Alright I am tired of reading this one page, I just created a part 2 so I'm not exhausted reading one page.
Here I am going to start figuring out the formula for the first part
First part: Calculate probability of losing the martingale
To create asymettry, I am going to say that the chance I win is 40%. The chance I lose is 60%.
If I bet for one dollar, I will have a 40% chance of winning a dollar, thereby ending the bet. I call it Pw
If I have the same bet, and I win, 60% chance of losing, thereby making me double the bet next time, I call it Pl
Now, in this case I have three numbers: 40% and 1 dollar and 1 dollar. In this case, I am risking 1 dollar, to gain 1 dollar, I have a 40% chance to win.
This can be (Pw, Dr, Dg). Probability winning, dollars risked, and dollars gained.
If, however, I increase my risk to 2 dollars, I effectively increase my probability of winning.
THe probability of winning = 100% - the probability of losing
The probability of winning = 100% - (60%)^2
The probability of winning = 100% - 36%
Probability winning = 64%
Now my numbers are (64%, 2, 1)
If we do it again, we get (78%, 4, 1)
Let's make a formula. Let's call it Pw = 1 - (60%)^(log2(Dr)+1)
But where does the dollars gained go into this process? I have only assumed that the game "ends" when I gain one dollar. In order to win multiple dollars, I must repeat the process
Pw = (1 - (60%)^(log2(Dr)+1)^Dg
Going to make a python script with that equation

Let's plot this! But how do we choose to graph it? I don't currently know how to plot in 3D, so I will have the dollars_risked stay constant. Let's keep it at 128

So now we have our graph. It looks like if we want an 80% chance of winning, we will win a little less than 20 dollars, which makes sense in terms of expected value. The percentage that you are certain is balanced out by how little you actually gain.
So this is the reality, but what is my expectation?? I know that I personally like to risk a little more if it can spell better amount, but when does it start decreasing??
In my mind I think of something like this:

This is what I imagine my risk to look like. I'm slowly willing to decrease my risk percentage as I win more money, but not too much. I just picked a random negative exponential function until it looked comfortable with what I would hypothetically bet
Looks good to me, I mean I feel good about this risk graph, so it's fine
Let's figure out where this overlaps
I created a graph, and...it looks like the optimal amount I can gain is 0 dollars..with a 100% probability.

Every other type of bet is too risky for me and the curve dips way lower than I want to. The only way to win this bet is to not bet at all..