A* = arg maxA (P(D|A) − [P(Ur|A) + w · P(Uir|A)]) w > 1
Take a breath. I'll walk you through it one piece at a time, and I think you'll be surprised how gentle it turns out.
A* — the option you should pick.
arg max over A — look at all your options, score each one, take the highest. That's all that grand-looking notation asks.
P(D|A) — the chance of the good thing, if you do this. The bar in the middle just means if you do.
P(Ur|A) — the chance of fixable damage, if you do this.
P(Uir|A) — the chance of permanent damage, if you do this.
w — how much extra permanent damage counts. And w > 1 means: it always counts extra.
Read back in plain English: score each option by taking the chance of the good thing, then subtracting the chance of fixable damage and the extra-weighted chance of permanent damage. Pick the highest score.
That's the whole formula. Subtraction, with one thing multiplied.
Watching it work
Take the framework's own example. You reckon the chance it goes well is 80%. Fixable damage, 10%. Permanent damage, 5%. And you set w = 2, so permanent counts double.
The penalty is Ur + w·Uir — that's 10% + (2 x 5%) = 20%.
Score = 80% − 20% = 60%
Now turn the dial. At w = 10, permanent damage counts ten times: 10% + 50% = 60%.
Score = 80% − 60% = 20%
Same action. Same risks. The score fell by two thirds, and nothing changed except how seriously you take the thing you can't undo.
That's the design, and the framework says it plainly: as w rises, even a small chance of permanent harm can come to dominate the decision. Which is right. Small chances of unrecoverable things should dominate. That isn't timidity — it's how anyone sane crosses a road.
You will never have these numbers
Nobody walks around knowing there's a 5% chance of permanent harm. Real life doesn't hand you decimals. That's fine. It isn't a flaw and it isn't something to apologize for.
The framework says so directly: it does not claim formal probabilistic precision. Its language is deliberately simplified to discipline reasoning, not to compute optimal solutions.
So what is the formula for, if you can't compute it?
It's for forcing the question. The value was never in the number that comes out — it's in what you have to do to get there. You have to stop and ask: what's the permanent one, here?
That question is the product. Most bad decisions in a life aren't made because someone did the arithmetic wrong. They're made because nobody ever separated out the box that couldn't be undone. It sat there, blended into everything else, invisible, cancelled out by a story about how the upside was huge.
The formula is a machine for making you look in box three. Whether you can put a number in it barely matters.
One more thing about w
It's a dial. Turn it up and you grow more cautious about permanent things. Turn it down toward one and permanent harm counts the same as fixable harm — the safety mechanism quietly switches off. Hence the insistence: w > 1. Always. Permanent always counts extra.
And then the framework does something rare. It asks a question it doesn't answer.
Is w a fixed number? Or does it change with the kind of permanence? Because permanent isn't one thing. Permanent loss of money; permanent damage to who you are; permanent damage to a relationship — same weight? Should they be?
The original raises it and leaves it open, calling it the edge where this becomes dynamic rather than rigid. Not answered. Marked.
I rather respect that. It would have been so easy to fill in a number and sound complete.