Miracles simulation results

[Gui]

Disclaimer: This is not a thread intended to hype on how Miracles are Broken, nor a thread to Bash Miracles, which is as much hype as the hype itself.

This is a thread about an idea I had, and some results I got through software simulation.

I made the following test:

Draw 7 cards;
See how many useless miracles you have;
See how many miracles you can fix on opening hand;
Proceed drawing and incrementing useful counter;
Reshuffle and repeat this several times (I repeated it 100000x for each result shown bellow);
Return the relative number of times miracles are useful (useful/(useless+useful))


My simulation took into account:

Whenever you draw a miracle via natural way, you can cast it;
If you drew it on your opening hand, you can't cast it unless you fix it with brainstorm;
If you have a Force of Will, or whichever pitch effect to fix it, the miracle wasn't useless, even tho it didn't work as intended, so I consider it to be useful;
The longer the game goes, more times the miracles are going to be useful.


I did this same simulation for 0, 4 and 8 fixing cards (like: 0, or 4 brainstorms, or 4 brainstorms + 4 FoW), up to 7 draws (roughtly 8 turns).

Here are my results:

1 Draw
For 1 miracles and 0 fixing effects: Useful 12% of the time
For 2 miracles and 0 fixing effects: Useful 12,4% of the time
For 3 miracles and 0 fixing effects: Useful 12,8% of the time
For 4 miracles and 0 fixing effects: Useful 12,7% of the time
For 1 miracles and 4 fixing effects: Useful 65% of the time
For 2 miracles and 4 fixing effects: Useful 56,2% of the time
For 3 miracles and 4 fixing effects: Useful 51,4% of the time
For 4 miracles and 4 fixing effects: Useful 48,4% of the time
For 1 miracles and 8 fixing effects: Useful 85,4% of the time
For 2 miracles and 8 fixing effects: Useful 78,4% of the time
For 3 miracles and 8 fixing effects: Useful 73,5% of the time
For 4 miracles and 8 fixing effects: Useful 69,8% of the time

2 Draws
For 1 miracles and 0 fixing effects: Useful 22,3% of the time
For 2 miracles and 0 fixing effects: Useful 22,3% of the time
For 3 miracles and 0 fixing effects: Useful 22,3% of the time
For 4 miracles and 0 fixing effects: Useful 22,1% of the time
For 1 miracles and 4 fixing effects: Useful 78,4% of the time
For 2 miracles and 4 fixing effects: Useful 69,6% of the time
For 3 miracles and 4 fixing effects: Useful 64,1% of the time
For 4 miracles and 4 fixing effects: Useful 59,8% of the time
For 1 miracles and 8 fixing effects: Useful 92,5% of the time
For 2 miracles and 8 fixing effects: Useful 87,1% of the time
For 3 miracles and 8 fixing effects: Useful 82,8% of the time
For 4 miracles and 8 fixing effects: Useful 79,5% of the time

3 Draws
For 1 miracles and 0 fixing effects: Useful 29,9% of the time
For 2 miracles and 0 fixing effects: Useful 30,5% of the time
For 3 miracles and 0 fixing effects: Useful 29,9% of the time
For 4 miracles and 0 fixing effects: Useful 30,4% of the time
For 1 miracles and 4 fixing effects: Useful 85,7% of the time
For 2 miracles and 4 fixing effects: Useful 77,2% of the time
For 3 miracles and 4 fixing effects: Useful 72,3% of the time
For 4 miracles and 4 fixing effects: Useful 68,4% of the time
For 1 miracles and 8 fixing effects: Useful 95,6% of the time
For 2 miracles and 8 fixing effects: Useful 91,8% of the time
For 3 miracles and 8 fixing effects: Useful 88,4% of the time
For 4 miracles and 8 fixing effects: Useful 85,6% of the time

