I made a summary plot of the likelihood of drawing a specific card during your setup draw and first draw of the game. It takes into account deck size and number of cards in the deck. Here is a link. I have a few additions I am thinking of adding, but please let me know if you have any suggestions.

Link

Sweet!! too bad I don't have excel on my computer... in general what is the chance of drawing a card if you put 3 in your deck with a 50 card deck?

If you are specifically looking for a three of card then it's about 50% after mulligan.

I thought it was just a little over 40% but yeah basically half of the time you will get that one card you need and other times you're just out of luck.. but the mulligan does certainly help.

Sweet!! too bad I don't have excel on my computer... in general what is the chance of drawing a card if you put 3 in your deck with a 50 card deck?

If you have 3 of a card and 50 total cards, then you have a 32% chance of drawing that card during your setup draw (6 cards) and a 37% chance of drawing it during your setup draw and first draw (7 cards).

There is a PDF summarizing this if you aren't able to open the excel file. I hope this is helpful!

With a deck of 50 cards, and a draw of 6 cards,

- If you have 3 of a card in the deck:

32,4% of drawing 1 or more in the setup,

54,3% of drawing 1 or more in the setup or after mulligan.

- If you have 2 of a card in the deck:

22,8% of drawing 1 or more in the setup,

40,4% of drawing 1 or more in the setup or after mulligan.

- If you have 1 of a card in the deck:

12,0% of drawing 1 or more in the setup,

22,6% of drawing 1 or more in the setup or after mulligan.

I would like to clarify a misconception mentioned in this thread: The mulligan has no affect on the probability of drawing a card. Once a mulligan is declared, you shuffle your hand back into your deck and the experiment begins again.

I would like to clarify a misconception mentioned in this thread: The mulligan has no affect on the probability of drawing a card. Once a mulligan is declared, you shuffle your hand back into your deck and the experiment begins again.

It depends on how you formulate the question...

If you ask, what is the probability of drawing a card in a draw? yes, it's the same every time you return the cards to the deck and draws another hand. The probability in the first draw is the same as the probability in the mulligan draw.

If you ask, what is the probability of having a card in your hand after setup? Then, the calculation is diferent and the probabilities are as shown in my previous post. (when i said "...1 or more in the setup or after mulligan." I would said "...1 or more in the first draw or after mulligan.")

- If you have 1 of a card in the deck:

12,0% of drawing 1 in the setup, or more is 0,0%, just saying.

P.S. This is a joke

- If you have 1 of a card in the deck:

12,0% of drawing 1 in the setup, or more is 0,0%, just saying.

P.S. This is a joke

Yes i abused copy-paste myself...

For anyone interested in a more detailed discussion of this topic, you should check out the recent post on the Tales from the Cards blog

http://talesfromthecards.wordpress.com/2014/03/20/a-note-on-probability/

He explains how to use the results of these calculations in your deck building. It's a really nice article.

For anyone interested in a more detailed discussion of this topic, you should check out the recent post on the Tales from the Cards blog

http://talesfromthecards.wordpress.com/2014/03/20/a-note-on-probability/

He explains how to use the results of these calculations in your deck building. It's a really nice article.

Thank you for the link. After reading this topic for the first time I was surprised by what some of the people were saying. There was a surprising lack of knowledge about probabilities (which I find odd for card players). This link though takes you to a great article that is easily comprehended. You do not have to be a math wiz to read this article. Although if you are a math wiz this article explains how the Classical Probability formula, and the General Rule of Multiplication formula can be applied to this game.

Also you do not need excel to calculate "starting" hands. The starting hand has such a small amount of events (not the card type) it can easily be done with a calculator and pencil. Anything beyond the starting hand though, and the pencil work may take a very long time.

Edits=Red