Chance of drawing either of two hands

Add a hand for alternate ways to draw your combination

Suppose the combination of cards I want to draw is more complex than some subset of each of the cards in the deck.  I started talking about this kind of situation in an earlier post How to calculate the probability when either one of two different cards will do

It may be easier to describe your combination as being either one of two different hands, call them hand A and hand B.  If the chance of drawing hand A is written as P(A), what is the chance of drawing P(A or B)?

P(A or B) = P(A) + P(B) - P(A and B)

The last term P(A and B) is needed so we do not double count hands that match both A and B.

The advanced calculator has a new button to [Add a hand].  This copies the right-most hand column so that you can describe another way to draw your combination.

How to draw 1GG mana on turn 3

If you want to draw lands from your Magic: The Gathering deck to cast a 1GG spell on turn 3, two of them need to be a Forest, but the other can be any land.  Start by describing your deck with the different kinds of land.  You can draw 2 Forests and 1 Swamp.

Click [Add a hand] to create another option for your combination.  Change this hand to draw 3 Forests.

Deck-u-lator calculates the chance of each of these hands individually, and then automatically adjusts the chance that your hand descriptions overlap.  In this case, an overlap would be drawing 3 Forests and 1 other land.  That hand matches both of your descriptions, but we can only count it once.

More alternate hands

You can add as many alternate hands as you need.  More alternate hands take longer to calculate.  Because each alternate hand generates more calculations, graphs and formulas are not presented.

Try the advanced calculator at https://deckulator-hrd.appspot.com/static/advanced.html