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Your math is correct.
May I suggest an alternate simulation though? Test the following two situations.
1) 10 step martingale, betting on every outcome, always on the same color
2) Wait for a streak of 10 consecutive matching results. Then, 10 step martingale on the opposite color. Each time you win a wager, you wait for another streak of 10 before betting again. If you lose all 10 in a row, you also wait for another streak of 10 before starting over at step 1.
The results of these two simulations over the same number of wagers (not spins) should demonstrate that the expected loss over both of these scenarios is equal. Gfkostas would bet his house that #2 will win more money in the long run than #1.
You keep saying the same and the same all over again when where i want to direct your attention is elsewhere not whether previous results change the probabilities of the next ones but you are too off balance in this discussion to get anything.
Also I can keep dragging you in this thread forever which shows to what extend some people go to prove that they are right.
As to your indirect implies that am dumb, I've got a record on this forum to be judged upon.
Better both of you stay quiet a be thought a fool rather than continue and remove all doubt.
Considering you cannot even type the quote properly it sounds rather stupid.
No need to get personal.
If I am using a 10 step martingale progression, the 11th step will cause a loss. My chance of losing 11 in a row is (19/37)^11 or 0.0655%. So for every 10,000 martingales used, I should have 6.55 losses.
I apparantly was not letting the simulator run long enough previously, since it was so slow. After I had won $50, $100, or $200 I just ended the test. I had never seen it fail until this longer 10,000 martingale test. I jumped to the conclusion that there was an advantage in waiting for the streak to begin betting. Obviously this is not the case.
Kudos for admitting that you were wrong
Happy 2007
Another point about simulations. Often people will say that computer simulations of gambling are not accurate as they are not like the real thing or it's all computer numbers so doesn't accurately represent things or basically that they don't mean anything or count for anything cos it's not a "real wheel" or whatever.
Computer simulations are used in so many different fields yet you never hear people shouting down their accuracy there. I mean we have population density simulations, traffic flow simulations, aeronautical type simulations the list is endless. The reason people use them is because they work !
Yet somehow when it comes to gambling these computer tests are branded as unrealistic and their validity is disputed !??!