A streak does not create a debt
After five heads on independent fair coin flips, the next flip still has a one-half probability of heads. The probability of the complete six-head sequence before any flips is one in 64. These are different questions: the rarity of the whole sequence does not change the conditional probability of the remaining flip after the first five are already known.
In a standard independent roulette model, several black results do not make red more likely next. Zero also remains possible. Increasing a stake because the opposite colour is due changes the money at risk without changing those probabilities.
Why long-run averages do not force compensation
The law of large numbers concerns the convergence of suitable sample averages. It does not require later trials to cancel earlier imbalances. An initial excess of one outcome can become a smaller proportion of a growing sample without the process actively favouring the opposite result.
Dependence is a different question
Cards drawn without replacement change the remaining deck composition. A documented collection feature can retain state between stages. Those mechanisms are not examples of independent unchanged trials. The useful distinction is whether the rules genuinely change the next outcome's distribution, not whether a player feels a streak has lasted too long.
Recognising the error in a claim
Watch for phrases such as overdue, must hit soon or guaranteed after enough losses without a rule-based mechanism. A screenshot of recent outcomes cannot establish a future entitlement. To assess a prediction, identify its probability model and evidence. A recent loss may affect a person's budget or decision to stop, but it does not create a mathematical obligation for the game to repay it.
Is the opposite belief also a mistake?
Assuming that a recent independent winning streak makes continued wins more likely can also lack a valid mechanism. A streak alone does not establish either continuation or reversal. In settings involving skill, changing conditions or retained state, new information can matter, but it must be analysed through that mechanism. Avoid converting an emotional impression into a probability claim. The appropriate question is what has changed in the process, not whether a run looks unusually lucky or unlucky on a history screen.