Thursday, January 01, 2009

Venn Diagram of Poker Hands

A couple of years ago, I took a course on teaching Discrete Math at Tufts. While we were talking probability, we used Venn diagrams to illustrate how to compute some probabilities. And it occurred to me that it would be interesting to make a Venn diagram of all the types of poker hands. After I did it, I looked on the web to see if there was one posted any where, searching with "venn" and "poker", but couldn't find any. This is the best I found today:



It's obviously got some gross mistakes. For example, the straight circle is by itself, rather than including straight flush. And the non-straight circle is an abomination.

The challenge is to make a correct Venn diagram of the poker hands. Every kind of hand should be properly nested in all the simpler kinds of hand. I'll post my answer in a week or so. Alternatively, if you can find a better answer on the web or elsewhere, I'd like to know where.

Update 1/17/09:
Here is the solution. No peeking until you've solved the problem!

3 comments:

Kazim said...

I'm not willing to do it myself, but here are a few more observations:

In my opinion, "Pair" should CONTAIN "Triple," "Quad," and "2 pair." "2 pair" should perhaps contain "quad," depending on how you define it. "Full house" would be at the intersection of "triple" and "2 pair."

"Flush" and "Straight" should intersect to form "Straight flush," and the bean shaped intersection would contain a smaller circle that is a royal flush.

I think that just about covers all the cases.

Kazim said...

Whoops, "Quad" would also be inside of "triple." That means that "quad" is both part of "triple" and "2 pair," as is "full house"... but they don't overlap, so you'll have to take that intersection and split it in two.

Mike Huben said...

Very nice! That's what I've got, except that the intersection is usually lentil shaped, not bean shaped. :-)

I'll post my diagram in another few days.