What if one small event was taken away from your past? How would your life be now?

The randomness of the outcomes of throwing dice depends on this characteristic to amplify small differences in initial conditions—the precise direction, thrust, and orientation of the throw—into significantly different dice paths and outcomes, which makes it virtually impossible to throw dice exactly the same way twice.

The butterfly effect is the concept that small causes can have large effects. Initially, it was used with weather prediction but later the term became a metaphor used in and out of science.
In The Vocation of Man (1800), Fichte says that "you could not remove a single grain of sand from its place without thereby ... changing something throughout all parts of the immeasurable whole".Chaos theory and the sensitive dependence on initial conditions were described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890. He later proposed that such phenomena could be common, for example, in meteorology.In 1898, Jacques Hadamard noted general divergence of trajectories in spaces of negative curvature. Pierre Duhem discussed the possible general significance of this in 1908.The idea that one butterfly could eventually have a far-reaching ripple effect on subsequent historic events made its earliest known appearance in "A Sound of Thunder", a 1952 short story by Ray Bradbury about time travel.
 In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The name, coined by Edward Lorenz for the effect which had been known long before, is derived from the metaphorical example of the details of a tornado (exact time of formation, exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier. Lorenz discovered the effect when he observed that runs of his weather model with initial condition data that was rounded in a seemingly inconsequential manner would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.
In 1961, Lorenz was running a numerical computer model to redo a weather prediction from the middle of the previous run as a shortcut. He entered the initial condition 0.506 from the printout instead of entering the full precision 0.506127 value. The result was a completely different weather scenario.
One meteorologist remarked that if the theory were correct, one flap of a sea gull's wings would be enough to alter the course of the weather forever. The controversy has not yet been settled, but the most recent evidence seems to favor the sea gulls.

Some scientists have since argued that the weather system is not as sensitive to initial conditions as previously believed. David Orrell argues that the major contributor to weather forecast error is model error, with sensitivity to initial conditions playing a relatively small role. Stephen Wolfram also notes that the Lorenz equations are highly simplified and do not contain terms that represent viscous effects; he believes that these terms would tend to damp out small perturbations.

The idea that small causes may have large effects in general and in weather specifically was used from Henri Poincaré to Norbert Wiener. Edward Lorenz's work placed the concept of instability of the atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos,clarification needed. The butterfly effect is exhibited by very simple systems.

The butterfly effect presents an obvious challenge to prediction, since initial conditions for a system such as the weather can never be known to complete accuracy. This problem motivated the development of ensemble forecasting, in which a number of forecasts are made from perturbed initial condition.