I have a question regarding probability.
Lets assume that roulette has just red and black, no green and an equal amount of both.
Lets also assume we start each game with a bet of 1 dollar. We also have enough dollars to be able to double our bet up to 40 times.
Now an example game is we bet our 1 dollar on black. If we lose we bet 2 dollars on black, the total expenditure is now 3 dollars. If we lose again we bet 4 dollars on black, the total expenditure is now 7 dollars.
If we win we get 8 dollars back. 1 of which is a profit.
Remember we can lose 40 times in a row before we cannot double up any longer.
The odds of getting 2 reds in a row is 25% so getting 40 reds in a row would be very low.
My question is what is the probability of making a profit after one entire game ( a game is where you keep doubling until you can or you profit)
and after 1000 games.