Decision Tree Solver

Decision Tree Solver

"Should we settle or go to trial" is not answered by instinct or by whoever argues longest — it is three numbers and a probability, and most people have never actually multiplied them. This skill extracts the tree hiding inside a messy decision (the choices, the chances, the payoffs, the costs of playing), computes the rollback with the bundled script, and — the part instinct can never do — finds the break-even: the probability at which the recommendation flips. Because "trial is worth it if you win 60% of the time" is an opinion, but "the answer flips at 90% — are you more than 90% sure?" is a decision made tractable. The script is deterministic, stdlib-only, and shows its arithmetic.

What This Skill Produces

• The extracted tree — decisions, chance nodes with probabilities, outcomes with values, and the costs of each path, pulled from the situation as described
• The rollback — expected value at every node, the best choice named at every fork, from the script
• The break-even scan — for each two-way uncertainty, the probability at which the top-level choice flips, which is the number that makes probability arguments productive
• The robustness read — whether the answer survives the probabilities being argued about, or hinges on a number nobody can defend
• The leaves-out list — what expected value cannot see here: risk appetite, one-shot vs repeated, the unquantified costs

Required Inputs

Ask for these if not provided:

• The choices — the real options on the table, including the do-nothing one
• The uncertainties — what could happen under each choice, and the requester's honest probability for each (pushing back on false precision is part of the job)
• The payoffs and costs — the money (or a stated proxy) at each end point, and what each path costs to walk: fees, time priced honestly, deposits
• The stakes context — one-shot or repeatable, and whether the worst branch is survivable — because expected value is the right tool for repeatable bets and needs a caveat for ruinous one-shots

Framework: Extract, Roll Back, Stress the Probabilities

1. Extract before computing. The tree is usually mis-drawn before it is mis-computed: options that are really the same option, a "risk" that is actually two sequential risks, a payoff that forgot the cost of getting it. Draw it in the script's JSON, read it back to the requester, fix it there.
2. Run the rollback.

   python3 scripts/decision_tree.py --input tree.json          # tree with EVs and best choices
   python3 scripts/decision_tree.py --input tree.json --json   # machine-readable
   python3 scripts/decision_tree.py --demo                     # settle-vs-trial worked example

   Outcomes carry values; chance nodes take probability-weighted sums; decisions take the best child; costs subtract along the way. The best path falls out, with the arithmetic visible.
3. Read the break-even before the recommendation. The scan reports where the choice flips. A decision that holds from p=0.3 to p=0.9 is robust and the probability argument can stop; one that flips at 0.55 when the room believes 0.5-to-0.6 is the argument itself, now named precisely.
4. Stress the values too. Nudge the big payoffs ±30% and rerun. An answer that survives sloppy values and sloppy probabilities is a real answer; one that does not is a request for better information, and the tree shows exactly which information.
5. Say what EV cannot see. A 10% chance of ruin is not "priced in" by multiplication for someone who cannot survive it once; reputational and relationship costs sit outside the tree unless explicitly valued. The recommendation carries these as words, not silently.