A Positive Expected Return Can Still Lose
Four sides win $1 and two sides lose $1. That gives this game a positive expected value of $0.33 per roll. It still does not guarantee that any particular run will finish ahead.
Positive Expected Value Dice Game
Roll once to watch an outcome, or run a larger batch to see how the result develops over time.
Each roll has one result. The number determines whether you win or lose.
Expected value is an average, not a promise
Over many repetitions, the average result should move toward the game’s positive expected value. Shorter runs can still end below zero because the sequence of outcomes matters.
The investing analogy has limits. Market returns are not fixed, independent dice rolls. The narrower lesson is that a favourable long-term average does not determine the result experienced over one specific period.
Positive expected value describes what should happen on average across many repetitions. It does not promise a positive result in any particular run.