DS9 Board Game: How Likely Is Each Square?

Summary[]

I was curious: in the 156 podcast episodes for which the DS9 board game is being played, how many times would we expect to land on particular board squares?

I simulated 100,000 complete podcast runs (i.e. 156 podcast episodes, simulated 100,000 times) using Python (source code is here), playing out the board game for each run. Here's what I found.

Question	Answer
How many drunkisodes (CoCo NoNo, Quark's Bar, Mornhammered) are expected?	About 23 (likely range: 18 - 27)
How many non-drunk special episodes are expected?	About 14 (likely range: 10 - 18)
How many trips to visit each other (Looking At Each Other During) are expected?	Either 1 or 2 (likely range: 0 - 3)
How many live streamed episodes (Fuck It! We'll Do It Live!) are expected?	Either 3 or 4 (likely range: 1 - 6)

Method And Assumptions[]

I calculated 156 turns through the entire duration of GG DS9, as follows:
- The first die roll was during episode 197, Space Butthole Curriculum (S01E19).
- There are 26 episodes per DS9 season from 2 through 7.
- There will be one turn for every episode except S07E26.
- Thus, there's 1 turn in S01, 26 turns in each of S02 through S06, and 25 turns in S07.
If the piece moves to a space butthole square, I assume the butthole is followed immediately: the next podcast episode will use the square that results from following the butthole.
Rolls that would move beyond square 100, land on square 100 instead. (For example, on board square 97, if a 4 is rolled, I assume the move is to square 100.)
Suppose at the end of podcast X, the piece moves to square 100. Then, I assume at the end of podcast X+1, the piece moves to square 1 (i.e., there is no die roll: the game starts over). At the end of podcast X+2, I assume the die is rolled once again.

Detailed Results[]

In the tables below, the "10-90% likely range" is the number of times we'd expect to land on a square in 80% of the 100,000 podcast runs (specifically, the 10th and 90th percentiles of the number of times we visit a particular square). For example, here's how many times we landed on "Looking At Each Other During":

Times	Count	Times	Count
0	18,141	4	3,829
1	35,000	5	687
2	28,739	6	71
3	13,529	7	4

The numbers in the "Count" cells add to 100,000. The 10th percentile of those "Times" values is 0, and the 90th is 3, but in about 4.5% of podcast runs, Ben and Adam will have to visit each other four times or more.

Special square occurrences[]

Square	Expected number	10-90% likely range
Drunkisodes	22.8	18 - 27
Non-drunk specials	14.0	10 - 18

Drunkisode square occurrences[]

Square	Expected number	10-90% likely range
CoCo NoNo	1.4	0 - 3
Mornhammered	1.9	1 - 3
Quark's Bar	19.5	15 - 24

Non-drunk special square occurrences[]

Square	Expected number	10-90% likely range
Caught in the Nebula	1.4	0 - 3
Fuck It! We'll Do It Live!	3.6	1 - 6
Looking At Each Other During	1.5	0 - 3
Measure of a Man	2.2	1 - 4
Starship Mine	1.2	0 - 2
The Naked Now	2.2	1 - 4
The Nth Degree	2.0	0 - 4