Hey all, I am trying to create a project which involves extensive amounts of statistics. The project is in relation to blackjack at a casino and the odds of winning.

Here is the situation:
I want to create a new blackjack betting pattern that will allow the player to almost be monetarily successful 100% of the time at every casino outing. The method is to bet a certain sum of money and everytime you win put the profit aside, while every time you lose bet double in the following bet. For example if my set bet was 15, I bet 15 on the first hand and win. I set 15 aside and put the bet of 15 back in my original sum of money. If I lose, I would then bet 30 on the next bet. If I lose again I would then bet 60, then 120, then 240, and so on if I keep losing. This betting pattern would make it so after every win I would have a payout of $15 more than I started with. After I win the hand, I would always go back down to the $15 bet and do it again.

Here is some statistics that I have already solved that would aid in this problem:
Overall chance of winning a black jack hand: 47.05% (Average player, obviously if the player was more advanced, it would be higher.)

Chance of winning at least once in the following hands:
1 hand- 47.05%
2 hands- 71.96%
3 hands- 85.15%
4 hands-92.14%
5 hands-95.84%
6 hands- 97.8%
7 hands-98.83%
8 hands-99.38%
9 hands-99.67%
10 hands-99.83%

As shown above, evidence from the probabilities show that this betting pattern seems like it would be successful, if you believe otherwise please explain because I may have some confusion.

Now, this is where I need the help. I am a freshman in college and absolutely don’t have enough knowledge in statistics to solve this. What I want to create is a formula that tells how much money a person should have, based on the betting pattern above (doubling it every time you lose), a starting sum of money (ex. $1000), a base bet price (in this case $15), and a certain number of bets (ex. 100).

Basically, I’m trying to create a formula where you can plug in:
*The starting sum of money (money you originally bring to the table)*
*Base bet amount (how much you will start the betting at)*
*Amount of bets (how many times in total you will bet)*

To find an amount, based on the probabilities above and the betting patterns, that would be how much a person will have after a certain number of hands, by using a certain base bet, having a certain starting sum of money, and following the betting patterns above.

I don’t even know i this is possible, (it seems so) but I know it’s a real complex problem with a lot of steps. Any and all help is greatly appreciated. THANKS