[Eyenigma]

I realize there's some pretty smart people here - so I'm hoping someone can help me shed some light on the correct way to look at Roulette probability. For the sake of commonality and simplicity we'll use a Vegas Roulette wheel, which has 2 green slots.



Long story short, I saw (what seemed) an anomaly where a roulette wheel had rolled 6 red numbers in a row. And while I realize each roll is mutually exclusive, I couldn't help but be puzzled on probability (assuming all was truly balanced and fair) that such a thing could occur.

Conventional probability would suggest each roll is mutually exclusive, and that the odds of landing in a red slot would be 44.7% probability. Thus, if I am correct - if you had bet black and greens, you'd have a better than 50% chance of hitting. So I ponied up a little cash (not a lot) and figured it seemed like a good bet. But red hit again. And again. And again. Each bet, I had bet on black and green... until finally I was cleaned out.

Now, after about 11 red rolls, it did finally hit black. But by that time I was cleaned out. I guess I just don't see the math or logic of how that could happen unless it was an unbalanced wheel? Or the dealer unknowingly altered what should be a random roll with repetitive muscle actions?

What am I not accounting for?
Conventional math would suggest:

(17/38)^11 = 0.000143654281% chance of occurring.
In other words - not even god should be able to have that happen.

But even assuming I did see a mathematical miracle, I routinely see 3, 4, and 5 consecutive rolls of the same color:

(17/38)^5 = 0.017919530

Again, I realize one should look at each roll as mutually exclusive. But if someone were to look at the display board and see a string of consecutive like colors - why would they not take the probability of repeating the result into account?

[Ghoser777]

Remember that probability isn't a guarantee of what will happen next. You actually could have red come up 100 times in a row, but the likely hood of that is very low. Oddly enough, the likely hood of getting alternating red and blacks for 100 spins has the exact same probability as 100 reds in a row! Getting alternating red and black seems more likely only because it seems more "fair," but a roulette table is not built in with emotions and does not consider pass spins with compassion for the gambler.

I was just playing a dice game with friends tonight, and one claimed that she had "broken statistics." In the game you roll three dice, and you win if you get three of the same number. She must have rolled 50 or so times, and she never got three of the same. Based on probability, she had a 1/36 chance of rolling three of the same, and yet she was 0 for 50. The problem with the situation is that you don't necessarily see the 1 out of 36 wins unless you play a ton of games - that is, as the number of games increases, the closer the wins to total games ratio will approach 1:36.

The main reason that you can't look at past spins to determine your next move (besides taking into account how much money you've won/lost) is that the roulette table does not keep track of how many red's have come up in a row and decide to institute some level of fairness.

Probability is tricky business (at least for me - I didn't gain a better understanding of it until I had to teach it). Hope my explanation was somewhat useful.

[red rocket]

There are underlying quantum effects at work. Since quantum mechanics does not operate according to Aristotelean logic, you can forget about ‘probability’ in the statistical sense.

Newtonian variables would include the wheel itself, the physical and kinetic characteristics of the dealer, air temperature, humidity, and the ball.
Quantum and sub-quantum variables would include the current spin states, the intentions of the players, the non-local intelligence field’s affinity for certain results at the particular time and place, your own subconscious, etc.

Basically, you should have bet on red. Why didn’t you?

[Spheric Harlot]

[finboy]

Originally Posted by red rocket 

There are underlying quantum effects at work. Since quantum mechanics does not operate according to Aristotelean logic, you can forget about ‘probability’ in the statistical sense.

It can still be modelled, taking into account all of the other stuff that you mention. "forget about 'probability' in the statistical sense" is usually something you hear from the casinos.