LessonThis is a lesson restated in new words. Any figure in it is an example from the source, not this desk's record.
Most algorithmic trading uses basic probability, and most backtests the lecture sees are still wrong. They record gain every time a signal fires and treat those gains as one distribution. If the market remembers its path, the same signal at two times is two conditional problems. Pooling them can show a negative average when one of the situations was favorable and the other was not.
Why it matters
Start with two fair dice and their sum. With no information, the sum has one mass function, and a long experiment's frequencies settle on it by the law of large numbers. The chance of 11 is about 6 percent, or 1/18. The mean sum is 7, the center of a symmetric mass. Sample frequencies of 11, and the running mean of the sum, settle on those numbers when every roll comes from that same unconditional experiment.
Condition on the first die showing 5 and the picture changes. The chance of 11 is then over 15 percent. The mean sum is 8.5, not 7. Condition on a 1 instead and you get another distribution again. Convergence still happens, but it happens to a different target. A backtest that ignores what it conditioned on is mixing those targets.
The idea in plain words
A stock price through time is a stochastic process, a sequence of random variables. The Markov, or memoryless, property says the conditional distribution of the future given the entire history equals the conditional distribution given only the current state. If that were true for prices, a forecast would need today's price and nothing older. History would already be baked into the level.
A classroom sum of ten dice shows the property cleanly. One path totals 38. The unconditional distribution of the total at step 10 is wide. Conditioning on the first five rolls replaces it with a narrower law, and the rest of the path is a draw from that law. Because each new die ignores the past, conditioning on all five rolls matches conditioning on the fifth roll alone. You do not need the memory. Markets, the lecture says, have plenty of evidence against that shortcut. The conditional law given the whole path is not the conditional law given the latest price. You can enlarge the state until the shortcut returns, but if the state must include the path back to the beginning, the simplification is gone. The dependence is also not only the price path. Volume and an unobservable volatility path sit in it too.
How to use it
Look at one system with the same entry at two times, drawn in the lecture as an orange mark and a red mark. The usual backtest throws every gain into one histogram. In the example that pooled histogram has a negative expected value, so the strategy looks untradable. The analysis is rejected because the two entries condition on different histories. Replay each entry many times, the lecture argues, and the two gain distributions would differ. A moving-average crossover that "loses money" in a single pool can be the same mistake as throwing the "first die is 5" sample and the "first die is 1" sample into one chart.
The repair is to compress path memory into state variables you can actually condition on: a volatility bucket, momentum, a sentiment regime. Some signals in the speaker's experience need a lot of that conditioning. Some are stable enough that the raw entry and exit already share a gain distribution. The goal is an empirical stand-in for the right theoretical law. Split carefully and the lecture's picture shows one bucket with positive expectancy and another with negative expectancy. Trade the first and skip the second, and the pooled "negative edge" was an averaging error.
What usually goes wrong
The Markov property is something you have to justify. Assuming it, then feeding a model only the latest price, throws away path information the conditional distribution needed. Assuming it is false, then still pooling every fill, produces an empirical histogram that need not converge to anything you meant to measure, because the rows came from different conditional laws.
Questions people ask
What changes when the first die is a five?
The sum's mean moves from 7 to 8.5, and the chance of 11 moves from about 6 percent to over 15 percent. The unconditional chart is a different experiment.
What does memoryless mean for a price?
That the future's conditional distribution given all past prices matches the one given only the current price. The lecture says markets often fail that test.
How should a backtest group trades?
By the state you believe fixes the conditional gain law: volatility, momentum, sentiment, or another compressed path variable. A single pool mixes those laws.