Posted by ddblt1970: No, you really can't have an infinite losing streak.
The probability of you not hitting your color is 19/37 (~0,51). The probability of you not hitting your color x times in a row is (0,51)^x
lim(x) (x goes to infinity) of (0,51)^x is ZERO
You can't miss infinite amout of times.
Just because a particular outcome has a chance of zero, does not mean you can exclude it from the set of all possible outcomes. By that logic you would have to exclude every single outcome, leaving none, since any specific sequence of reds and/or blacks has a chance of zero, when doing an infinite amount of spins. But taken all together (including all blacks and all reds), the sum of these zero chances add up to 1.
It's like considering all numbers between 0 and 1 (an infinite amount of numbers). Any number selected by drawing an infinite amount of random digits after the decimal point, has a chance of zero. But it is clear that for example 0.5 exactly (first digit 5 followed by only zeros), has zero chance, but is still clearly part of the interval. If you exclude it, you'd have to exclude every number.
Of course, given an unlimited bankroll, I'd decide on the amount I would like to win, say a billion $ (don't want to collapse world economy by being greedy), and make that my initial bet size, and stop as soon as I win one, there is nothing clever about that..
We are however talking about the math problem, not real world situations (since infinite bankrolls are not all that real world, except for those acquired by governments through taxation, that is).
The math says that martingale will result in minus infinity with a probability of 1.
Joined: May '08
Age: 34 (M)
btw if we get to a real life situation (lurking at the casino hoping to become the next roulette millionaire)- i believe that Martingale is seen as a winning strategy to the players by the casino operators/owners... think about it- why there are table limits? surely in the past casino's got stuffed by some hardcore Martigalists
Joined: May '08
Age: 54 (M)
Wrong conclusion pochui. If a Martingale player bets really high, he will only win a small amount of money. The rest he has lost in the previous spins. But if a whale marches into the casino and starts betting really high from the get go, he can win a lot of money. Without limits those guys could potentially bust a casino.
I would think a casino would be delighted to increase the max bet to any size, for anyone walking in with a $10 million bankroll, that wants to try out martingale. As long as he doesn't start with a huge bet size.
They'll gladly pay his $10 double-ups all night for months, for the chance to get their hands on that $10 million, when that fatal losing streak hits... For them to get the entire $10 mil, he just has to lose 18 spins in a row, by spin 17 he has lost $5242870, and can't cover the next bet.
All the casino stands to lose is a few hundred dollars every night.
Joined: Nov '11
Location: Bosnia and Herzegovina
Age: 42 (M)
Too much talk about unreal situations...
Let's simplify it: 200 spins, chances of hitting 6 of the same colour in a row 95% (math fact, assuming the perfect distribution of reds and blacks - 100 of each, neglect 0 for the sake of the argument or count it as the opposite from what you played).
What to play?: Reverse martingale is the best (not perfect and not guaranteed to win, but the best choice) Wait for 2 in a row of the same colour and place bet to continue the streak up to 6 in a row. If 3rd in a row hits, move all in to the 4th, then all in to the 5th (you can even stop now ). If lost, wait again for 2 in a row and repeat. Limit yourself to 200 spins, as I said before 95% are chances to hit 6. In case of not perfect distribution (let's say 60:40 in favour of 1 colour) chances are even bigger than 95% to have 6 of the same colour in a row within 200 spins.
Joined: May '08
Age: 34 (M)
yeah soneneso is right, playing reverse martingale (or any other system that requires to raise stakes after a loss) is the way to go- whenever you increase you bets, you do so using casino's money... if you happen to hit big- great walk away and enjoy life with 3 blonds... if you lose (sadly but that's a distinct possibility) you just lose relatively small amount compared to using standard martingale