> The standard model of coin flipping was extended by Persi Diaconis [12] who proposed that when people flip a ordinary coin, they introduce a small degree of ‘precession’ or wobble—a change in the direction of the axis of rotation throughout the coin’s trajectory. According to the Diaconis model, precession causes the coin to spend more time in the air with the initial side facing up. Consequently, the coin has a higher chance of landing on the same side as it started (i.e., ‘same-side bias’).
[12] Diaconis P, Holmes S, Montgomery R. Dynamical bias in the coin toss. SIAM Review 2007; 49(2): 211–235.
After reading this the first thought I had was how do you stop people flipping the same way? Like, give me a baton and I could throw it at varying heights and control which side I caught it on. In theory the same applies to coin flipping. You can get quite consistent with your positioning and power.
You could probably control for it by making people alternate which side was face up before the flip.
> Two-up is a traditional Australian gambling game, involving a designated "spinner" throwing two coins, usually Australian pennies, into the air. Players bet on whether the coins will both fall with heads (obverse) up, both with tails (reverse) up, or with a head and one a tail (known as "Ewan"). The game is traditionally played in pubs and clubs throughout Australia on Anzac Day, in part to mark a shared experience with diggers (soldiers).
Two-up sounds pretty fun. Your comment in turn made me think of Chō-han, which is somewhat similar but involves rolling dice instead of flipping coins.
https://en.m.wikipedia.org/wiki/Ch%C5%8D-han
It’s wild and raucous and usually takes place outside pubs and local workers’ clubs, lawn bowl clubs etc. The spinner puts the coins on a flat stick made for the game, but basically a popsicle stick but wider like a tongue depressor. They toss the coins up and flick the stick to tumble the coins. If you called the two matching coins correctly, you double your bet in winnings. Each game takes like 30s-1m and they go on from mid-morning til early afternoon ish.
The losers indirectly pay the winners based on your call of two heads or two tails and if there’s a split, the house wins that game.
Most of the time is spent drinking your beverage of choice, yelling and cursing your own luck and talking smack to the coins, the spinner being booed or cheered for a well run game or a bad string of luck, but the bets are typically fairly low in my experience, although it’s up to each individual player what they bet, but the spinner or venue sets the bet amount per section or per spinner. Each spinner usually takes a set amount, like $5/$10/$20/$50, even $100 in some cases. It’s all cash and pretty much the honor system in that they aren’t handing out receipts or tickets with your bet, so that sets an upper limit on how many bets each spinner can keep straight. No one wants to see someone lose their shirt, so most folks play against their friends/mates for fun, and ultimately you’re all playing your own game because you decide your bet and it’s actually fairly unpredictable due to the crowds milling around the spinners, of which there will be many, all taking bets and running games independently and simultaneously, and players can place bets in any or all of the games around them if they want.
I would guess it's rather mathematical. Each coinflip has some number of half-flips. Now analyze the distribution of that number. If this distribution were to start at its maximum with 0 half-flips and decay as it increases, summing over the even values (same side up) clearly gives more than summing over the odd values. Now the distribution isn't going to be like that, but I expect that it's generally "front-loaded" in a way that causes a similar effect.
Yeah, and seeing that the bias occurs only in some people, perhaps it occurs in people who do as little rotation as possible. Not sure if this study has a graph including amount of rotations occurred in general. E.g. you could take all coin flips where 0-5 rotations occurred and compare them to 6-11 rotations.
> The standard model of coin flipping was extended by Persi Diaconis [12] who proposed that when people flip a ordinary coin, they introduce a small degree of ‘precession’ or wobble—a change in the direction of the axis of rotation throughout the coin’s trajectory. According to the Diaconis model, precession causes the coin to spend more time in the air with the initial side facing up. Consequently, the coin has a higher chance of landing on the same side as it started (i.e., ‘same-side bias’).
[12] Diaconis P, Holmes S, Montgomery R. Dynamical bias in the coin toss. SIAM Review 2007; 49(2): 211–235.