Two meanings of a similar word
The relevant question is not “when must the streak end?” but “what payments and losses are possible before it ends?” Even positive expected value for a single operation does not remove personal constraints, and expected utility differs from expected money. The distinction is explained in the university material on uncertainty.[1]
Finite reserve versus doubling
Take a fictional sequence of stakes 1, 2, 4, 8, 16 and 32. After six failures, total loss is 63. The next stake needs another 64. At that point cumulative need reaches 127 although the starting stake was 1. Required reserve grows much faster than the number of repetitions.
In an idealised game with independent equally likely outcomes, six consecutive failures have probability 1/64, about 1.56%. A real financial series need not have independent outcomes with probability one half. This is a description of a specified game, not an estimate of market-loss probability. Do not insert the toy probability into a real trade because it looks small.
Even there, “the next win recovers everything” requires unlimited continuation capacity, no costs and exact payout proportions. Position limits, lack of money and a negative post-commission result break the simplified story. Debt adds another boundary: a creditor can demand money before the desired outcome arrives.
Average price falls, obligations remain
Another mechanism is buying more of an asset after it becomes cheaper. First buy 10 units at 100, then 10 at 80. Total spent is 1,800, quantity 20 and average price 90. At current price 80, the position is worth 1,600 and the loss is 200. The displayed average looks better, but total investment increased and the loss did not disappear.
If price then falls to 60, value is 1,200 and loss is 600. Without the additional purchase, the initial 10 units would be worth 600 against the original 1,000 cost, a loss of 400. Increasing the position increased exposure to the next fall. Compare full alternative cash flows, not only the new average.
Planned contributions are not chasing losses
A pre-limited programme of regular contributions differs from automatically increasing risk to compensate for a loss. In the first case, funding source, period, permitted share and instrument rationale are defined. In the second, the loss itself causes the increase. Even planned buying does not guarantee recovery or remove asset and concentration risk.
Ask whether the new purchase would make sense if the former position did not exist. What new information changed the valuation? What is the total investment limit, and what fact would falsify the hypothesis? These questions distinguish an independent decision from an attempt to improve an unpleasant app line. The historical purchase price is not an obligation of the market to the owner.
Costs often omitted from the story
Every position increase creates new turnover and possible commissions, spread and slippage. Barber and Odean’s historical study of individual investors shows why gross and net results differ in active trading; its figures concern a specific U.S. sample, not current tariffs.[2] Set costs explicitly and equally for alternatives.
Check [mean reversion](/guides/mean-reversion-extrapolation/), but do not use it to justify indefinite waiting. Calculate capital, mandatory payments and adverse continuation. [Trading frequency and costs](/guides/trading-frequency-costs/) adds to the analysis. A lower average price is an accounting description of purchases, not evidence that total risk fell.
A limit that cannot be increased after a loss
For an educational test, fix the maximum total contribution before the sequence begins. Then state at which step the rule no longer fits that limit. Do not move the boundary whenever the scenario becomes inconvenient: that tests an assumption of infinite reserve rather than a limited plan. Show mandatory payments separately; their existence limits acceptable risk even when the displayed average is attractive.
Sources and verification limits
[1] Lecture 20: Uncertainty, MIT OpenCourseWare: expected monetary value and expected utility.
[2] Trading Is Hazardous to Your Wealth, Barber and Odean: historical customers of one U.S. broker; not current tariffs or a 2026 forecast.
Anti-martingale changes size after a gain
Here, anti-martingale means a pre-set increase in the next risk after a successful outcome and a decrease after an unsuccessful one. It does not claim a win raises the probability of another win. In an independent educational game it does not. The name describes a sizing rule, not a discovered advantage.
Let the account be 1,000; each attempt wins or loses the stake. Start at 100, double after each win up to 400 and return to 100 after a loss. In win, win, loss, the account goes 1,100, 1,300, 900. With a constant 100 stake, the same path gives 1,100, 1,200, 1,100. Increasing after gains did not preserve accumulated gains: the final larger stake outweighed them. This is a counterexample to a guarantee, not proof that constant sizing dominates every sequence.
A constant fraction of the current account is different. At 10%, money risk rises after growth and falls after decline without explicit doubling. After +10% and −10%, 1,000 becomes 990 because percentages use different bases. In real execution losses can exceed the intended fraction because of gaps, debt and missing counterparties.
Pyramiding adds volume to the same position
Pyramiding increases an already profitable position, not necessarily the size of the next independent trade. Buy 10 units at 100; after a rise to 120 add 5. Total acquisition cost is 1,600, quantity 15 and average price 106.67. At 120 profit is 200. If price falls to 100, the position is worth 1,500 and loses 100 relative to cost; without the addition, the first 10 units would return to zero profit.
Profit from the first units is not an external reserve that can be withdrawn while protecting the whole position. The new units were bought at a higher price and amplify reversal exposure. A protective order also does not guarantee its execution price. Recalculate total size, related risks and a gap scenario before adding; “only with profit” does not change the arithmetic.
Fixed contribution and target value create different cash flows
Investor.gov defines dollar-cost averaging as equal regular investments regardless of price fluctuations.[1](#source-cp-dca) It is a contribution rule, not a fixed number of units. In the next author-created model, value averaging means bringing portfolio value to a pre-set target after each step. Contribution equals target minus pre-contribution value; a negative result means a withdrawal. Both rules require a calendar and funding source.
There is no starting portfolio; prices at three dates are 100, 50 and 150. Fractional units are allowed, with no costs or return on cash. A constant contribution of 1,000 buys 10, then 20, then 6.6667 units. After the operations, quantity is 10, 30 and 36.6667; value is 1,000, 1,500 and 5,500. Contributions total 3,000 and profit at the last date is 2,500.
For the second rule, target values after operations are 1,000, 2,000 and 3,000. On the first date, contribute 1,000 for 10 units. On the second, those units are worth 500, so 1,500 rather than 1,000 is required to reach 40 units worth 2,000. On the third, those units are worth 6,000; reaching a target of 3,000 requires selling half and withdrawing 3,000. Twenty units remain; net contribution is 1,000 + 1,500 − 3,000 = −500. Difference between final value and net contribution is 3,500.
Comparing only final 5,500 and 3,000 is incorrect because 3,000 has already been withdrawn in the second case. Nor does 3,500 versus 2,500 prove general algorithmic superiority: it is one deliberately specified path with different timing and flows. With the same initial resource of 3,000 and zero return on the reserve, the first ends at total 5,500 and the second at 6,500: 3,000 in the asset, 3,000 withdrawn and 500 unused. Different paths, costs and reserve returns change the result; do not call profit a return divided by a negative net contribution.
Funding needs can stop a target algorithm
A participant may have only 1,000 free funds on each date. Then the second-step requirement of 1,500 is unavailable and the target is not met. If only 1,000 is contributed, value is 1,500, not 2,000. Do not continue as if the missing 500 appeared for free. A deeper fall requires a larger outside contribution and may coincide with lost income.
An honest test specifies total resources, available reserve, return on its storage, possible withdrawals and a rule for abandoning the target when money is insufficient. Debt is not a free reserve; commissions and sale consequences require separate checks, without inserting universal tax rates. A rule forbidding sales differs from the value-averaging model shown: excess remains in the portfolio. No variant guarantees recovery, determines a suitable asset allocation or makes waiting for a crisis a reliable entry method. Test cash-flow feasibility before the chosen path’s result.