draw 5 cards. I realize that's 6 turns, but this is how it was being discussed previously.
This goes copies in deck, odds you don't start with any in hand, and odds you miracle once or more (whether or not it was in your hand):
4, 60%, 30%
3, 68%, 23%
2, 78%, 16%
1, 88%, 8%
Say you're running 4 and get one in your opening hand, and the rest of your hand is average or slower. You ship it thinking you can do better. The odds of having one or more in your hand before and after a mulligan are only 14% (the odds are better that you can run only 2 and miracle it in 5 draws).
If you never hardcast the card, it does an average of 1.25 dmg/card in 6 turns on the play. For comparison, Lightning Bolt does 1.8 dmg/card (this is accounting for when you see no copies). This is only slightly better than Shock. It does, however, produce an average 1.5 dmg/mana (again, thunderbolt is 1.8 dmg/mana with its CMC of 1).
Although, my numbers all count for 6 turns on the play. That means it could be hardcast 1 time from an opening hand. This significantly improves TW's stats. granted, if you have a better play on turn 6, you're only improving your speed. The following shows the card, average dmg/card, and dmg/mana for the listed cards. TW will be never hardcasting a TW, and TW* will include a single hardcast.
A card with a similar rate to TW* would do about 4.75 damage for a CMC of 2. I'd play that. Again, when turn 6 comes, you shouldn't have two other cards left in your that you want to play. By that point, you've seen 15 or 16 to 21 mana to cast 12 cards. Your hand probably doesn't have 2 cards left that can beat 5 damage, other than the TW you started with (it might have TW and one other card, but it isn't doing 5 direct damage, whatever it is). The one hardcast is just like a Fireballeffect to top the curve. I'm not even going to bring up kicking Burst Lightning or flashing back Bump.
Here's a list I would try TW in. I think between a 3-of and a 2-of is the sweet spot, so I'll try 3. I'm sticking to Mono R, but I'm working on some stuff with fetches and/or splashing.
I'm interested to hear from you all what I should cut TW for in this deck.
Otherwise, the slots I really didn't know about are the last 5 for Flames and Fallout.
I debated on the split and on Flamebreak vs. Fallout. I decided on Fallout because I prefer the consistency of being uncounterable and flexibility of being instant speed over the extra point here. If I decide to try fecthes/splashing, these slots instantly go to Searing Blaze. I also considered the Devil, but I decided without more sweepers, I would leave him out.
Obviously no SB yet. I have no idea what meta I would be facing. I'm probably designing for MTGO for the time being, so I would like advice on that.
He's not making it up. 29% is from a previous calc on it miracling once. It turns out this should be 33%. The 6% is the chance that you get two in your opening hand.
So.. Any thoughts on my deck? I am really worried about the Sideboard.
Also, silly idea maybe, but what about mainboarding 2-3 Smash to Smithereens for Vials and assorted Swords I have seen around?
I don't think I really have the experience to comment that extensively, but I would definitely not recommend MD StS. Trying to anticipate your meta that much is a trap. People might be trying new things, or you may not face any of the people you've seen playing those cards you're preparing for.
I also don't really like Vexing Devil in a list this creature light.
I also don't think 4 Pillars is right. I would consider some Magma Jets.
Did you consider the fetch packages, with Searing Blaze, maybe Grim Lavamancer, and possible splashes for black or white SB?
They're not independant events (the terms you're looking for, I think): The probability that your second draw is a miracle is directly dependant on weather your first draw was a miracle.
The deck is advertised as having a five turn clock, this means that the turn you have a success on your miracle is irrelevent. Yes it's BETTER to do it on turn two instead of four, but if our goal is to win-in-five it's irrelevent which turn we do it on, so long as it's less than six. This is also why we can use another hypergeometric distribution to determine the chances on the next five.
The hypergeom. dist. formula uses three combinations in the calculation. For a combination, the order doesn't matter. Therefore, it would say that drawing it only on draw 1 and not on draws 2 through 5 occurs with the same probability as drawing it only on draw 5 and not on draws 1 through 4. This is not true.
