/sci/ - Science & Math

Simple statistics & probability question:

Let's say that I'm playing a dice game. I have to choose a number between 0 and 99 and bet on the lucky number being higher or lower than the number I chose.

If I lose, the next bet will be increased by a percentage until I either win or run out of balance.

How do I calculate the probability of running out of balance (the amount that I would have to bet is higher than the balance itself)?

e.g

Betting that the lucky number is going to be less than 5. What's the probability of losing the total balance of $3.000.000, if my initial bet is $50 and each time I lose the bet gets increased by 5.84%

Betting that the lucky number is going to be more than 24. What's the probability of losing the total balance of $3.000.000, if my initial bet is $250 and each time I lose the bet gets increased by 300%

Which is more risky? This one I can tell just by calculating the probability of running out of balance.

Any help will be appreciated. I got stuck trying to make a probability-of-getting-rekt calculator and Google isn't helping. I can calculate the number of times that it takes to run out of balance but got stuck on getting the probability itself, I know it's a very basic question.

Simple statistics & probability question:

Let's say that I'm playing a dice game. I have to choose a number between 0 and 99 and bet on the lucky number being higher or lower than the number I chose.

If I lose, the next bet will be increased by a percentage until I either win or run out of balance.

How do I calculate the probability of running out of balance (the amount that I would have to bet is higher than the balance itself)?

e.g

Betting that the lucky number is going to be less than 5. What's the probability of losing the total balance of $3.000.000, if my initial bet is $50 and each time I lose the bet gets increased by 5.84%

Betting that the lucky number is going to be more than 24. What's the probability of losing the total balance of $3.000.000, if my initial bet is $250 and each time I lose the bet gets increased by 300%

Which is more risky? This one I can tell just by calculating the probability of running out of balance.

Any help will be appreciated. I got stuck trying to make a probability-of-getting-rekt calculator and Google isn't helping. I can calculate the number of times that it takes to run out of balance but got stuck on getting the probability itself, I know it's a very basic question.