4 Draws
For 1 miracles and 0 fixing effects: Useful 36,8% of the time
For 2 miracles and 0 fixing effects: Useful 36,2% of the time
For 3 miracles and 0 fixing effects: Useful 36,3% of the time
For 4 miracles and 0 fixing effects: Useful 36,2% of the time
For 1 miracles and 4 fixing effects: Useful 89,9% of the time
For 2 miracles and 4 fixing effects: Useful 83% of the time
For 3 miracles and 4 fixing effects: Useful 78,4% of the time
For 4 miracles and 4 fixing effects: Useful 74,8% of the time
For 1 miracles and 8 fixing effects: Useful 97% of the time
For 2 miracles and 8 fixing effects: Useful 94,5% of the time
For 3 miracles and 8 fixing effects: Useful 91,9% of the time
For 4 miracles and 8 fixing effects: Useful 89,5% of the time

5 Draws
For 1 miracles and 0 fixing effects: Useful 41,6% of the time
For 2 miracles and 0 fixing effects: Useful 41,5% of the time
For 3 miracles and 0 fixing effects: Useful 41,6% of the time
For 4 miracles and 0 fixing effects: Useful 41,5% of the time
For 1 miracles and 4 fixing effects: Useful 92,3% of the time
For 2 miracles and 4 fixing effects: Useful 87% of the time
For 3 miracles and 4 fixing effects: Useful 82,9% of the time
For 4 miracles and 4 fixing effects: Useful 79,5% of the time
For 1 miracles and 8 fixing effects: Useful 97,9% of the time
For 2 miracles and 8 fixing effects: Useful 95,9% of the time
For 3 miracles and 8 fixing effects: Useful 94,1% of the time
For 4 miracles and 8 fixing effects: Useful 92,4% of the time

6 Draws
For 1 miracles and 0 fixing effects: Useful 46% of the time
For 2 miracles and 0 fixing effects: Useful 46,2% of the time
For 3 miracles and 0 fixing effects: Useful 46,2% of the time
For 4 miracles and 0 fixing effects: Useful 46,2% of the time
For 1 miracles and 4 fixing effects: Useful 94,3% of the time
For 2 miracles and 4 fixing effects: Useful 89,9% of the time
For 3 miracles and 4 fixing effects: Useful 86,1% of the time
For 4 miracles and 4 fixing effects: Useful 83,5% of the time
For 1 miracles and 8 fixing effects: Useful 98,6% of the time
For 2 miracles and 8 fixing effects: Useful 97% of the time
For 3 miracles and 8 fixing effects: Useful 95,6% of the time
For 4 miracles and 8 fixing effects: Useful 94,2% of the time

7 Draws
For 1 miracles and 0 fixing effects: Useful 50% of the time
For 2 miracles and 0 fixing effects: Useful 50,3% of the time
For 3 miracles and 0 fixing effects: Useful 50,2% of the time
For 4 miracles and 0 fixing effects: Useful 50% of the time
For 1 miracles and 4 fixing effects: Useful 95,6% of the time
For 2 miracles and 4 fixing effects: Useful 91,8% of the time
For 3 miracles and 4 fixing effects: Useful 88,7% of the time
For 4 miracles and 4 fixing effects: Useful 86,1% of the time
For 1 miracles and 8 fixing effects: Useful 99,2% of the time
For 2 miracles and 8 fixing effects: Useful 97,9% of the time
For 3 miracles and 8 fixing effects: Useful 96,8% of the time
For 4 miracles and 8 fixing effects: Useful 95,6% of the time


Hope this helps clarifying how and when miracles are more consistent, and why playing it without Brainstorm + FoW just seems wrong.

Any doubts, feel free to ask. As a friend of mine usually says: "Argh, Math!"

Gui.

[klaus]

What specific insights do your numbers provide beyond "don't run Miracles w/o blue"?

[Gui]

What specific insights do your numbers provide beyond "don't run Miracles w/o blue"?

Hmmm... I'd say that the fact that it almost doesn't matter if you run 1, 2 or 3 instead of 4 miracles, given that you run the same number of "fixers" is also useful.

Also, the fact that it gets way better after a lot of turns may be an indicator to run it in control decks.

