alternate poker

Suppose your deck has more than four suits, or some number other than thirteen cards per suit. What happens to the ranks of poker hands?

              1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3
    5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2

 4  F F F * B B B * O O O A A A A A A A A A A A A A A A A A 
 5  F F F F F F F B B B B B O O A A A A A A A A A A A D D D 
 6  F F F F F F F F F F F B B B B B B A A D D D D D D D D D 
 7  F F F F F F F F F F F F F F F B C C C C E E D D D D D D 
 8  F F F F F F F F F F F F F F G G G G G C C C C C E E E D 
 9  F F F F F F F F F F F F F G G G G G G G G G G C C C C E 
10  F F F F F F F F F F F F G G G G G G G G G G G G G G G G 
11  F F F F F F F F F F F G G G G G G G G G G G G G G G G G
12  F F F F F F F F F F G G G G G G G G G G G G G G G G G G
13  F F F F F F F F F F G G G G G G G G G G G G G G G G G G
14  F F F F F F F F F G G G G G G G G G G G G G G G G G G G
15  F F F F F F F F F G G G G G G G G G G G G G G G G G G G
16  F F F F F F F F F G G G G G G G G G G G G G G G G G G G

O: the familiar case: straight flush > four of a kind > full house > flush > straight > three of a kind > two pair > one pair.
A: four > full house > straight > flush.
B: four > flush > full house > straight.
C: four > flush > straight > full house.
D: four > straight > full house > flush.
E: four > straight > flush > full house.
F: flush > four > full house > straight.
G: flush > four > straight > full house.
*: surprisingly only two cases where two of the scoring hands are equally rare: with four suits and twelve ranks, flush = full house; with four suits and eight ranks, flush = four.

Posted in games, mathematics | 3 Comments

place-names and personal-names

In my county there’s a village named Van —–. I think that if my name had a Van or equivalent, and someone proposed to name a town for me, I’d prefer they drop the particle.

On another hand, Jan van Steenbergen has said he finds it odd to be referred to as “Steenbergen”.

An old book on place-names mentions a patch of London that has (or had) a street for every word of the former owner’s peerage title(s), including Of Alley.

(Websearch for “Couver” turns up only the French verb.)

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how {e|p}lastic was my valley?

If you had never seen a nonhuman mammal, would a dog’s face fall in your uncanny valley?

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I’m just sayin’

A free market would not say to the poor, “It’s cute that you want to earn money by providing a service, but first we need you to save up for a license.”

Posted in economics, politics | Leave a comment

adrift in a sea of time

In Donna Tartt’s The Secret History (1992), the narrator says or implies that the events happened many years ago; so I’ve been watching for details that date it. Oprah Winfrey, whose show premiered in 1986, is mentioned; I think that’s the terminus post quem. More than anything else I’ve been struck by names of cigarettes: Silva-Thin, Vantage, Kool. Maybe these seem dated to me because I’ve been less exposed to tobacco advertising since ~1981.

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Awake how often?

The protagonist of the TV series Awake lives in two worlds: one in which his wife died in a car crash, and one in which their son died instead. As we see it, he spends a day in Hannah’s timeline and then a day in Rex’s, alternating.

But (in the four episodes I’ve seen so far) no one ever asks him where he goes on the other days. On the other hand, if he lives each calendar day twice in sequence, he ought to be able to use knowledge of events unrelated to his family to win the occasional bet, and I haven’t seen him do that.

So I choose to suppose that his awareness forks each morning, and rejoins when he sleeps, so that he always has two yesterdays, neither preceding the other.

Posted in cinema | 3 Comments

elusive avoidance

I’ve been designing printable models of the Lawson-Klein surface

w = cos(u) cos(2v)
x = cos(u) sin(2v)
y = sin(u) cos(v)
z = sin(u) sin(v)

As you can plainly see, this figure lives in S3 (positively curved 3-space), so stereographic projection can bring it into E3 (Euclidean 3-space) without adding more self-intersections. (It crosses itself at u=nπ.)

To minimize the distortion of the projection, I want the projection center to be as far as possible from the surface. One thing I tried was pursuit: starting with an arbitrary point P in S3 and an arbitrary point L(u,v) in the surface, move (u,v) to bring L closer to P while simultaneously moving P away from L. This gets me nowhere so far: either it fails to converge or P converges to the antipodes of L, which is also in the surface (change u by π).

Posted in mathematics, merch | 2 Comments