Reading a distribution of outcomes
The full picture of a decision is a shape, not a number.
5 minute read
Equity summarises a hand in one number, but the outcomes behind it have a shape. A set against a flush draw wins most run-outs by a lot and loses a few; a coin flip wins half and loses half; a drawing hand loses most and wins big. Same average, different lives.
Add the turn and river that actually came to see how that run-out compares.
The longest losing run in a simulation is the number people underestimate most. At an 18% loss rate, a run of three losses in a thousand attempts is not just possible; it is near-certain, and four in a row is likely. A downswing is not a signal until it is far larger than the distribution predicts.
Quick check
At an 18% loss rate, what is the chance of losing three in a row on any given attempt? Roughly how many such runs would you expect in 1,000 attempts?
Show answer
0.18³ ≈ 0.6%. About six starts of three-loss runs in a thousand attempts — so at least one is close to guaranteed.