I understand your point that, for practical purposes, the turn you miracle it on doesn't matter as long as it's early enough. It just happens to matter statistically.
I believe for 5 draws your answer will be really close, and for the sake of the discussion it's probably good enough. I'm just really interested/invested in this now, and I want to find the theoretically correct answer. I want to later apply this to the "deck thinning" application of fetch lands. I know there is an article from around 2006 that "disproves" this with a simulation, but that article has several mistakes I found immediately (for example the number of possible opening hands), and I want to see for myself.
I disagree, it's just more hypergeometric probability, this time we have a smaller population (53 instead of 60). The idea here is that if your miracle once, the card was a success (five damage for R is worth two cards, so that's why I did it for having up to 1 in hand)
Furthermore I went back over my math. I did remember to compensate for having one in hand, so it looks like I have more foresight at noon than recollection at midnight.
Okay, okay. I've found an error I made with my calcs. It's tough to explain, but it does cause me to underestimate all my odds after draw 4, and when fixed, it would remove the discrete second derivative error there (the kink).
I also understand why it's not just repeated hypergeometric calcs like I showed in my last post. Say you want the odds for succeeding exactly once in five draws. The hypergeom. dist. would treat [XOOOO] the same as [OOOOX] (hitting draw 1 only vs. hitting draw 5 only), but they're not. I believe the terminology here is dependent vs. independent. Hitting only on draw 5 is more likely than hitting only on draw 1 because the population is smaller for draw 5, but the successes available are the same.
I promise not to post further here until I have new, correct data. (I tried to find a place for a thread like this, but I didn't know where it would go...)
I disagree, it's just more hypergeometric probability, this time we have a smaller population (53 instead of 60). The idea here is that if your miracle once, the card was a success (five damage for R is worth two cards, so that's why I did it for having up to 1 in hand)
Furthermore I went back over my math. I did remember to compensate for having one in hand, so it looks like I have more foresight at noon than recollection at midnight.
I'm still getting the exact reason for you why this isn't true, but I promise it's not. Using this method, I attached a similar graph to what I made before using a different method. It seems obvious to me that the chances are overestimated near the end.
I'm pretty sure there's some obscure rule about being unable to check the power and toughness of the creature if it's removed with something other than the ability relevant. At least I think... *cough* can I get a rules check if possible? *cough*
If exiling the creature is part of the cost of activating the ability, it won't be there for any other card to exile it. It's completely independent of GY hate at that point.
And for the record, a creatures p/t are the same in all zones, barring weird cases like */*.
I would imagine that Scavenging a creature would have exiling it as a cost. It would then be similar to Flashback. Someone could still exile your graveyard while not in one of your main phases, but if you go to Scavenge your Deadbridge Goliath, I believe responding by exiling your graveyard doesn't prevent the counters from being placed.
I can't exactly show my work, (used Google spreadsheet, and some online calculator for the more advanced calculations, such as the odds for individual counts of a card in your hand) but I can give basic equations.
Basically for the miracle calculation, I assumed that you had no miracles in your opening hand, and did the probability of drawing at least one in the next five (5 picks from a sample size of 53). Then I multiplied that by the probability that the event would happen at all. Looking back I think I overlooked the "realist" results because when you have one in your opening hand, it also decreases the success rate of sample picks. (Basically, I did math suggesting that if you have one in hand, you still had four in deck, which is wrong.)
I believe I know what site you used for the hypergeometric calc. Those aren't that difficult, and that site is helpful but limited. The hypergeometric formula is just a few combinations (basically arithmetic with factorials). You can't run the hypergeometric calculation for miracling though, if that's what you're saying you did. Doing so doesn't account for the fact that drawing cards reduces the deck size slightly, or that succeeding once dramatically reduces future successes. It treats drawing 5 card as single event, which we can't do. We have 5 separate dependent events to look at.
All you do for that is simply (TW left in deck)/(cards in deck). With none in hand, the odds go 4/53, 4/52 etc. This is happening 60% of the time, so you can multiply all those by 60%. Pretty much going any further is where it gets hairy.
This confuses me: If everything was equal, then wouldn't there be no real reason for or against it's use?
