Volkl said:
If you wait for ten blacks in a row and bet against black only in this situation I.e(after ten blacks in a row), you will win more than 50 percent of the time, because it is less likely to have 11 blacks in a row over time.
As has already been suggested, I
highly suggest you simply write a simulation program and test these ideas first hand.
In fact, you don't even really need a real program. Go here:
http://www.random.org/files/
Save one of the text files (warning they are about 2 megs each), open it up and search for the string '111111111', every time you find it check what the next number is. You will find it is equally likely to be 1 or 0.
Consider what would have to be true otherwise. The source of randomness (roulette wheel or radioactive decay) would somehow have to 'know' what the previous results were and be influenced by them. What if you looked at an entire casino's worth of roulette wheels at once, combining all the results into one giant stream of reds and blacks. However, someone else looked at just a single wheel. If the single wheel had a streak of blacks, but the casino as a whole was on a red streak, what would that individual wheel be more likely to produce? Now, what if you look at all the casinos on Earth? What if you come up with some complex method to combine the results (eg 10 from one wheel, 3 from the next, 17 from the next, alternating between wheels #4 and #5 for 20 choices after that, etc)? It should be clear there would be an infinite number of ways you could combine the data from many wheels. How could there still be a force influencing the results when the data could be combined to produce streaks in any different way?
To use an example I've seen before somewhere, imagine you had a standard fair coin, and flipped it until a long streak occurred (say 10 heads). Now you put the coin in a jar with many other coins and shook it up. Would that single coin still want to be tails? What if you chose another random coin, would it tend to be tails? What if you spent the coin, and a new person who knew nothing of this flipped it, would it still tend to be tails? What if you redefined tails as the side with a picture of a face, and heads as the side with a picture of a bird (or whatever it is)? Now would it tend to be tails (as you defined it), or the 'real' tails?
My point in all this is that when you start to think that sources of randomness are influenced by past events, it leads to many silly outcomes. There are simply too many systems you could use to combine events to produce random choices, and those systems would contradict each other if there were a force which tended to reverse long streaks.
Again, you really should just write a program to test this. You could also just use a spreadsheet. Or, you could actually get a coin and start flipping it. Every time a streak of 3 comes up make a bet against the streak continuing to 4. Keep track of you total winnings.