Last, using Thunderous Wrath instead of Temporal Mastery in UR decks seems weaker to me than people seem to be realizing, even if it's a blue deck, without FoW to fix, it looks like it would be too bad most of the time.

And besides, provide data is useful to prove points, as some people seem to believe miracles will do well without decks adjsted accordingly.

But well, the data was helpful for me, can't blame me for sharing?

[rxavage]

Thank you. I find the data relevant and insightful. I had assumed TM would be better as a 1-2 of.

[SpikeyMikey]

You're delineating the usefulness rate of drawn miracles but you're not making any effort to incorporate how often they'll be drawn. So, for instance, it looks like 1 miracle and 8 fixers is a better deal than 4 miracles and 4 fixers. But with 1 miracle, you're seeing the card in 11.66% of opening hands as opposed to 39.95% as a 4 of. Without taking both into account, the data is useless at best and misleading at worst.

[dontbiteitholmes]

I didn't get why that one UR Delver deck in RI at the SCG was running 1x ThunderWrath when it seems like 1x Fireblast is going to be better most of the time. Oh well.

[Teknique]

I didn't get why that one UR Delver deck in RI at the SCG was running 1x ThunderWrath when it seems like 1x Fireblast is going to be better most of the time. Oh well.

I think Shiels agrees based on his comment in Top 8 profiles:

The one Thunderous Wrath I played was the only one. It could not have been worse.

[Gui]

You're delineating the usefulness rate of drawn miracles but you're not making any effort to incorporate how often they'll be drawn. So, for instance, it looks like 1 miracle and 8 fixers is a better deal than 4 miracles and 4 fixers. But with 1 miracle, you're seeing the card in 11.66% of opening hands as opposed to 39.95% as a 4 of. Without taking both into account, the data is useless at best and misleading at worst.

Not really. It doesn't matter if it is more or less seen in the opening hand, in this case.

Get this scenario for example: For 1 miracles and 4 fixing effects: Useful 50,8% of the time

It doesn't matter if I had the 1 miracle 11% of the time in my opening hand, because, for all the times it was useful, it was also useless once, statistically.

Even if I draw it more, if I could fix them more, to the point where it's more times useful than useless, than it's more playable than the option, since it's pretty terrible to have a stuck card in hand.

[Gui]

My apologies, I found a major bug in my testing routine:

I didn't take into account that, whenever you draw a fixer card, you fix a dead card from opening hand. This leads to different conclusions. With these results, I can see miracles being used (as earlier results were pretty much bad.).

Please refer to the opening post to see the right results.

Sorry, and thanks for your time.

[CorpT]

Does Jace count as a Fixer?

[Gui]

Does Jace count as a Fixer?

It should, but only for after you have him in table, so only effective after 4th draw, I guess.

SDT otoh doesn't.

[Malchar]

I think that this is the most useful statistic:

1 Draw
For 1 miracles and 8 fixing effects: Useful 85,4% of the time

I assume that running 8 fixing effects has no cost, since you would probably want to run 4 brainstorm 4 force no matter what. If you run 1 miracle, for the worst-case scenario (only 1 draw), it is still useful about 85% of the time, which isn't too bad in my opinion.

If you want to do mana cost analysis on temporal mastery, it comes out like this:
15% of the time it is "useless" = :5::u::u: = cmc 7
85% of the time it is "useful" = :1::u: = cmc 2

15%*7 + 85%*2 = 2.75

So, the "average" cmc of temporal mastery is 2.75 (after 1 draw).
Using a similar process, the first few values would be
2.75 after 1 draw
2.375 after 2 draws
2.22 after 3 draws
2.15 after 4 draws

This doesn't account for the times when you use it to pitch to fow, so the correct interpretation should be that you're either able to cast a time walk for this much mana OR pitch it to fow. This also doesn't count the extra mana used to brainstorm it. Since mana costs are discrete, this might not be that useful anyway, but if you're dead-set on casting a time walk, this will tell you how much it costs.

[rufus]

What specific insights do your numbers provide beyond "don't run Miracles w/o blue"?

