Coin-Toss Experiment
Is a coin toss truly random? Not according to the "D-H-M model" which proposes that a tossed coin is slightly more likely to land on the same side that it started.
To test this model, a team of researchers at the University of Amsterdam arranged for a group of subjects to flip coins a total of 350,757 times. Their conclusion: "the data reveal overwhelming statistical evidence for the presence of same-side bias."
What this means as a money-making strategy:
More info: "FAIR COINS TEND TO LAND ON THE SAME SIDE THEY STARTED: EVIDENCE FROM 350,757 FLIPS"
To test this model, a team of researchers at the University of Amsterdam arranged for a group of subjects to flip coins a total of 350,757 times. Their conclusion: "the data reveal overwhelming statistical evidence for the presence of same-side bias."
What this means as a money-making strategy:
If you bet a dollar on the outcome of a coin toss (i.e., paying 1 dollar to enter, and winning either 0 or 2 dollars depending on the outcome) and repeat the bet 1,000 times, knowing the starting position of the coin toss would earn you 19 dollars on average. This is more than the casino advantage for 6 deck blackjack against an optimal-strategy player, where the casino would make 5 dollars on a comparable bet, but less than the casino advantage for single-zero roulette, where the casino would make 27 dollars on average.
More info: "FAIR COINS TEND TO LAND ON THE SAME SIDE THEY STARTED: EVIDENCE FROM 350,757 FLIPS"
Comments
Two things:
1) That's a bloated author list (50)!
2) Wouldn't be surprised to see this win in the next Ig Nobel awards
1) That's a bloated author list (50)!
2) Wouldn't be surprised to see this win in the next Ig Nobel awards
Posted by crc on 04/11/24 at 06:10 AM
crc -- yeah, they included all the coin-tossers in the author list.
Posted by Alex on 04/11/24 at 10:59 AM
One of the things I'll probably never know if it's true:
Sharpers in Elizabethan times would drill a hole into the edge of a silver coin, fill it with gold, and close it up with silver. With a little practice (supposedly), they could make it land either head or tail by how they positioned the coin for flipping (weighted side towards them or away from them).
I found this mentioned in a story by a contemporary of H. G. Wells (don't remember which author, I was just getting a feel for what others were writing at the same time). I researched it as much as I could, but the only other reference I found was a newspaper article on ways small time grifters cheated people. And that's it -- only two references; one was fiction and the other was probably not fact-checked to any great degree.
I've always wondered if the difference in weight distribution would actually be a large enough effect that it'd be worth the time/trouble/expense. It couldn't (imo) have been 100%.
Sharpers in Elizabethan times would drill a hole into the edge of a silver coin, fill it with gold, and close it up with silver. With a little practice (supposedly), they could make it land either head or tail by how they positioned the coin for flipping (weighted side towards them or away from them).
I found this mentioned in a story by a contemporary of H. G. Wells (don't remember which author, I was just getting a feel for what others were writing at the same time). I researched it as much as I could, but the only other reference I found was a newspaper article on ways small time grifters cheated people. And that's it -- only two references; one was fiction and the other was probably not fact-checked to any great degree.
I've always wondered if the difference in weight distribution would actually be a large enough effect that it'd be worth the time/trouble/expense. It couldn't (imo) have been 100%.
Posted by Phideaux on 04/11/24 at 02:53 PM
@Phideaux: I doubt they'd use gold, when lead is even heavier and cheaper as well. (And if I used that trick, I'd put iron in the other side for a double effect.)
Posted by Richard Bos on 04/14/24 at 04:58 AM
I wonder what this depends on - whether the coin is *truly* fair, which I don't believe any real monetary coin is, though casino chips may be; and how you flip, catch and display it.
I'm sure there is a trick for *making* it turn up either way, but that's another matter. For example, if you put a beer mat on the edge of a table, tip it into the air with the back of your fingers, and catch it with the same hand - a common bar trick - you'll almost always catch it upside-down. But that's intentional. Here, they're trying *not* to make it predictable, and yet it seems to be.
Therefore, I wonder if there is a technique to evade this effect. After all, there is a reason why roulette wheels have baffles, and why the rules craps demand that your dice hit the wall. We should be able to find something similar for coin tosses. For example, in my country there is a (not consistent) tradition of flipping a coin high, catching it while it falls, and then slapping it down on the back of your other hand. It might produce fairer results.
I'm sure there is a trick for *making* it turn up either way, but that's another matter. For example, if you put a beer mat on the edge of a table, tip it into the air with the back of your fingers, and catch it with the same hand - a common bar trick - you'll almost always catch it upside-down. But that's intentional. Here, they're trying *not* to make it predictable, and yet it seems to be.
Therefore, I wonder if there is a technique to evade this effect. After all, there is a reason why roulette wheels have baffles, and why the rules craps demand that your dice hit the wall. We should be able to find something similar for coin tosses. For example, in my country there is a (not consistent) tradition of flipping a coin high, catching it while it falls, and then slapping it down on the back of your other hand. It might produce fairer results.
Posted by Richard Bos on 04/14/24 at 05:12 AM
Category: Money | Experiments