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.
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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