Blades in the Dark Resistance Roll Stress Values

Someone on G+ asked about the expected Stress values for Resistance rolls depending on the size of your dice pool, so I calculated them.

https://docs.google.com/spreadsheets/d/1npGJbX4salI56zjyxOT6OCwMcwgq9MDcRwbJYCVIkr8/edit#gid=0

At 3 dice, on average you’ll spend just under 1 Stress

At 4 dice, you have a ~52% chance of not spending Stress, with a ~13% chance that you’ll actually gain back a Stress.

I first tried to tackle this in Anydice, but my skills are rudimentary. I wound up writing a Python script to count the possibilities for each Stress outcome.

import itertools

def stress_outcomes(dice):
    counts = {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 66: 0}
    all_rolls = list(itertools.product([1,2,3,4,5,6], repeat=6))
    for roll in all_rolls:
        if max(roll) == 1:
            counts[1] += 1
        elif max(roll) == 2:
            counts[2] += 1
        elif max(roll) == 3:
            counts[3] += 1
        elif max(roll) == 4:
            counts[4] += 1
        elif max(roll) == 5:
            counts[5] += 1
        elif max(roll) == 6:
            if roll.count(6) > 1:
                counts[66] += 1
            else:
                counts[6] += 1
    print("\n%d dice" % dice)
    print(counts)
    total_count = len(all_rolls)
    print(total_count)
    print("\n".join([("= %d/%d\t= %2.1f" % (count, total_count, 100.0*float(count)/total_count)) for count in counts.values()]))

for i in range(3, 7):
    stress_outcomes(i)

Output:

3 dice
{1: 1, 2: 63, 3: 665, 4: 3367, 5: 11529, 6: 18750, 66: 12281}
46656
= 1/46656       = 0.0
= 63/46656      = 0.1
= 665/46656     = 1.4
= 3367/46656    = 7.2
= 11529/46656   = 24.7
= 18750/46656   = 40.2
= 12281/46656   = 26.3

4 dice
{1: 1, 2: 63, 3: 665, 4: 3367, 5: 11529, 6: 18750, 66: 12281}
46656
= 1/46656       = 0.0
= 63/46656      = 0.1
= 665/46656     = 1.4
= 3367/46656    = 7.2
= 11529/46656   = 24.7
= 18750/46656   = 40.2
= 12281/46656   = 26.3

5 dice
{1: 1, 2: 63, 3: 665, 4: 3367, 5: 11529, 6: 18750, 66: 12281}
46656
= 1/46656       = 0.0
= 63/46656      = 0.1
= 665/46656     = 1.4
= 3367/46656    = 7.2
= 11529/46656   = 24.7
= 18750/46656   = 40.2
= 12281/46656   = 26.3

6 dice
{1: 1, 2: 63, 3: 665, 4: 3367, 5: 11529, 6: 18750, 66: 12281}
46656
= 1/46656       = 0.0
= 63/46656      = 0.1
= 665/46656     = 1.4
= 3367/46656    = 7.2
= 11529/46656   = 24.7
= 18750/46656   = 40.2
= 12281/46656   = 26.3