Card draw calculating
Hello, welcome to calculating card draw. There are two thing I want to say. First, don't forget auto draw takes away from the amount of cards you have in your opening hand. Second, don't forget auto draw takes away from the chances of drawing any time during a game where you will automatically auto draw.
== Chances of Drawing a Card After Opening Hand ==
There's a lot to cover here so I'm going to make this page short and sweet.
You have to take into consideration any base buildings you have auto drawn that weren't in your deck. For instance you are playing a mono MF deck with 40 cards and you originally put 1 Dwarven Hall in it. That hall gets destroyed so the game graciously auto draws another Dwarven Hall for you. Now that 40 card deck has become a 41 card deck. You also have to consider mulligans.
This equation is assuming you have added your own base buildings. If you didn't, you need to add for the building. I'll go over calculating after auto drawn buildings that weren't in the deck second. It also assumes you haven't mulliganed.
X = The round it is Outs = The amount of cards "LEFT" in your deck that you'd like to draw (the 7 is taking into consideration the first cards you have already draw. The number 7 in the equation will have to be changed to the amount of cards you have mulliganed down to.
(Outs)/(Total deck size - (7+X)
SAMPLE SCENARIO: (Pay close attention to the quotes if you did not understand the equation above) You "did not mulligan." Its turn "16" , going on 17 and you either need an Ascent or an Entangle or your going to lose for sure. Your deck starting out was "43" cards. In the 43 card deck was "2 Ascents" and "3 Entangles". You added your own base buildings so you "did not auto draw any cards." You have already "played 1 Ascent and 2 Entangles." What are the odds of getting either one that you so direly need?
1 ascent left, 1 entangle left = 2 outs.
So 2 divided by 20 is .10. So since its .10 that means you have a 10% chance of drawing a card that you need in this case. Now keep in mind .10 is the same as .1 or .100 or even .100000000. That's the way decimals work.
CRASH COURSE IN CALCULATING WHEN YOU HAVE AUTO DRAWN OR MULLIGANED:
X = The round it is Y = The number of base buildings you have auto drawn (adding to deck size) Z = The number of cards you have mulliganed down to Outs = The amount of cards "LEFT" in your deck that you'd like to draw
(Outs)/(Total deck size + Y) - (Z+X)
Remember Z is the number of cards you had after you were finished with your mulligans. So if you mulligan twice you will have 5 cards left. Its important for the next section.
== Chances of drawing 1 of a card in your opening hand with only one in the deck ==
This is the simplest calculation and easiest to understand. Its here as a foundation for the next section.
You automatically draw 7 cards. Also remember auto drawing. If you didn't put any base buildings in your deck your going to auto draw one and this will increase your deck size by 1. This section will not cover that. Remember you can auto draw more than 1 base building if you are playing a 2 or more domain deck.
X = Total cards drawn Y = Total deck size Z = Number of base buildings
(X - Z)/(Y - Z)
SAMPLE SCENARIO: Yes, That simple. If your playing a "mono" sylvan deck with "40" cards and its own "base building added" and do not mulligan the equation will be:
(7-1)/(40-1) or 6/39 or 15%
That's right, the equation is your odds. It's insanely simple. Just remember to compensate on both sides for auto draw.