Roll of the dice simulation
I have 3 dice and a $1 wager. I roll the first dice. Whatever the result, I want to roll the second dice such that it is lower than the first. So, if I roll a 3 on the first dice, I want to roll a 1 or a 2 on the second dice. If I'm successful, I get a 50% return on my money. So if I wagered $1, I get $1.50 back. I can stop there or continue with the third dice which I also want to roll lower than the first. If I'm successful, I double my wager, so my $1 becomes $2. If I'm unsuccessful on either the second or third roll, I lose my $1 wager. What are the mathematically expressions for combinations (ie "choose") that show all probabilities for this simulation.