Why 70% favourites lose 30% of the time
A probability is a long-run frequency, not a promise about the next hand.
6 minute read
Pocket aces against kings is 82%. That sentence contains its own bad news: kings win 18% of the time, about one hand in five and a half. A player who gets aces against kings a hundred times will lose roughly eighteen of them — and will remember every one.
Add the turn and river that actually came to see how that run-out compares.
Losing k of n independent spots
C(n, k) × p^k × (1 − p)^(n − k)
p = 0.18: losing exactly 3 of the next 10 aces-vs-kings spots is 17%; losing 3 or more, 24%.
The point is not that variance is unfair. It is that a good decision and a good result are different things, and only one of them is under your control. If the money went in with the best of it, the run-out is not information about the decision.
Quick check
You are an 80% favourite five times in a row. What is the chance you win all five?
Show answer
0.8⁵ ≈ 33%. Losing at least one of five is the more likely outcome — 67%.