Aaron, thanks a lot for your help here. I also considered running a simulation, but then I couldn't think of how to test the cases of the additional rules in terms of beating the game and devising a strategy about when to double if you are permitted. I guess I could try two possible options: doubling whenever the hand is a favourite and doubling only when the hand is better than 50%.

Would you be able to post/send me your code so I can make some modifications as necessary? Thanks!