So, we played this game last night:

https://boardgamegeek.com/boardgame/137336/archer-danger-zone-board-game

The game is a good game for terrible people, although nowhere near as terrible as Cards Against Humanity, but as many of the reviews say, those who don’t know the show ‘Archer’ will likely not enjoy it anywhere near as much.

But this is not a review. This is a design and decision blog post.

During the game, your character chooses to attempt various challenges. To attempt a challenge, you roll 1,2, or 3 dice. You have four skills (Booze, Guns, Sex, and Smarts), one of which you will need to use for each challenge. Each of your skills allows you to roll a number of dice to overcome that type of challenge. The challenges (mostly) come in the four types above, and three difficulty levels.
Level 1 challenges earn you 1 victory point, and require you to roll 6 or higher.
Table:
Level: 1, 1VP, roll 6+
Level: 2, 2VP, roll 8+
Level: 3, 3VP, roll 10+
Level: 4, 4VP, roll 14+

(Level 4 challenges are considered ‘personal’, and you can use any skill to overcome them.)

So, this decision tree seems pretty simple. For a game of sufficient length, you can just play the odds and go by the best expectation value [XV]:

1d6:
Level 1 1/6 (16.7%) [XV 0.167]
Level 2,3,4 Impossible
2d6:
Level 1 26/36 (72.2%) [XV 0.722]
Level 2 15/36 (41.7%) [XV 0.834]
Level 3 6/36 (16.7%) [XV 0.500]
Level 4 Impossible
3d6:
Level 1 206/216 (95.4%) [XV 0.954]
Level 2 181/216 (83.8%) [XV 1.676]
Level 3 135/216 (62.5%) [XV 1.875]
Level 4 35/216 (16.2%) [XV 0.648]

So, with no special abilities/powers, the expectation values (for a game of sufficient length) suggest the following ranking:
3d6 for level 3
3d6 for level 2
3d6 for level 1
2d6 for level 2
2d6 for level 1
3d6 for level 4
2d6 for level 3
1d6 for level 1

Which kind of makes sense, where you have characters playing to their strengths, makes each character different and encourages role-playing. (My character, Krieger, spent almost all his time in his lab, trying to insult any character who got too close.)

All of this becomes more complicated when you factor in a few other game rules.
1) ‘Insults’. Whenever you roll a 5 or 6, you get to draw an ‘Insult’ card which either increases your score or decreases someone else’s score. The increase to your score is in average 1/2 point. The average decrease to others’ score is also about 1/2 point. (As you generally only decrease one other character’s score, this is less useful, unless there’s only one character in front of you, and it’s mean.) We’ll allocate 0.75 expectation value to this, assuming there are two characters in front of you, on average. So, 1d6 would add 0.75*2/6, 2d6 0.75*4/6, and 3d6 would add 0.75*6/6 XV, respectively

This gives you:

1d6:
Level 1 1/6 (16.7%) (+0.25 insults) [XV 0.417]
Level 2,3,4 Impossible
2d6:
Level 1 26/36 (72.2%) (+0.5 insults) [XV 1.222]
Level 2 15/36 (41.7%) (+0.5 insults) [XV 1.334]
Level 3 6/36 (16.7%) (+0.5 insults) [XV 1.000]
Level 4 Impossible
3d6:
Level 1 206/216 (95.4%) (+0.75 insults) [XV 1.704]
Level 2 181/216 (83.8%) (+0.75 insults) [XV 2.426]
Level 3 135/216 (62.5%) (+0.75 insults) [XV 2.625]
Level 4 35/216 (16.2%) (+0.75 insults) [XV 1.398]

This makes the 3d6 skills even stronger, giving the ranking:
3d6 for level 3
3d6 for level 2
3d6 for level 1
3d6 for level 4
2d6 for level 2
2d6 for level 1
2d6 for level 3
1d6 for level 1
(Not sure if you can roll for impossible missions, just enough to deliver insults)

2) The ‘Break Room’ allows you to roll 3d6 for any type of challenge, but if you don’t overcome the challenge, you lose one VP. This changes the decision to the following:

3d6:
Level 1 206/216 (+1 95.4%), (-1 4.6%) [XV 0.906] + 0.75 from insults = 1.656
Level 2 181/216 (+2 83.8%), (-1 16.2%) [XV 1.514] + 0.75 from insults = 2.264
Level 3 135/216 (+3 62.5%), (-1 37.5%) [XV 1.500] + 0.75 from insults = 2.250
Level 4 35/216 (+4 16.2%), (-1 83.8%) [XV -0.190] + 0.75 from insults = 0.56

Giving the ranking:
3d6 for level 2
3d6 for level 3
3d6 for level 1
3d6 for level 4

Making this strategy more risk averse, but probably higher scoring, if you’re getting a lot of challenges which are not suited to your skills, such as if you’re sitting right behind the other character who has the same strong skill as you. (Each character has 1 skill at 3d6, 2 skills at 2d6, one skill at 1d6.)

3) The ‘Applied Research Lab’ allows you to re-roll each of your dice once. This is quite powerful… The question is which dice you re-roll when? This should really be a table (a *large* table):

1d6:
1-5 1/6 chance (16.7%)
If you miss, re-roll on 1,2,3,4 (5 gives you an insult, which is worth more (0.75) than re-rolling (0.42).
[Overall XV 0.167->0.333]
[Including insults: 0.42->0.64]
2d6:
Level 1 challenges (6+)
If you miss, re-roll any dice with 1,2,3
[Overall XV 0.72->0.93]
[Including insults: 1.22->1.55]
Level 2 challenges (8+)
If you miss, re-roll any dice with 1,2,3
[Overall XV 0.83->1.45]
[Including insults: 1.33->2.16]
Level 3 challenges (10+)
If you miss, re-roll any dice with 1,2,3,4 (you can re-roll only 1,2,3 in some cases, but easier to remember to just re-roll 1,2,3,4)
[Overall XV 0.50->1.19]
[Including insults: 1.00->1.97]
(Level 4 challenges are impossible with 2d6)
3d6:
Level 1 challenges (6+)
If you miss, re-roll any dice with 1,2
[Overall XV 0.95->0.998]
[Including insults: 1.70->1.78]
Level 2 challenges (8+)
If you miss, re-roll any dice with 1,2,3
[Overall XV 1.68->1.96]
[Including insults: 2.43->2.82]
Level 3 challenges (10+)
If you miss, re-roll any dice with 1,2,3 (you also choose only to re-roll the 1 if you have 1,3,5 and need 10, interestingly…)
[Overall XV 1.88->2.71]
[Including insults: 2.62->3.67]
Level 4 challenges (14+)
If you miss, re-roll any dice with 1,2,3 (if you get 4,4,4 or 4,4,5, you should re-roll one 4)
[Overall XV 0.65->1.76]
[Including insults: 1.40->2.88]

Conclusions? Left as an exercise for the reader… 🙂 (Best summary in the comments gets a secret prize, which may include glory…)