Does anyone have good links or resources on card odds? What are the differences in going from 49 to 54 cards? Etc.
You are looking for the concept of “hypergeometric distribution”, a nice calculator for which can be had here: http://stattrek.com/probability-distributions/hypergeometric.aspx
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How good is your math?
What you’re looking for is Hypergeometric Distribution. I’m sure there are calculators online. I know you have roughly a 25% chance to draw any given 3-of in a 49 card deck. You can toy around with it to figure math in 49 vs 54 card decks, and for 1-ofs and 2-ofs. If you know how to do factorials (or punch them in somewhere) the math isn’t too difficult. The Wikipedia article is highly informative.