Still, the article states that there's a 50:50 chance of landing on black or red, which is simply not true.
Additionally, unfair coins can trivially be used as fair coins, but unbalanced roulette wheels cannot easily be used as fair roulette wheels.
In this case, caller calls in the air after flipper hides the side that starts up. 0.5 * 0.51 + 0.5 * 0.49 = 0.5
For any other case, flip a coin twice. Assign one person HT and the other person TH, reflipping TT and HH. Since p * (1 - p) = (1 - p) * p, the dual flip is a fair flip.
Please don't mention the possibility of sleight of hand next.
-- There are a hundred tickets in a hat. 99 of the tickets win you $1. The last ticket loses $10,000 dollars.
the sentence "it is nevertheless a legitamte strategy to "beat" roulette in the short term" is absolutely false. The expected value of each roll of the dice is negative, summing a bunch of negative expectations leads to an even large negative expectation.
EDIT: Also, some people will talk about infinite bankrolls, there is no such thing! even if there was, infinity + X = inifinity, why are you gambling?
Probability is often not intuitive. It is easy to think you "beat" the system because you won a couple bucks.
This game may better illustrate my point.
There is a hat with 100 tickets. 99 of the tickets produce a $1 win. The last ticket requires you kill yourself. Would you play this game once or twice?
I would not play your second game, but the reason I wouldn't has nothing to do with expected values (notwithstanding the fact that it's technically impossible to calculate an expected value for an unquantifiable outcome like death). In your first game, I feel that I would come out ahead, and in the second game I feel like it's not worth it.
What the author is describing is a 'Martingale' strategy, and it is indeed a surefire way of making a profit (with one critical caveat: you need an unlimited bankroll).
After each win, you always earn a profit of X (where X is your base bet), regardless of how many rounds you have lost before.
Without a sufficiently large bankroll relative to X, however, probability of bankruptcy is high.
I bet 50, and lose.
I bet 100, and lose.
I bet 200, and lose.
I bet 400, and lose.
I bet 800, and lose
1600, 3200, 6400, 12800, 25600, 51200, 102400, 204800, 409600, and then...
The reason they have limits is so that Sheik Abudab can't come in and lay down 500 million dollars and bust them. That is one valid reason to take bad odds: If you can destroy something as a side effect, without really being in danger yourself.
But now that I think about it, you could always just move to another table with a higher limit. Of course, if you're going through all this trouble to make $50, you probably don't have the bankroll to keep going.
Maybe another reason for tables having different limits is that the pit bosses don't trust the dealers (or security?) in the low-roller areas to handle money above a certain amount?
That doesn't sound very practical. And why play roulette for money (rather than just for fun) if you already have unlimited money?
New Scientist appears to be in serious decline.
First of all, if your money is doubled when you hit the right colour, you don't make any profit in the long run. You will stay on the same amount.
Second of all, there is a 0, and often also a 00 on the roulette wheel, which is neither red nor black. This means that the chance you're correct is less than 50%, so you stand to make a loss in the long run.
There is no way to win at roulette, without using a computer to predict where the ball is going to be, based on the movement and spinning of the wheel. And I seriously doubt that even that is possible using just human observation and a trigger in your foot.
[edit: the author is female, sorry about that]