Although the bulk of them are in blue, there are some plausible non-blue pitch or discard effects.

Chrome Mox
Blazing Shoal
Smallpox
Faithless Looting

[Gui]

To me, these are the most important numbers:

For the 4th draw:
For 1 miracles and 8 fixing effects: Useful 97% of the time
For 2 miracles and 8 fixing effects: Useful 94,5% of the time
For 3 miracles and 8 fixing effects: Useful 91,9% of the time
For 4 miracles and 8 fixing effects: Useful 89,5% of the time

This is, by 3rd to 5th turn, depending on whether you had ponder or not, you have almost no drawback on running the miracles in a deck such as Canadian, using FoW, Brainstorm and Ponders (FIY, ponder is not a fixer, but helps finding one). This assures it can be played with almost no harm, so I guess it will eventually see more play.

[catmint]

Good work.

Unfortunately Force as fixing only counts for Temporal Mastery and not for the white/red miracle cards.

The math "useful" or "not useful" is not yes/no but more a grey zone. And I don't mean the obvious "how useful" is the effect of the spell in a given situation, but the situations where you want to shuffle other stuff away with Brainstorm or want to pitch another useless spell with Force.

Anyway it shows that 2 Temporal Mastery can go in a lot of blue decks....

[Gui]

Good work.

Unfortunately Force as fixing only counts for Temporal Mastery and not for the white/red miracle cards.

The math "useful" or "not useful" is not yes/no but more a grey zone. And I don't mean the obvious "how useful" is the effect of the spell in a given situation, but the situations where you want to shuffle other stuff away with Brainstorm or want to pitch another useless spell with Force.

Anyway it shows that 2 Temporal Mastery can go in a lot of blue decks....

Yeah, agreed, it's not about the card's effect being useful or not, but rather, how often you have a brick in your hand instead of a card. This is the main drawback for miracles, imho.

There are other drawbacks too, like, having to cast it ASAP, or having the mana to use it.

Also, there are others (or at least sort of) 'fixers' available, like Pirokinesis or Chrome Mox, or cards like Faithless Looting, that can be used instead of FoW. The problem is that Brainstorm is the best one available anyways.

[SpeedOfDark]

Well done Gui!

Your simple analysis is like an oasis in a swamp of speculation :P

[Gui]

Well done Gui!

Your simple analysis is like an oasis in a swamp of speculation :P

Thanks. But to be honest, what bothers me most is the discussion between the Doomsayers and the Naysayers, in which either part treat the opposing part as clueless.
At least I tryed to add some info to the discussion.

[lyracian]

Great. Thanks for doing the hard work. I shall have a study of this later.

[DragoFireheart]

For some reason, I read the topic title as "Miracle stimulation results".

My next question would have been "up the butt?"

[Gui]

For some reason, I read the topic title as "Miracle stimulation results".

My next question would have been "up the butt?"

Look man, I don't wanna know how your sexual dreams with miracles in mtg looks like :tongue:

[Syaoran]

I've been running miracles in a deck with 12 effects to make them useful, but running only 3 miracles.

Have you also considered "can't cast on the first turn/ 2 turns"? because that'll lower the numbers significantly.

[Gui]

I've been running miracles in a deck with 12 effects to make them useful, but running only 3 miracles.

Have you also considered "can't cast on the first turn/ 2 turns"? because that'll lower the numbers significantly.

This is true, I didn't. I intend to do it, and also consider "on the draw" and "on the play" since a Temporal Mastery, for example, can be useless before the third natural draw.

[lyracian]

Having had a change to study the number and seeing around a 50% increase in usefulness going from 0 to 4 fixers as opposed to around 5% improvement going from 4 to 8 fixers it seems clear (to me) Miracles are not good enough to use in a deck without Brainstorm.

Given that they get better as the game goes long added to the Hawk interaction it seems Terminus is the best of the bunch. Although I am not yet convinced it is better than Wrath when you are not using squadron hawk. Counterburn decks should be able to get good use out of Thunderous Wrath with just Brainstorm as well.