The "Trigger" Game
You have a system that relies on the outside ECs. The wheel doesn't have a zero, and you're using an up as you lose progression.
You're triggers are based on waiting for a miss of five reds... before you begin betting that black will hit within the next five spins, while using your progression.
How long must you wait for five reds to miss before you can begin to bet? Answer, the chance that a red will hit in five spins is 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/ 32. So you'll have to wait around for about 32 spins before you can bet.
Now that you've waited, what is the chance that you won't hit on one of the next five spins? Spin one miss 1/2 x spin two miss 1/2 x spin three miss 1/2 x spin four miss 1/2 x spin five miss 1/2 (1/2 x 1/2 x 1/2 x 1/2 x 1/2) = 1/ 32. Or put another way, this means that your progression will fail about once every 32 spins.... hmmm interesting.
Summarizing so far: You stand around for about 32 spins waiting to bet... and find that your progression fails about every 32 spins.
With a $5 starting chip if you win the 31 times you are entitled to (you said it), you make $155. And one time in a 5 step progression loss, you lose $155. So you are saying things even out. Enter 0 or 0 and 00 and you lose to the HE.
Though this analysis may seem brilliant at first glance, it has serious faults.
First of all you really don't have to wait around for 32 spins. A suitable situation can be found sooner than the 32 spins waiting time suggests, if you have 5+ roulettes around you and you track all the EC types. Not just B/R.
Realistically you are not going to find exactly a streak of 5 identical EC's as the last 5 freshest numbers on the board. If they are in the middle or lower part of the board, it already happened and you obviously cannot act on it. You can only take action on the last 5 numbers that you came upon.
The most likely event will be to come upon less than 5 numbers in the streak, or more than 5 numbers. If it's less than 5 numbers you wait for the streak to complete and start betting, or if it breaks you move on to another roulette. If you found more than 5 numbers in the streak, you have a situation where not only you have a ready made trigger, but also a few bets that saved you money if you had bet on them from the start. If you see 7 red, it means that you have saved the cost of 2 bets and that you only have to bet 3 spins to complete the 5 step progression. Hence the importance of virtual loss.
The second and most serious fault in your analysis is that it fails to incorporate the money factor.
Though the analysis pinpoints the 31 wins vs. 1 loss, it doesn't say anything about the amount wagered during some the 31 winning spins or the amount at risk when the loss happens.
Your analysis makes sense only if the amount of bets remains constant. But since you finally agree that I am entitled to 31 wins out of 32 tries, I am confident that any increase on the starting chip, after the 1 and only loss, will result in the full recovery of the loss.
Then the process repeats at the regular starting chip value.
In other words after losing that $155 during the one and only loss I am destined to suffer,
a $100 starting bet in the next round will bring me close to recovery. And one more win out of the 31 I am entitled to, will bring me back to a winning position.
After that, I can revert back to $5 starting chip as usual.
Could it be that after losing a 5 step $5 progression will be followed by an immediate $100 chip progression loss?
Well, it could happen. But 31 wins out of 32 tries is an overwhelming success rate I can count on.
If I employ virtual losses in some of the progressions, it has nothing to do with gambler's fallacy.
You insist that the success ratio 31:1 is valid.
Y would that ratio change if some of the bets are virtual? I don't see any reasoning for that.
But it makes a big difference in the risk.