B Another Probability Freak

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On July 14, 2025, a bridge player was dealt two hands where the highest card was a seven, an occurrence with odds of approximately one in 250 million. The discussion highlights the confusion surrounding the calculations, with participants providing varying estimates, including one of about 234 million. Despite the discrepancies, there is a consensus that the rarity of this event is astonishing. The conversation also references a Wikipedia article on "Go and Mathematics," which discusses similarly improbable scenarios. The rarity of such hands in bridge showcases the game's unpredictability and the fascinating nature of probability.
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I admit I'm not into bridge but the comments to the OP you linked to makes it look pretty confusing. At least for someone like me who don't really get the game...

EDIT: I mean they don't seem to agree...

EDIT2: Oh, overlooked this one:

"
I got 1 in 234,484,904.

I think we can all agree that it's approximately 1 in 234 million. Do we really need to worry about being more precise?
"

Pretty wild, I'll admit.
 
There's a "Go and Mathematics" article on Wikipedia which also "sports" some pretty wild numbers.
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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