John goes to the casino every day of his life. Except for his birthday (the day after tomorrow) Starting today.
With the exception of his casino-visits. His normal life income equals his expenditure exactly.
John has $100.000,00 of cash.
Every time John visits the Casino he only plays Dutch Bacarat. In this game you have a 50% chance of winning and 50% of losing (draws are excluded).
The minimum stake is $ 5,00
The maximum stake is $ 4.000,00
John wil bet $5,00 unless he lost 2 or more games in a row. After losing 2 games he wil double to $10, if he loses the third game in a row he wil double to $20, etc etc untill he is not able to double anymore. If he loses his final double he will go back to the minimum stake.
From mon-fri John plays 200 games a day if he loses game #200 he wil play another game and so on until he wins the final game of the day.
Every Saturday John plays 196 games a day if he loses game #196 he wil then play another game and so on until he wins the final game of the day.
Every Sunday John plays 271 games a day if he loses game #271 he wil then play another game and so on until he wins the final game of the day.
As soon as John L. reaches $1.100.000,00 of cash he wil immediatly stop going to the Casino. As soon as John L. reaches $ 0,00 he stops going to the casino. (duh)
Questions:
1)after a time period of 1 day:
a- What is the chance for John of having more then $100.000,00
b- What is the chance for John of having less then $100.000,00
2)after a time period of 1 week:
a- What is the chance for John of having more then $100.000,00
b- What is the chance for John of having less then $100.000,00
3)after a time period of 1 month:
a- What is the chance for John of having more then $100.000,00
b- What is the chance for John of having less then $100.000,00
4)after a time period of 1 year:
a- What is the chance for John of having more then $100.000,00
b- What is the chance for John of having less then $100.000,00
5)after a time period of 1 year:
a- What is the chance for John of having more then $100.000,00
b- What is the chance for John of having less then $100.000,00
6)after a time period of 10 year:
a- What is the chance for John of having $ 1.100.000,00?
b- What is the chance for John of having more then $100.000,00?
c- What is the chance for John of having exactly $100.000,00?
d- What is the chance for John of having less then $100.000,00?
e- What is the chance for John of having $ 0,00?
7) Who is the first to answer all questions correct?
-EDIT- question 6a)
I wouldn't attempt to answer ALL those questions, but as for 6a) : I think the chance is almost zero. He will lose in the long run because of the double-up system. He can only double 9 times. Whenever he loses 11 games in a row he will lose >$5000.00. This will happen aproximately once in every 4096 games. He will win 11 straight with same frequency but then only wins $55.