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RESOURCE: Building a Bankroll - Supplemental Function RESOURCE: Building a Bankroll - Supplemental Function

01-23-2010 , 09:54 PM
Hey all,

Here is a neat equation / function that is meant to guide you to building a bankroll through giving you a sample bankroll day-by-day growth. Also I try to let you know just how to use the equation to maximize its benefits.

(SKIP BELOW DOTTED LINE IF YOU JUST WANT TO REVIEW THE EQUATION IN ACTION)

For the past week I've been trying to figure out a function that serves as a "success trendline" in building a bankroll from a small initial deposit to a large profit of around 20,000$. I find it extremely useful in conjunction with excel, because you can graph the function (along with your day-to-day bankroll) and use it as a kind of timeline to achieving your goal of turning, say 10$ into 20,000$. It tells you how much money you should earn each day to stay on progress to finishing your challenge however fast you choose (e.g., 365 days, 550 days, 730 days, 880 days, etc). Also, if you stick to the trend-line, then you are inherently following bankroll management principles.

Now, I'm a physics major, NOT a math major, so if this equation probably has its inaccuracies! But I've tested it to be very useful for building up to no higher than 25,000$. It basically works like an investment that accumulates interest.

It is of the form:

Ce^(kt) - B

C: This value effects the beginning stages of your project. The higher this number is, the faster you have to start off. Increase this number if you are going to be grinding the $0.25 games all day and want to blast through these micro limits ASAP.

e = the number e (2.711......)

k: This value is the growth rate. The larger this value, the faster you will need to build your bankroll. It is VERY sensitive to increases and decreases. For realistic cases, it should be between .0035 and .0075.

t = number of days progressed where you actually played (don't count days without poker)

B: Say you deposit 10$. And say you choose the value of C to be 800. Then B is 790. Basically, you make the value of "B" such that C - B = your initial bankroll.
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Here's the 'custom' equation that I am currently using. My goal is to convert 10$ into 20,000$ in 550 days:

946e^(.0057X) - 936

This equation basically means I start out with 10$ (C - B = 10; 946 - 936 = 10). It also means that I hit the ground running, so I need to go through the micro limits VERY fast. Here are the benchmarks:

-Day 0 (x = 0): 10$
-Day 1 (x = 1): $15.40
-Day 2 (x = 2): $20.80 [basically an increase of 5$ / day. Note this is quite fast for micro stakes; it almost makes it a requirement to multi-table for several hours / day]

-Day 16: $100.33
-Day 17: $106.26 [increasing about 6$/ day]

-Day 70: $473.85
-Day 80: $481.91 [increasing about 8$ / day]

-Day 126: 1000$ reached [increasing 12$ / day]

-1 year: $6640 [increasing $43 / day]

-Day 430: $10000 [increasing 63$ / day]

-Day 550: $20000 [increasing almost $124 / day]


If you think you could earn more, simply increase the k-value (only by a little). Or if you want more time, decrease the C value (and the k-value, if you think it is unrealistic where it is).

NOTE:
*If my bankroll goes above the trendline bankroll...
--cash it out
--spend it by taking a shot in a higher stake tournament
--combination of both (cashing out is probably best)

This way, you stay on the learning curve. If you win an MTT and just use 100% of it to your bankroll, then you will go way above the trendline. This means you might skip 2 or 3 levels (e.g., go from 5$ to 20$ Sit and Go's.) By doing this, you are missing out on the learning curve and you might have trouble at that new stake. Therefore it is highly recommended to just cash out the winnings and stay on track instead of trying to finish faster.

*If I get very far behind...
--Simply update the k-value of the equation until I am caught up. Then return it back to normal (if desired).

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For those who are embarking on any bankroll challenge I highly recommend plugging this function into excel along with your bankroll graph so that you can stay on task. It has been very useful for me so far.

HOW TO DO THIS IN EXCEL:

Column A: Day (1, 2, 3, 4 ...)
Column B: Bankroll Amt at end of the day
Column C: Plug in the equation as a function of A as follows:

STEP 1:
= C*EXP(k*A1) - B [see explaination on what those values would be]

STEP 2: Highlight the cell where you plugged in the equation. Then, hover your mouse to the bottom right corner. Click and drag all the way down the spreadsheet. Values where appear for every day you have written down.

NOTE: Where the A-column is empty, you will receive no value (or #VALUE!) for the C-cell.
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Comments/Questions/Ideas about the equation, or for help setting a custom equation to meet your goal...let me know! Remember the equation is NOT perfect but it is essentially accurate enough to be very helpful.
RESOURCE: Building a Bankroll - Supplemental Function Quote
01-23-2010 , 10:03 PM
Wow you sure did an impressive amount of math here.

I think an easier way to think of this is, How many Buyins do we need to play a given stake with an appropriate risk of ruin. Ok then what is our winrate at that level in terms of BB/hand. So then how many hands do we need for a double in our winrate, which would afford us to move up one double in stake. Then how much does our winrate decline for the next level.

So lets say we think we need 50 Buyins for our risk tolerance. And we are winning at 3BB /100 hands. Ok then we need to play 83k hands on average to move up one double of stake. How many hands can you play in your 550 days? to go 10$ to 20k, you might need 6 or 7 doubles.

Now you see the problem, way too many hands are going to be required. So we must need a far larger winrate, and perhaps also less buyins, greater risk of ruin.

I think one issue here is that no winning poker player wins every day. Setting a bar for yourself in terms of each days growth will probably serve to drive you insane in the long run. We should make our best decisions, and we will need to account for days with losses. We should focus on playing the appropriate stakes for our bankroll, and maximizing our hourly earn, while at the same time keeping a somewhat level head and realistic mindset towards the game. You will have long periods of losing results, even when you are a very strong winning player. A daily nut won't make it easier. The goal of turning 10 to 20k is an admirable one, but I think you need to be realistic. Your winrate WILL decline as you go up in stakes. You will need to double your roll 11 times in 550 days. That means doubling your roll every 50 days. Its certainly possible, but you will need to absorb a somewhat large risk of ruin in order to do so, and you will need to have a Great winrate in order to have a surmountable number of hands in each time period. I think setting a mark 40 days out to double your roll is a much better way of trying to reach your mark rather than focusign on a daily nut.

4Card

Last edited by 4CardStraight; 01-23-2010 at 10:14 PM.
RESOURCE: Building a Bankroll - Supplemental Function Quote

      
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