white dice live wallpaper

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the dice are meant to introduce an element of chance to these games, we expect that the outcomes of the rolls will be truly random. however, new theoretical models and high-speed movies of dice rolls of numerous shapes and sizes confirm this is not strictly the case. they show that dice thrown with a 1 on the top are slightly more likely to land as a 1 than as the other values for every type of the various kinds of dice they studied. but at the same time, it's usually too hard for someone to predict the outcome of the throw of a single die you'd have to know the starting conditions of the throw and its environment so precisely that for all practical purposes, the result could be considered random.

exploring a question that was debated in the 17th century by scientists and mathematicians blaise pascal and pierre de fermat, and many others before and since, doctoral student marcin kapitaniak at the university of aberdeen, scotland and his co-authors created a sophisticated theoretical model of the die throw in three dimensions. they considered how the effects of gravity, air resistance, friction of the table, and other factors influence the outcome of the roll. in addition, they observed the fall of the die with a high-speed camera that could capture the die's trajectory at a rate of 1500 frames per second. what did they find to be the most important factor?

the initial position of the dice, tomasz kapitaniak,of the university of lodz in poland, wrote to me in an email. small changes in the position can significantly affect the outcome. other factors are less significant. the air resistance can be neglected, he said. however, he quickly added, friction is important. with a high-friction table, in which the dice can't slide across very easily, the dice tend to bounce around more times, tumbling and twirling, and making the results harder to predict. with a smooth, low-friction, or soft table, the dice tend to bounce fewer times. even bouncing doesn't always mix things up. the high-speed video showed that dice frequently did not change their face even after a bounce. could gamblers use the knowledge from this paper to their advantage, by placing the desired value of their roll as the highest-lying face of their die?

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