Congratulations on the new addition to your family and thank you for the well put together statistics. so I guess the rule of thumb is to go big or go home.
Thank you. Is there anything else i can code for you? For now the best strategy other than single bet was martingale with tripling instead of doubling (much more agressive martingale).
Using math you can also prove that some strategies are actually slightly better than others
Yes, but brute force simulation is easier to do and easier to explain to others.I believe one sequence of martingale gives you better odds than 1 single bet. For example if you have 1 BTC, it's better to split it in a few smaller amounts and bet using martingale, I don't remember exactly how you had to split it in order to have a better chance.
Some people believe in flat earth 
Rule is simple. The bigger your trading volume is the more money is sucked by hose edge and the closer you get to statistic distribution. Find your strategy and bring here.