He's making a point similar to mine about weighted averages. If starting with one is equal and opposite to miracling one, and you start with 1+ 40% of the time but only miracle 1+ 20% of the time, it's twice as bad as it is good.
As I've mentioned, I plan on doing a series of calcs where I account for this. That is, I will figure out on average what it contributes to game vs. whatever card it might replace.
In Legacy, the only Miracles that have now seen extensive play and good tournament results have been Terminus, and Entreat the Angels. You could make a case for Temporal Mastery as well, but U/R decks packing Thunderous Wrath have not made a huge splash, save for maybe a couple lists on opening weekend for Avacyn Restored.
The reason for this is simple. Legacy's U/W Control has access to Sensei's Top, Brainstorm, Jace, Ponder, Preordain, and even Scroll Rack. Also, U/W Control is a control deck, and as such can usually afford the temporary disadvantage of holding a Terminus or Entreat until the late game, while slowing the opponent with the rest of the deck. U/R Legacy Delver, and therefore Modern Delver and Burn variants, simply cannot afford to durdle around with 6-mana spells into the lategame. We don't have Brainstorm in Modern, and so drawing a TW is literally just dead in hand unless you somehow manage to hit 6 mana.
Another thing you need to look at is the card itself. Terminus has a huge impact on the board in most cases, and very often creates card advantage. Thunderous wrath during your draw step is great, but it's not creating card advantage, and it's not even always going to be the optimal play.
I feel like the discussion of the other miracles' impact on Legacy is moot. They're different in every way from TW, and they fit into completely different decks. As far as its impact (vs say a Terminus), it's huge in light of the deck's game plan. I believe there will be obscure, infrequent cases where you may miracle TW and not want to cast it, but I can't even call a specific one to mind.
If TRAMD's experience was that TW wasn't great in U/R Delver, regardless of the exact reasons why, I would think that would at least provide us with 1 veritable case study on the card.
This is exactly the kind of logic I'm trying to fight by providing the statistics. I wouldn't expect the card to be good in a deck that has blind draws. That adds to the situations when you wouldn't want to see it.
If you are having success with it RAMEN, then keep on testing it. Some people have different experiences and will naturally like one card better, even if it is risky. But tailored statistics aren't going to help prove to the rest of us that Thunderous Wrath is worth all the drawbacks.
You can still cast Goblin Guide on turn 5, regardless of how "Bad" he is at that moment.
That's just dismissive and not true. You can ignore the statistics if you think your experience or intuition are better, but I think the statistical investigation has more weight than anything except for straight up results. For people with no alliance to one side or the other, some numbers may convince them to try it for themselves.
And my statistics aren't "tailored". If anything, I'm erring against TW with my assumptions and math.
I took the liberty of running numbers on this, to help out the use of Thunderous Wrath and my conclusion is that it is worth it to be run as a four-of. I'm also known for playing high-risk decks.
WARNING! HYPERGEOMETRIC PROBABILITY AHEAD!
All numbers rounded to the nearest percent.
First, the probability of having the card in your opening hand:
As a four of:
Any Number: 40%, Exactly 1: 34%, 2: 6%, 3: 0%, 4: 0%.
Three of:
Any: 32%, 1: 28%, 2: 3%, 3: 0%.
Two of:
Any: 22%, 1: 21%, 2: 1%.
One of:
1: 12%
These are basically disappointment numbers. For example, if you're running four copies, 40% of the time you will have at last one in your opening hand. A disappointment, but I consider ONE dead card in a hand of seven to be acceptable, and the odds of that happening are 34%. It's only 6% (approximately 1/20) that you'll have the completely unacceptable two or more copies in your hand.
So now we know the bad, but we're not running this card to just pollute our hands. The next set of numbers is the chances we'll run into a Miracle.
This assumes you'll only have five opportunities to achieve the miracle. Playing things like Needle Drop, or Magma Jet can increase that, but honestly who plays Needle Drop? Being on the draw and not on the play also alters this math slightly, but not too significantly.
