For example, if the deck has 26 red cards on top, you'd end up dwindling your initial $1.00 stake to 0.000000134 before riding it back up to 9.08
This is what most people discover, you need to play like every toss of the coin(i.e tosses over a very long periods of time). In series, like the whole strategy for it to work as is. You can't miss a toss. If you do you basically are missing out on either series of profitable tosses, or that one toss where you make a good return. If you draw the price vs time chart, like a renko chart you pretty much see a how any chart for any instrument would look.
Here is the catch. In the real world stock/crypto/forex trading scenario that means you basically have to take nearly trade. Other wise the strategy doesn't work as good.
The deal about tossing coins to conduct this experiment is you don't change the coin during the experiment. You don't skip tosses, you don't change anything at all. While you are trading all this means- You can't change the stock that you are trading(Else you would be missing those phases where the instruments perform well, and will likely keep landing into situations with other instruments where its performing bad), you can't miss trades, and of course you have to keep at these for very long periods of time to work.
Needless to say this is not for insanely consistent. Doing this day after day can also be draining on your mental and physical health, where there is money there is stress. You can't do this for long basically.
A person tosses a coin, so tosses are are connected to each other.
Ask yourself this question- Would your thumb hurt if you toss a coin 5000 times? If so, would that change the results?
https://www.stat.berkeley.edu/~aldous/157/Papers/diaconis_co...
The paper does discuss coins allowed to land on a hard surface; it is clear that this will affect the randomness, but not clear if it increases or decreases randomness, and suggests further research is needed.