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Percentage Guide to Card Draw

Brownlee

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"You'll love my new recipe."

Everyone wonders, during mulligan, which cards to hold onto, which cards to get rid of.  Using math, you can optimize your chances to get the ideal starting hand for your play situation.  You can also know, absolutely, turn-by-turn, what the chances are that you will draw into the card you need.  This information can help you to make informed play decisions and measurably increase your win-loss ratio.

Going First: you'll start with a hand of three cards.  Already, you've had three opportunities to get the card(s) you need.  The chart below indicates your chance, from here, to draw one card you need, whether a one-of or two-of, depending on how many cards you choose to hold.  This does not indicate your chance to draw two cards that you have two of, or your chance to draw two cards, one each, of two kinds of card you have two of.
 
# Cards Held # Cards Drawn One-Of Two-Of
0 3 10.4% 20.7%
1 2 6.9% 14%
2 1 3.8% 7.4%
3 0 0% 0%

Remember, at the start of your turn, you'll receive one additional chance to draw a card you need.  (See the third chart in this article; using the row with 27 cards remaining.)

Going Second: you'll begin with a hand of four cards, plus a Coin.  The same rules apply as listed before the first chart, except that you've now had four chances to draw the card you need.
 
# Cards Held # Cards Drawn One-Of Two-Of
0 4 14.1% 28.1%
1 3 10.7% 21.4%
2 2 7.3% 14.5%
3 1 3.7% 7.4%
4 0 0% 0%

Remember that you'll have one more chance, at the beginning of your turn, to draw the card you need.  (Use the third chart in this article, the row that lists 26 cards remaining in your deck.)

The following chart denotes your chance, as a percentage, to draw a card you have one or two of remaining.  Cards that have you have two of, which you've drawn or played one of, should be treated as a one-ofs thereafter.  And, of course, cards you have one of, which you've drawn or played one of--as well as cards you have two of, which you've drawn or played two of, you have no chance of drawing, since none remain in your deck.
 
# Cards Left One-Of Two-Of
27 3.7% 7.4%
26 3.8% 7.7%
25 4% 8%
24 4.2% 8.3%
23 4.3% 8.7%
22 4.5% 9.1%
21 4.8% 9.5%
20 5% 10%
19 5.3% 10.5%
18 5.6% 11.1%
17 5.9% 11.8%
16 6.3% 12.5%
15 6.7% 13.3%
14 7.1% 14.3%
13 7.7% 15.4%
12 8.3% 16.7%
11 9% 18.2%
10 10% 20%
9 11.1% 22.2%
8 12.5% 25%
7 14.3% 28.6%
6 16.6% 33.3%
5 20% 40%
4 25% 50%
3 33% 66%
2 50% * 100% *
1 100% 0%
(*If the only cards remaining in your deck are a pair of the same two-ofs, you have a 100% chance to draw one.  If the cards left in your deck are two different one-ofs, you have a 50% chance of drawing each.)
 
You'll notice that the fewer cards left remaining in your deck, the greater the relative chance that you will draw one of a particular card.  This is because each time you draw a card, there is one fewer other possibility.

What's the best way to use this now?  That varies from person to person.  For some, it is enough just to understand this trend in numbers as the game progresses.  For others, it helps to have these charts beside you as you play for reference, maybe also a chart where you can check off cards as you play them and keep track of what remains in your deck.  If you need a Swipe and have a Starfall, you can decide, based on your chance to draw a Swipe, whether you should just play the Starfall or if you should hold out for the Swipe.  If math takes the fun out of playing for you, don't use the charts--it's not worth it.  But if you're looking for a sharper competitive edge, numbers don't lie.  (Also, the numbers say to like and comment on this post, and to also share this article with your friends on Facebook, Twitter, etcetera.)

Until next time, this is Brownlee--thanks for reading.
 
"For science!"
 
  
  
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