# Mathematical Challenging Question :O

#### Ezrolith

##### Dormant account
Hi,

Was wondering if anyone could help me out with something i've been wondering. We're playing BlackJack, to make matters the simple, the house edge is 0%, so you've got a 50% chance to go up or down if you don't include draws. Lets ignore things like BJ, and just say you've got an equal chance to increase or decrease by say 1. You have a starting balance of 100. The questions are:

What are the odds of increasing by 10.
What are the odds of losing 100.

These aern't as simple questions as they seem, I am a degree maths student and can't figure it out easily. Best way to do it would probably be to have done loads of simulations or be really smart - or I could just be missing something

Any help would be appreciated.

Thank you,
Peter.

Doh, after thinking about it for another 10 minutes i've concluded you've got 10x more chance of losing 100 as winning 10. I'll save the complex mathematics

Ezrolith said:
Doh, after thinking about it for another 10 minutes i've concluded you've got 10x more chance of losing 100 as winning 10. I'll save the complex mathematics
Huh? How did you come to this conclusion? I recommend you find a good book on probability (like Feller) and look for "symmetric random walk" in the index.

Btw, the probability of losing all your money is 1 if you play long enough, even though it is a fair game. The probability of winning 10 before you lose 100 is 10/11.

Ezrolith said:
Hi,

Was wondering if anyone could help me out with something i've been wondering. We're playing BlackJack, to make matters the simple, the house edge is 0%, so you've got a 50% chance to go up or down if you don't include draws. Lets ignore things like BJ, and just say you've got an equal chance to increase or decrease by say 1. You have a starting balance of 100. The questions are:
What are the odds of increasing by 10.
What are the odds of losing 100.
How many hands are you going to play? Without this information I doubt your question is rather meaningless.
When I calculate the risk of ruin, normally I'd use the total hands that a player can play in a life time.
Just on top of my head. The more hands you play, the more likely you will win/loose 100 units or more. Eventually it will be close to 50% to loose all of your 100 units or more.
The chance of gaining x units (be it 10 or 100, just no zero) exactly will increase initially, then decrease as the sample get larger.
The chance of breaking even will always decrease with the size of the sample.

Ezrolith said:
What are the odds of losing 100.

Sounds to me you are really flipping a coin.

I think your chances of losing your 100-unit bankroll, if you were to play a maximum of 10,000 hands, would be almost 32%.

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