Since I was redirected (by you
) to this thread, I'll repeat my question here.
Is it possible to know exactly how big your highest bet during the whole experiment was?
With that information
1. I would estimate the minimum bankroll needed for your strategy to work
Bankroll as such is irrelevant
What you need is the capacity to endure a long enough losing streak for a given multiplier. Which means, you need a big enough
bankroll. So, it's not irrelevant actually
It is irrelevant as long as your base bet can be any. In other words, "a big enough bankroll" is only as big as you base bet is. Put shortly, "big" is relative here, and depends on very specific parameters
For example, at ~40% win chance it is pretty much a safe bet if you can survive 35 losing rolls in a row. If I remember correctly, at 37% win chance I've seen a losing streak of 30 rolls only once.
That would result in a pretty big final bet
Your "final" bet will always be half of your balance (or something to that tune), when you stake all of what is left. Indeed, I calculated the rolls in such a way that I would be able to win back everything with this last all-or-nothing roll and earn as much (actually, more as my win chance was below 50%)
I have no explanation how it is ever possible, but winning chances below 37% bring about an exponential surge in variance, and martingale no longer remains safe. I can't come up with any plausible reason for this phenomenon but I've read about it before and can confirm it (call it broscience or a gambling street wisdom of sorts, or whatever)
I think it's simply a question of proper adjustment. If you lowered your "increase on loss" exactly in accordance with how the win chance was lowered, your strategy would work just fine
Without any additional info, proper adjustment assumes linear change. This is not what I observed. If variance changes abruptly (like spikes exponentially), and you don't know by how much exactly, there is no way to lower the increase on loss that would match this spike. Finding it out empirically would probably mean busting in the process