A series is consecutive success
A length-five streak means five successes with no failure between them. In twenty coin tosses, H H H H H is a five-head streak; eight heads separated into smaller groups are not. Each simulated experiment scans N throws, resets its current run after failure, and records a hit if the longest run reaches the requested length. The model assumes independent trials with one fixed probability p.
Read the estimate as a proportion
For each of R experiments, the page asks whether at least one qualifying series occurred. If 1,842 of 10,000 experiments hit, the estimate is 18.42%. It is not a promise that 1,842 of the next 10,000 real sequences will hit. The page also reports the mean longest run, a separate summary of the simulated experiments.
A real-number example
Set 100 throws, length 5, success chance 50%, and 10,000 experiments. One run might show 96.31%, 9,631 hits, and a mean longest run of 5.98. A rerun can differ slightly because simulation samples random experiments. Five heads in one specified block has chance (1/2)^5 = 3.125%, but there are 96 overlapping five-toss windows in 100 tosses, so simply multiplying is not a valid final probability.
Why more experiments help
The approximate standard error is sqrt(p(1−p)/R). Near p=.5, 10,000 experiments have about a half-percentage-point standard error, while 100 have about five points. More runs reduce sampling noise but cannot repair a bad model. Keep throws, threshold, and success rate fixed when comparing estimates; changing any of them describes a different event.
Limits of the model
Drawing cards without replacement, fatigue, a changing opponent, or a faulty machine may make trials dependent. This simulator cannot diagnose whether a real sequence is biased, and it is not a gambling forecast. It is useful for teaching, game design, and checking intuition about opportunities for runs. A surprising streak can be common when many overlapping chances exist.
How this differs
An exact dice probability calculator uses a formula for a stated number of successes. This page simulates an overlapping run event, so its estimate varies from run to run. A random picker creates one result rather than thousands of experiments. All simulation occurs in the browser; no settings or results are sent to DiceDecide.
The output should be read with its experimental count. A value based on 10,000 runs carries much more information than the same rounded percentage based on 100 runs. Copy both the settings and the hit count when discussing a result, because a percentage without its denominator cannot show how much simulation noise it contains.
Changing one input at a time
Start with a fair coin, then change only one value. Keeping 100 throws and 10,000 experiments, raise the required series from 5 to 8; the estimated chance must fall because every eight-success run contains a five-success run, but not vice versa. Keeping the length at 5 and raising p from 50% to 60% also raises the chance. These directional checks are more useful than expecting the same decimal on every run.
The number of throws is an opportunity count. Ten independent throws leave only six possible starting positions for a five-throw block, whereas one hundred throws leave ninety-six. Overlap means the positions are not independent, but more positions still create more opportunities for a streak. This is why a run that is striking in one short game can be routine in a long sequence.
For a reproducible classroom comparison, write down all four inputs and the observed hit count, not just the rounded percentage. A second browser will legitimately obtain a different estimate with the same settings. Agreement should be judged by whether both values fall within ordinary sampling variation, not by whether they match digit for digit. A deterministic formula and a simulation answer different questions.