“People might think after a run of heads they’re overdue for a pair of tails, but that’s not how it works,” he says. With a two-coin game of two-up you’re looking at more like 340 flips for it to occur.”Ī lot of players go into a game with a clear strategy but, according to Roberts, people can often be too eager to see patterns in the data. “For example, if you’re looking at the average number of flips to get four heads in a row, it takes around 30 flips for that to happen with one coin. Roberts says the game of two-up, traditionally played on Anzac Day, is a good example of how adding extra coins changes the odds. “Even something as simple as flipping a coin can have a surprising amount of mathematical depth and plenty of real-world applications.” “Probability theory has a long history - people have been studying it for hundreds of years,” Roberts says. But there’s much more to probability than quick calculations, and false theories can mess with our judgement. Roberts can tell you how many times you should shuffle your deck (seven) and how many coin tosses it’s likely to take to get four heads in row (30). He’s an expert on the mathematics of card shuffling, coin flips and games. are examples of complementary events.If you’re playing a game of cards, Associate Professor Dale Roberts is a handy person to have around.
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