people, I made a little tool for probabilistically describing Texas hold 'em hands, both from a player perspective (where you see your pocket cards, then the board unfold), and from an audience perspective (where you just see the board as it unfolds, and then presumably see some players' hands at the showdown).

(I guess it's a specific audience, like a live view, rather than on TV where the cameras show you the pocket cards.)

It's kind of cool!

I dealt out the following board:

🂫🃞🃎 🃕 🃓

After just the flop (first three cards), there's roughly 40% chance your hand ends up as a pair, 40% a two-pair, 10% a trip, 10% a full house, and epsilon the other results (±3%-ish).

Usually the probabilities aren't that symmetric, so I was moved to deal out ten pockets (pairs of personal cards). Not four but SEVEN two-pairs!, and, surprise!, a flush too!

Was surprised to see flush at <1% odds after the flop, since club-suited pockets are ~5% right?

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Yar, these are my 鳳凰堂 (Phoenix Hall) playing cards from Byōdō-in in (just outside ) featuring the flying bodhisattvas that encircle the giant bostatu, and that are now in the adjacent museum.

As far as I can tell, examining the cards and the book I got featuring these thousand-year-old collection of wooden carvings, none of the bodhisattvas are shown playing cards—many musicians, dancers, some just in meditation, but no gamblers. I am sure that was an oversight on part of the artist.

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At the flop and the turn, the probability of a flush is <1% but after the river (fifth card on the board), that probability jumps to 4%.

It's pleasing to see a 40%-ish probability after the flop manifest seven in ten times, and a 4% probability after the river manifest one in ten times.

Binomial distribution indicates 4% chance of the former, but 30% chance of the latter.

Neat. Getting a feel for these numbers is more satisfying than I'd expected.

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Isn't it unnerving that an event with 3% probability is 26% likely to happen at least one time out of ten?

Do something that rare—and 3% seems very rare right??—ten times a day and you're encountering it twice a week.

Kind of freaky.

Bernoulli magic.

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