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52 ! = 8.06581752 × 1067

I haven't checked your math but that would be the same odds for any sequence. The same as for the sequence that I just dealt. It happened even though the odds of it happening are 52 ! = 8.06581752 × 106752 ! = 8.06581752 × 1067 according to you!

You are busted.

You are busted.

In your mind. Reread the post. I gave the universe of possibilities, then I specified a particular sequence. I then specified a method to generate that particular sequence. What you describe is the probability of shuffling a sequence which is one, certainty. Like this...

Probability space

If the space concerns one flip of a fair coin, then the outcomes are heads and tails: $\textstyle \Omega = \{H,T\}$ . The σ-algebra $\textstyle \mathcal F = 2^\Omega$ contains $\textstyle 2^2 = 4$ events, namely, $\textstyle \{H\}$ : heads, $\textstyle \{T\}$ : tails, $\textstyle \{\}$ : neither heads nor tails, and $\textstyle \{H,T\}$ : heads or tails. So, $\textstyle \mathcal F = \{ \{\}, \{H\}, \{T\}, \{H,T\}\}.$ There is a fifty percent chance of tossing either heads or tail: $\textstyle p(H) = p(T) = 0.5;$ thus $\textstyle P(\{H\}) = P(\{T\}) = 0.5.$ The chance of tossing neither is zero: $\textstyle P(\{\})=0,$ and the chance of tossing one or the other is one: $\textstyle P(\{H,T\})=1.$