Tag Archives: gambling

Coin Flips Are Biased

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2023/10/coin-flips-are-biased.html

Experimental result:

Many people have flipped coins but few have stopped to ponder the statistical and physical intricacies of the process. In a preregistered study we collected 350,757 coin flips to test the counterintuitive prediction from a physics model of human coin tossing developed by Persi Diaconis. The model asserts that when people flip an ordinary coin, it tends to land on the same side it started—Diaconis estimated the probability of a same-side outcome to be about 51%.

And the final paragraph:

Could future coin tossers use the same-side bias to their advantage? The magnitude of the observed bias can be illustrated using a betting scenario. 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. These considerations lead us to suggest that when coin flips are used for high-stakes decision-making, the starting position of the coin is best concealed.

Boing Boing post.

Gaining an Advantage in Roulette

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2023/04/gaining-an-advantage-in-roulette.html

You can beat the game without a computer:

On a perfect [roulette] wheel, the ball would always fall in a random way. But over time, wheels develop flaws, which turn into patterns. A wheel that’s even marginally tilted could develop what Barnett called a ‘drop zone.’ When the tilt forces the ball to climb a slope, the ball decelerates and falls from the outer rim at the same spot on almost every spin. A similar thing can happen on equipment worn from repeated use, or if a croupier’s hand lotion has left residue, or for a dizzying number of other reasons. A drop zone is the Achilles’ heel of roulette. That morsel of predictability is enough for software to overcome the random skidding and bouncing that happens after the drop.”

On the Randomness of Automatic Card Shufflers

Post Syndicated from Bruce Schneier original https://www.schneier.com/blog/archives/2022/10/on-the-randomness-of-automatic-card-shufflers.html

Many years ago, Matt Blaze and I talked about getting our hands on a casino-grade automatic shuffler and looking for vulnerabilities. We never did it—I remember that we didn’t even try very hard—but this article shows that we probably would have found non-random properties:

…the executives had recently discovered that one of their machines had been hacked by a gang of hustlers. The gang used a hidden video camera to record the workings of the card shuffler through a glass window. The images, transmitted to an accomplice outside in the casino parking lot, were played back in slow motion to figure out the sequence of cards in the deck, which was then communicated back to the gamblers inside. The casino lost millions of dollars before the gang were finally caught.

Stanford mathematician Persi Diaconis found other flaws:

With his collaborator Susan Holmes, a statistician at Stanford, Diaconis travelled to the company’s Las Vegas showroom to examine a prototype of their new machine. The pair soon discovered a flaw. Although the mechanical shuffling action appeared random, the mathematicians noticed that the resulting deck still had rising and falling sequences, which meant that they could make predictions about the card order.

New Scientist article behind a paywall. Slashdot thread.