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.

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.