Why is flipping a coin not 50 50?

According to Diaconis' research, a spinning penny will land tails side up roughly 80 per cent of the time. This is because the heads side of the penny, the one with the portrait of Abraham Lincoln on it, is slightly heavier than the tail side.

business-standard.com - Guessing heads or tails isn't really a 50-50 game: study

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If a coin is flipped with its heads side facing up, it will land the same way 51 out of 100 times, a Stanford researcher has claimed. According to math professor Persi Diaconis, the probability of flipping a coin and guessing which side lands up correctly is not really 50-50. He claims that a natural bias occurs when coins are flipped, which results in the side that was originally facing up returning to that same position 51 per cent of the time, the 'Daily Mail' reported. Diaconis came to this conclusion after determining that no matter how hard a coin is flipped, the side that started up will spend more time facing up most of the time. One way of thinking about this, as noted in an article from Coding Wheel, is to look at the ratio of even and odd numbers starting from one. What you'll discover is that no matter what number you stop at, there will never be more even numbers than odd numbers in that sequence, the paper said.

The coin flips work in much the same way.

Diaconis first realised that coin flips were not random after he and his colleagues managed to rig a coin-flipping machine to get a coin to land heads every time. He and his team then asked humans subjects do the same thing over and over, recording the results with a high speed camera. Though the results were a little more random, they still ended up with the 51-49 per cent margin. Diaconis noted that the randomness is attributed to the fact that when humans flip coins, there are a number of different motions the coin is likely to make. For instance, he showed how coins don't just move end to end, but also in a circular motion, like a tossed pizza. He also found that there are ways to flip a coin where it looks like it is tumbling in the air, but in reality, it doesn't move at all. Diaconis proved this by tying a ribbon to a coin and showing how in four of 10 cases the ribbon would remain flat after the coin was caught. In another startling discovery, Diaconis determined that the probability of guessing which side comes up of a spinning penny is also skewed more in one direction. According to Diaconis' research, a spinning penny will land tails side up roughly 80 per cent of the time. This is because the heads side of the penny, the one with the portrait of Abraham Lincoln on it, is slightly heavier than the tail side. This causes the coin's centre of mass to lie more toward the head side than the tail. So when it is spun, the penny will naturally fall toward its heavier size, which means there is considerably higher chance that it will land with the tail side up.

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What does a 35 to 1 payout mean?

This means you'll win x dollars for every 1 dollar you bet. For example, a single-number bet offers a payout of 35:1. So, if you win, you'll get your dollar back plus $35.

casino.org - A guide to understanding roulette odds - Casino.org

Before jumping into odds and payouts, we’d recommend familiarizing yourself with roulette bet types first, or this might get confusing. Being able to recognize the names of different bets and where you’d place your chip on the table for each one will be especially useful. For each bet type, the potential payout odds in roulette are stated in the form of x:1. This means you’ll win x dollars for every 1 dollar you bet. For example, a single-number bet offers a payout of 35:1. So, if you win, you’ll get your dollar back plus $35.

Calculate your roulette winnings with our roulette payout guide

The roulette payout chart below shows the odds for the different bets you can make in both European roulette and American roulette, as different roulette variations affect the odds. All the calculations are done for you, so you can check your potential roulette winnings at a glance as you play. Note: If you’re curious about the math behind these, it’s not too complicated. Divide the number 36 by the number of squares your bet covers on the table. Then, subtract 1 from that figure to get the payout odds. For example, a three number bet means dividing 36 by 3 to get 12, then subtracting 1 to equal 11. The payout rate for a three-number bet is therefore 11:1, meaning a $10 bet would result in a $110 payout if you won.

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