Poker blind interest equation

Question

I'm trying to find the equation that will calculate my blinds for me based on number of players and target length of a tournament. I have most of it. I'm only missing one part.

Given a starting blind and the blind at the target end time, I need an equation that will tell me what percentage the blinds should go up each level.

I need to input 1) the starting blind 2) the ending blind, and 3) the number of levels and get back the percent increase.

For example, if I start with a big blind of 50 chips and I want to end with a big blind of 4300 chips at the three hour mark, with 20 minute levels (that's a total of 9 increases), I can play around in Excel and by trial and error I know that if I increase the blind by 0.65 each time, I will arrive at my target big blind of 4300.

I realize that this is an interest rate problem.

What I need the equation that will get that interest rate given a starting value, ending value and number of interest periods.

(I realize that this should be a simple problem, but I'm a computer programmer, not a mathematician. Feel free to mock me.)

Thanks in advance.

Answer 1

There shall be no mocking here.

Say you start with $a$ blinds and after $n$ (exponential) increases end up with $b$. Then there is some constant $C$ so that

$$b = a \cdot C^n$$

Solving for $C$ gives

$$C = \left(\frac{b}{a}\right)^{\frac{1}{n}}$$

Meaning: At each step, the new big blind is the earlier big blind multiplied by $C$.

Your example: Here, initial big blind is $a=50$ and ends up with $b=4300$ after $n=10$ increases.

$$C = \left(\frac{4300}{50}\right)^{\frac{1}{10}} \approx 1.56$$

($1.56$ means an increase of $56 \%$)

Answer 2

@naslundx fully explains the interest equation and how to change it to isolate C. So, read his answer if you want to fully understand the concept.

Here I'll provide the answer I was looking for in the simplest terms.

If these are the variables:

a : The starting big blind

b : The ending big blind

n : The number of blind increases. So, if there are 10 blind levels including the first blind, then there are 9 blind increases.

C : the percentage that the big blind needs to increase each level in order to start at a, and arrive at b after n increases.

Like @naslundx said, the equation is this:

$$ \Large C=\left(\frac ba\right)^{\left(\frac1n\right)} $$

(I just wanted to repost it explaining where the variables each come from so if somebody comes along and just wants the answer–and not the theory behind it–they can grab it here)