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Thursday, 2016 March 17, 13:28 — games

steam and circuitry

One of my favorite games is Ticket to Ride (despite its silly name), in which a strategic element is choosing tickets: pairs of cities to be joined. The value of a ticket is the length of the shortest path that could fulfill it.

It occurs to me that, if each segment of track is considered as a resistor, the resistance between two cities may be considered a measure of the difficulty of the ticket: you’re less likely to be blocked if redundant paths exist. One could then make a list of tickets ranked by payoff divided by resistance. But each move changes this: after a route is claimed, it has zero resistance for its owner and infinite resistance for others.

Your first act in the game is to choose two or more tickets from a draw of three or four or five; it’s not obvious how to apply this idea to find the most compatible set.

Saturday, 2015 May 9, 19:24 — games, mathematics

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.