A multiplication example
For two independent fair coin flips, the chance of heads on each is one-half. Both heads has probability one-half times one-half, or one-quarter. Seeing heads on the first flip does not change the second flip's one-half chance. The combination and the conditional next outcome answer different questions.
If three independent events have probabilities 60%, 50% and 40%, the chance all occur is 0.6 × 0.5 × 0.4 = 12%. An accumulator's larger potential return therefore comes with the need for several events to succeed. The calculation uses probabilities, not simply descriptive labels like likely.
Correlation is not the only issue
Events can be dependent because they share a match, participant, weather condition or underlying state. A team winning and that team scoring several goals are not automatically independent. Cards drawn without replacement also change the remaining composition. A game feature carrying state between stages can differ from independent base rounds.
Past streaks under an independent model
If rounds are independent with unchanged probabilities, earlier losses do not create a debt the next round must repay. A history display records a sequence but does not change its model. If genuine rule changes or retained state exist, those should be described explicitly rather than explained as luck balancing itself.
Checking an independence claim
Identify the mechanism, shared inputs and whether information from one event changes the other. A statistical pattern from a small sample is not enough to prove or disprove independence. When no suitable model exists, avoid presenting a multiplied probability as an exact forecast. State the assumption so readers can evaluate its relevance.
Do independent events have to be equally likely?
No. Independence concerns whether one event changes the other's probability, not whether their individual probabilities match. A 20% event and a 70% event can be independent, giving a 14% chance of both. Two 50% events can instead be strongly dependent. Equal-looking odds therefore do not prove independence, and different odds do not disprove it. Examine the underlying relationship and shared information. For a combined forecast, state the independence assumption rather than deriving it from the price format or market names.