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.