Joe Cecil

Counting more extreme orders

I've been drawing tarot cards without replacement as part of a project to learn the cards. Lately, I've been getting lots of Swords. I'm curious: Can I quantify how early the Swords are in this shuffling of my deck? Eventually I will have drawn

I can't believe it's not normally-colored

allRGB is a pretty cool website. It collects (and encourages the creation of) images that contain every 24-bit color exactly once. Why? Well, why not? It's completely pointless, a totally arbitrary constraint based on technical happenstance. That's what makes it delightful. See: Tunnel Man. Art. Lipograms.

What is the null probability of a distribution of straights in a hand of cards? 1/?

(In which I go insane trying to figure out the answer. Don't mind the gaps.) (Previously: One, two, three.) In Max Shinn's post about optimally shuffling cards, he describes looking at the "joint distribution of these frequencies compared to a null distribution." This is

What is the null probability of a given combination of ranks?

Following on previous posts about shuffling... In Max Shinn's post about optimally shuffling cards, he describes looking at the "joint distribution of these frequencies compared to a null distribution." This is slightly ambiguous, but I'm going to interpret this in a similar way as

What is the null probability of a given combination of suits?

In Max Shinn's post about optimally shuffling cards, he describes looking at the "joint distribution of these frequencies compared to a null distribution." What does that mean? Two possible interpretations: 1. We compute a single suit-related number from the hand. We use the "null distribution&

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