4: 33%
3: 26%
2: 18%
1: 9%
So if You're running four copies, you have a 33% chance of at least one miracle, assuring you don't have it in your opening hand. If you have one copy, or were only playing three copies to begin with you have a 26% chance of witnessing a miracle within five turns. The next set of numbers is the chances of "Living the dream" with having no miracles in your opening hand, and being able to use it without drawback.
4: 20%
3: 18%
2: 14%
1: 8%
Not too much difference between four and three copies. Next up is for those of us who had a good hand, six Good Cards (tm) and one worthless miracle in hand. These are the chances of being effective with your miracles.
4: 27%
3: 22%
2: 16%
1: 8%
So now we know the risk, and we know the reward. Here's math on risk management (Presented as RISK | REWARD)
For the Dream:
4: 40% | 33% Difference -7%
3: 32% | 26% Difference -6%
2: 22% | 18% Difference -4%
1: 12% | 09% Difference -3%
For the realist:
4: 6% | 27% Difference +21%
3: 3% | 22% Difference +19%
2: 1% | 16% Difference +15%
1: 12%| 9% Difference -3%
Alright, so here's the grand finale. If your build is consistent enough to mulligan down to six two out of every five times, four copies of Thunderous Wrath is the way to go. If this is not acceptable, then run closer to zero copies.
I like that someone is putting out some effort and for the argument of TW. However, I unfortunately have numbers that disagree with yours. For example, I get lower values for the chances to miracle. Can you show how you got that? I did my work in Excel, and it's rather messy; but I'm confident I did it correctly.
The first problem is a big one. You assume that the positive of getting to miracle Thunderous Wrath is equal to the negative of having it in your opening hand. It isn't.
Can you elaborate on this? Having it in your hand loses you another card, granted, but hitting the miracle gives you insane value. Even if you want to say that's two cards and a mana for 5 damage, there are plenty of two card combinations that are worse.
...So even if the pros of miracle TW are equal to the cons of opening TW, it still isn't worth running.
This is definitely true. The best way would be to do a weighted average of the different scenarios. Again, this is something I will do sometime soon, probably this weekend.
You also give numbers for being on the play, a scenario that is more favorable for TW because you skip one draw where the card would be dead.
It's not that big of a difference. For example, my math shows that on the play it will be in your starting hand about 40% of the time, and you will miracle one or more by turn 5 (4 draw steps) about 23% of the time. On the draw, these numbers go to 44.5% and 22.4%.
I've thought a lot about numbers and I've tested the card in a deck that it is better in than Burn. It isn't worth running in Burn. Maybe if it did 6 damage or the regular cost was 2RR. As it stands, the card sucks. I wanted it to be the second coming of Goblin Grenade too, but it isn't.
Assuming you're referring to U/R Delver, I disagree that it's better there. I would obviously have to see the list, but I would assume there are cards in it that occasionally cause you to have a blind draw? And weren't you also playing it in Legacy?
I would say that a turn one or two guide averages about 4-5 damage.
Wow, sorry. I jumped formats in my mind as I've discussed this in the Legacy Burn thread before. I have not tested TW in burn in any format, only UR Delver in Legacy.
I thought more about it in U/R/x and realized how it could be worse, unless you forewent all the draw power blue offers and the specific ways blue offers card advantage. With just the Rack and Brainstorm, I fail to see how TW or any miracle wouldn't be the stone nuts. However, in any blue deck I've ever played, you would have plenty of blind draw situations, some at sorcery speed, which would hurt TW's case.
A lot of people like Hellspark in the slot if there is one for the extra creature. This gives consistency and reliability. Personally, I think it depends on your build overall. Coming in the extra turn early is nice, but later when your top decks threaten to lose you the game, Unearthing a Hellspark can be clutch. I've used both in test lists before, but I can't give solid results one way or the other.
What was the final list you ran with?
This goes copies in deck, odds you don't start with any in hand, and odds you miracle once or more (whether or not it was in your hand):
4, 60%, 30%
3, 68%, 23%
2, 78%, 16%
1, 88%, 8%
Say you're running 4 and get one in your opening hand, and the rest of your hand is average or slower. You ship it thinking you can do better. The odds of having one or more in your hand before and after a mulligan are only 14% (the odds are better that you can run only 2 and miracle it in 5 draws).
