Coin Flip Probability
Physical Physics, 50/50 Myth
While considered 50/50, physical coin flips are slightly biased depending on the side facing up before the flip, aerodynamic properties, and the surface it lands on.
A guide to randomness in decision-making, covering coin flip probability, tabletop dice (D4-D20), true random vs pseudorandom, and simulations.
While considered 50/50, physical coin flips are slightly biased depending on the side facing up before the flip, aerodynamic properties, and the surface it lands on.
In tabletop gaming, different dice offer different distributions. A D20 gives a flat 5% chance per face, while rolling multiple dice (like 2D6) creates a bell curve favoring middle numbers.
Physical dice can be biased by air bubbles or uneven weight. You can test them by floating them in salt water and observing if they consistently roll to the same number.
Computers generally use pseudorandom algorithms (like Math.random) based on math. True random numbers (like random.org) are generated by measuring atmospheric noise or radioactive decay.
A statistical technique that uses repeated random sampling to understand the probability of different outcomes in complex systems, heavily used in finance and physics.
Research suggests using random selection for trivial choices can combat decision fatigue, freeing up cognitive resources for more important matters.
Physical randomization (rolling dice) offers tactile feedback and transparency, while digital tools provide speed, logging, and complex algorithmic balancing for digital groups.
Lottery generators use algorithms to pick numbers without human pattern-bias, though mathematically, every combination still has the exact same probability of winning.
Understanding expected value and variance is crucial. The house always has an edge, meaning over infinite iterations of random events, the casino mathematically wins.