Casino

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)

Originally posted by metbierop

7) Who is the first to answer all questions correct?

PBJ6 . . . edit: I mean PBE6

Originally posted by Coconut
PBJ6 . . . edit: I mean PBE6

7) No one! 😏😏😏

Originally posted by Coconut
PBJ6 . . . edit: I mean PBE6

Awesome, I've become the nerd on call. 😳

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.