If you never hardcast the card, it does an average of 1.25 dmg/card in 6 turns on the play. For comparison, Lightning Bolt does 1.8 dmg/card (this is accounting for when you see no copies). This is only slightly better than Shock. It does, however, produce an average 1.5 dmg/mana (again, thunderbolt is 1.8 dmg/mana with its CMC of 1).
Although, my numbers all count for 6 turns on the play. That means it could be hardcast 1 time from an opening hand. This significantly improves TW's stats. granted, if you have a better play on turn 6, you're only improving your speed. The following shows the card, average dmg/card, and dmg/mana for the listed cards. TW will be never hardcasting a TW, and TW* will include a single hardcast.
Card...........Dmg/Card....Dmg/Mana
TW...............[1.25].........[1.5]
Lightning Bolt..[1.8]..........[1.8]
Shock............[1.2]..........[1.2]
Incinerate......[1.8]..........[0.9]
TW*............[2.85]..........[1.4]
A card with a similar rate to TW* would do about 4.75 damage for a CMC of 2. I'd play that. Again, when turn 6 comes, you shouldn't have two other cards left in your that you want to play. By that point, you've seen 15 or 16 to 21 mana to cast 12 cards. Your hand probably doesn't have 2 cards left that can beat 5 damage, other than the TW you started with (it might have TW and one other card, but it isn't doing 5 direct damage, whatever it is). The one hardcast is just like a Fireball effect to top the curve. I'm not even going to bring up kicking Burst Lightning or flashing back Bump.
4 Goblin Guide
4 Keldon Marauders
4 Hellspark Elemental
Burn Spells (28)
4 Lightning Bolt
4 Lava Spike
4 Rift Bolt
4 Shard Volley
4 Magma Jet
2 Flames of the Blood Hand
3 Volcanic Fallout
20 Mountain
I'm interested to hear from you all what I should cut TW for in this deck.
Otherwise, the slots I really didn't know about are the last 5 for Flames and Fallout.
I debated on the split and on Flamebreak vs. Fallout. I decided on Fallout because I prefer the consistency of being uncounterable and flexibility of being instant speed over the extra point here. If I decide to try fecthes/splashing, these slots instantly go to Searing Blaze. I also considered the Devil, but I decided without more sweepers, I would leave him out.
Obviously no SB yet. I have no idea what meta I would be facing. I'm probably designing for MTGO for the time being, so I would like advice on that.
He's not making it up. 29% is from a previous calc on it miracling once. It turns out this should be 33%. The 6% is the chance that you get two in your opening hand.
You also probably have too much artifact hate SB. I don't see many lists on here with that many slots dedicated to artifacts.
I don't think I really have the experience to comment that extensively, but I would definitely not recommend MD StS. Trying to anticipate your meta that much is a trap. People might be trying new things, or you may not face any of the people you've seen playing those cards you're preparing for.
I also don't really like Vexing Devil in a list this creature light.
I also don't think 4 Pillars is right. I would consider some Magma Jets.
Did you consider the fetch packages, with Searing Blaze, maybe Grim Lavamancer, and possible splashes for black or white SB?
The hypergeom. dist. formula uses three combinations in the calculation. For a combination, the order doesn't matter. Therefore, it would say that drawing it only on draw 1 and not on draws 2 through 5 occurs with the same probability as drawing it only on draw 5 and not on draws 1 through 4. This is not true.
From the site you used: http://stattrek.com/probability-distributions/hypergeometric.aspx Look in the blue box.
I understand your point that, for practical purposes, the turn you miracle it on doesn't matter as long as it's early enough. It just happens to matter statistically.
I believe for 5 draws your answer will be really close, and for the sake of the discussion it's probably good enough. I'm just really interested/invested in this now, and I want to find the theoretically correct answer.
Okay, okay. I've found an error I made with my calcs. It's tough to explain, but it does cause me to underestimate all my odds after draw 4, and when fixed, it would remove the discrete second derivative error there (the kink).
