LessonThis is a lesson restated in new words. Any figure in it is an example from the source, not this desk's record.
The Kelly criterion is a bet size, not a forecast. Given a win probability, a loss probability, and the net gain per unit risked, it returns the fraction of the bankroll that maximizes expected logarithmic growth. The fraction is only as good as those inputs, and the lecture's pictures show a bad estimate turning a helpful rule into a harmful one.
Why it matters
Expected gain is the average winner times the win probability, plus the average loser times the loss probability. Positive, and repeated draws tend to lift wealth. Negative, and they tend to sink it. Each trade is one draw. Bet size decides whether you last long enough to see the average. After 1,000 trades a small fixed stake tops out near 20,000 on lucky paths. A large stake reaches toward 60,000 and goes broke more often. You live one path.
The idea in plain words
A fixed dollar stake is a strange rule once the bankroll changes. A million-dollar account would not keep risking 20 dollars a trade. Something nearer 20,000 is the scale the lecture uses to make the point. Betting a fraction of current wealth changes the math. The time average, what one path experiences, need not match the ensemble average, the mean across paths. A few fraction-staked paths grow so large that they pull the average up, while most paths in that picture sit below the start, or near zero, by trade 1,000.
The lecture's numbers make the trap obvious. Start with 1,000 and bet a fraction of the bankroll inside a system whose expected gain is positive. Average wealth after 1,000 trades is 1,757, so the average path is up 757. The chance of finishing above the original 1,000 is 47 percent. Most paths lost money relative to the start, and a minority of huge paths created the positive average. The lecture compares this to a swimming hole whose posted average depth is 7 feet because one spot is very deep and the rest is shallow.
The repair is to maximize the geometric mean of growth rather than the arithmetic mean. You still cannot pick your path. You can pick a betting rule whose typical path is the one you would prefer to draw at random. Solving that maximization produces the Kelly fraction: a function of the win probability, the loss probability, and the net gain per unit risked. The lecture does not claim you observe those inputs. You estimate them.
How to use it
Compare two proportional rules on the lecture's charts. Both risk a share of the bankroll. Only the Kelly share is chosen to maximize expected log growth. The non-Kelly share is the earlier case, with about a 47 percent chance of ending above the start. Walk a Kelly path instead and, by trade 10,000 in that comparison, 76 percent of paths finish above the starting capital. Median terminal wealth is 1,018 on the Kelly paths and 836 on the other proportional rule. Those horizons differ from the 1,000-trade average of 1,757, so they are a separate experiment, not a revision of it.
Then spoil the inputs on purpose. Win probability, loss probability, and the size of winners and losers all wobble in the lecture's simulation. A volatile market, a policy change, inflation, or the level of rates is a reason to estimate them differently, not a reason to pretend one backtest froze them. Feed the noisy estimates into the same Kelly function and the paths stop looking like the clean set. With accurate inputs, 71 percent of paths end above the start. With inaccurate inputs, 41 percent do. Both books are "using Kelly." Only one of them has the inputs the fraction was derived from.
What usually goes wrong
Reading the ensemble average, 1,757 after 1,000 trades, as your own result misses the 47 percent figure. A fixed dollar stake ignores the bankroll. A fixed fraction that is not the growth-maximizing one is a different rule. Estimated win rates are not constants. The lecture's claim is that these returns are not ergodic: the average across paths is not the path you walk. Bad inputs move the share of paths that finish ahead from 71 percent to 41 percent.
Questions people ask
What goes into the fraction?
The win probability, the loss probability, and the net gain per unit risked. The lecture presents the fraction as the solution of a log-growth maximization, estimated from trades rather than known.
Why can a positive edge still leave most paths down?
Because a few very large paths dominate the average. In the proportional example, average wealth was 1,757 from a 1,000 start, while only 47 percent of paths finished above 1,000.
What changes between the 76 percent and the 41 percent?
The 76 percent is a Kelly book with the inputs treated as known, by trade 10,000. The 41 percent is a Kelly book whose inputs are estimated badly. The rule is the same. The estimates are not.