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Hypergeometric Probabilities

I was inspired earlier due to a discussion of people wanting to have a table that enumerates the probabilities of drawing the card you need while at a physical tournament. I ended up making something you could probably find a use for in PbF as well.

Here you go!

Card Draw Probability Spreadsheet

Feel free to discuss or point out errors.


Row 4 column 3
{75.0%, 50.0%}

What does it mean ?
Drawing 3 cards from 4 card deck result in 50% chance of drawing your card if you have 2 copies of it ? 75% if you have just one?

That’s great, thanks !


The second number used to be showing the probability to draw exactly 1, without adding the probability for drawing exactly 2. So now the second number shows 1 or more when there are 2 copies in your deck, and the first number shows the probability to draw exactly 1, because there is only 1 in your deck.

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Nice, it makes sense now.

Neat! Thanks for making this

A couple suggestions that might make it easier to read:

  • Take out the { } in each cell. It adds a bit of visual clutter that makes it harder to quickly scan the numbers
  • Maybe add a color gradient with conditional formatting from high to low probabilities? Might be hard to do if there are two numbers. I suppose you could split the table for 1 card vs. 2 card, but it’s useful to have both numbers in case you are considering how many copies of something to tech in order to get a card after reshuffle.
  • Color coding the 1 vs. 2 card case would make it easier to scan, although I don’t know how to do that without tedious manual formatting. You’d probably need to have separate columns for each number

I like your suggestions, I think it would be doable. I could implement a color gradient, but i think that wil just tell you what you already know, the probability gets much better as you move to the right, and worse as you move down.

I think for visual-oriented folks, the color gradient would be useful, even if you already know it.


question: the table at the end, you cannot modify the numbers. is it intended?

If you want to modify, use the Google sheets copy sheet function, under the file menu to make a local copy for yourself and you will be able to modify it then.


I changed it so the shared sheet can be modified in those specific 4 cells for the formula, though note that does mean anyone can see what you are doing if you are looking at it at the same time.

So for a real game, I still recommend copying the sheet to your personal google sheets.

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