I also understand why it's not just repeated hypergeometric calcs like I showed in my last post. Say you want the odds for succeeding exactly once in five draws. The hypergeom. dist. would treat [XOOOO] the same as [OOOOX] (hitting draw 1 only vs. hitting draw 5 only), but they're not. I believe the terminology here is dependent vs. independent. Hitting only on draw 5 is more likely than hitting only on draw 1 because the population is smaller for draw 5, but the successes available are the same.
I promise not to post further here until I have new, correct data. (I tried to find a place for a thread like this, but I didn't know where it would go...)
I'm still getting the exact reason for you why this isn't true, but I promise it's not. Using this method, I attached a similar graph to what I made before using a different method. It seems obvious to me that the chances are overestimated near the end.
If exiling the creature is part of the cost of activating the ability, it won't be there for any other card to exile it. It's completely independent of GY hate at that point.
And for the record, a creatures p/t are the same in all zones, barring weird cases like */*.
I believe I know what site you used for the hypergeometric calc. Those aren't that difficult, and that site is helpful but limited. The hypergeometric formula is just a few combinations (basically arithmetic with factorials). You can't run the hypergeometric calculation for miracling though, if that's what you're saying you did. Doing so doesn't account for the fact that drawing cards reduces the deck size slightly, or that succeeding once dramatically reduces future successes. It treats drawing 5 card as single event, which we can't do. We have 5 separate dependent events to look at.
All you do for that is simply (TW left in deck)/(cards in deck). With none in hand, the odds go 4/53, 4/52 etc. This is happening 60% of the time, so you can multiply all those by 60%. Pretty much going any further is where it gets hairy.
He's making a point similar to mine about weighted averages. If starting with one is equal and opposite to miracling one, and you start with 1+ 40% of the time but only miracle 1+ 20% of the time, it's twice as bad as it is good.
As I've mentioned, I plan on doing a series of calcs where I account for this. That is, I will figure out on average what it contributes to game vs. whatever card it might replace.
I feel like the discussion of the other miracles' impact on Legacy is moot. They're different in every way from TW, and they fit into completely different decks. As far as its impact (vs say a Terminus), it's huge in light of the deck's game plan. I believe there will be obscure, infrequent cases where you may miracle TW and not want to cast it, but I can't even call a specific one to mind.
This is exactly the kind of logic I'm trying to fight by providing the statistics. I wouldn't expect the card to be good in a deck that has blind draws. That adds to the situations when you wouldn't want to see it.
That's just dismissive and not true. You can ignore the statistics if you think your experience or intuition are better, but I think the statistical investigation has more weight than anything except for straight up results. For people with no alliance to one side or the other, some numbers may convince them to try it for themselves.
And my statistics aren't "tailored". If anything, I'm erring against TW with my assumptions and math.
I like that someone is putting out some effort and for the argument of TW. However, I unfortunately have numbers that disagree with yours. For example, I get lower values for the chances to miracle. Can you show how you got that? I did my work in Excel, and it's rather messy; but I'm confident I did it correctly.
Can you elaborate on this? Having it in your hand loses you another card, granted, but hitting the miracle gives you insane value. Even if you want to say that's two cards and a mana for 5 damage, there are plenty of two card combinations that are worse.
This is definitely true. The best way would be to do a weighted average of the different scenarios. Again, this is something I will do sometime soon, probably this weekend.
It's not that big of a difference. For example, my math shows that on the play it will be in your starting hand about 40% of the time, and you will miracle one or more by turn 5 (4 draw steps) about 23% of the time. On the draw, these numbers go to 44.5% and 22.4%.
Assuming you're referring to U/R Delver, I disagree that it's better there. I would obviously have to see the list, but I would assume there are cards in it that occasionally cause you to have a blind draw? And weren't you also playing it in Legacy?
I thought more about it in U/R/x and realized how it could be worse, unless you forewent all the draw power blue offers and the specific ways blue offers card advantage. With just the Rack and Brainstorm, I fail to see how TW or any miracle wouldn't be the stone nuts. However, in any blue deck I've ever played, you would have plenty of blind draw situations, some at sorcery speed, which would hurt TW's case.