Exact costs, when a mistake has a price tag

The postures are shorthand for a cost model. If you know the actual numbers, give them instead:

import gut
 
gut.likely(email, "the customer threatens to cancel",
           cost_false_yes=2,     # a CSM spends twenty minutes on a calm customer
           cost_false_no=50,     # we lose the account
           cost_human=1)         # someone reads the ticket and decides

Given a probability p:

expected cost of saying YES        = (1 - p) · cost_false_yes
expected cost of saying NO         =      p  · cost_false_no
expected cost of asking a human    =         cost_human

gut takes the cheapest. Ties prefer UNSURE, then NO. With no human in the loop this reduces to

YES  ⟺  p > cost_false_yes / (cost_false_yes + cost_false_no)

which for 2 and 50 is 0.038. Nobody guesses 0.038.

threshold= and unsure_band=(lo, hi) are there if you already know the number you want. Mixing exact costs with posture words in one call is an error — one of them would have to win silently.

The trap in that formula

The expected cost of asking a person is flat in p, while the cheaper of yes and no peaks where those two lines cross. Put cost_human above that peak and there is no probability at all where a person is worth asking: the third branch you carefully wrote is unreachable, silently. The ceiling is

cost_false_yes · cost_false_no / (cost_false_yes + cost_false_no)

1.92 for 2 and 50. A cost_human of 5 never fires; 1 does. gut warns when you cross it, and Policy.max_useful_cost_human tells you where it is. This is not theoretical — an early demo of this library shipped with exactly that mistake, and sent zero tickets to a human with no error anywhere.

The postures cannot do this to you. They are defined as bands and the costs derived, and a band is reachable whenever its ends are in the right order.

Every policy will tell you where its boundaries are, rather than leaving you to work them out from the costs:

import gut
 
for preset in gut.presets():
    print(preset)
 
print(gut.policy(cost_false_yes=2, cost_false_no=50, cost_human=1).describe())
# no below 0.02, ask a person from 0.02 to 0.5, yes above 0.5

A cost model is a claim about these probabilities. Change the backend and the same costs can land somewhere else on the new model's distribution; see limitations.