Thursday, July 2, 2009

Probabilities when Drawing

I was rereading one of Jackalware's blog entries about probabilities in Guardians, and I decided I was going to do the math on this one for myself. Yes, I've been away from teaching for less than one week, and already I'm doing recreational mathematics.

Anyway, my numbers were way off. I thought I was doing it right, but I must've been entering something incorrectly. I finally gave up and used the formula that Excel has just for this sort of thing, and which Jackalware originally used as well.

Here's what the results look like:

How do you read this?

The "60" in the upper left is the number of cards in the deck.

The rest of the numbers in column A represent how many of card "X" you have in the deck (terrain, shields, Vampires, Knights, etc.).

The rest of the numbers in row 1 represent how many you may get in your initial 12 card draw.

The formula is shown. Note the dollar signs ($). They are important for cutting and pasting in Excel. Don't forget them. Notice that $A$1 has two of them. Doubly important.

You can expand the list by adding more rows and columns and copying & pasting the formula into more cells. It you paste into an invalid cell (e.g., drawing 3 copies of a card when there are only 2 in the deck), you will get an error.

The formula has a 12 in it. That stands for the 12-card draw.
You can adjust this for other card games (do you play other card games?) just by changing that number.

How NOT TO read this

Let's say you have 8 Shields and 8 Terrain in a deck of 60 cards.
There is a 33.66% chance of getting 2 Shields in the initial draw.
There is a 33.66% chance of getting 2 Terrain in the initial draw.
There is NOT a 67.32% chance of getting 2 Shields and 2 Terrain!
Nor if there a (33.66*33.66)% chance. (In other words, don't add or multiply).

It's a little more complicated than that.
The chart just gives you a basic idea, such as if you put 8 in your deck, you are most likely to get 1 or 2. If you put 10 in your deck, you are likely to get 2 or 3.

If you 5 each of 8 creatures, you will most likely get 1 of any specific one, but you could easily get 2 of some and none of the others.


Jackalwere said...

I like the way you have laid this out visually...I never thought of doing that. Very nice!

I'll have to work on part 2 soon...

(x, why?) said...

Glad you liked it.

I seriously thought that I could handle the math without using the formula, and if I didn't know that the formula existed, I would have eventually found my mistake. Most likely.

But once you know it's available, it's hard not to just go the easy way.