I went ahead and ran the longest test last night. It was still running when I woke up this morning, but finally finished.
This simulator is running a 37 number wheel, French rules. You lose 50% of your bet when zero appears. My sequence is a bit unique in that if zero appears, you then skip one spin, then resume with the full bet (instead of the minimum half bet) in the next level of the martingale sequence. This often gives you a bit more pop since you only lost half of your bet on zero, thus the full bet is not needed on the next level of the sequence. For example, if zero appeared on a $256 bet, you would only lose $128, so if you win the martingale you win more than $1, you actually win $129.
In these tests I am betting high/low, using a 10 step martingale (1,2,4,8,16,32,64,128,256,512). I ran for 10,000 martingales each test. The first result below is waiting for a streak of 15 high or low, then betting on the opposite using the 10 step martingale.
profit / drawdown / peak profit / sessions / losses
765.5 -3145 2825.5 10000 10
We made a small profit here with peak profit of +$2825.50, worst drawdown of -$3145 and 10 martingales that failed.
Next I ran 5 tests with no delay, just betting the opposite immediately, using a 10 step martingale. These tests are very fast, so I went ahead and ran 5 for comparison.
profit / drawdown / peak profit / sessions / losses
501.5 -2941 2259.5 10000 11
-996 -3630.5 694.5 10000 12
-2813 -5557.5 1569 10000 13
2355.5 -2618 2355.5 10000 8
-2506 -5329 1869.5 10000 12
These last 5 tests show the randomness of the roulette wheel, with varied results. 3 tests lost money, 2 won money. The number of martingales lost per test were similiar, though, in the 8 to 13 range.
Judging from these results, there appears to be no advantage in waiting for a 15 streak of an even chance to begin betting. The results are similar if you just start your betting immediately.
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.
Interesting study.