300 BB bankroll far too little???

I was looking at my statistics over my last 100 hours and noticed that twice I had losing streaks between 50 and 70 big bets, yet I was able to average about 1.8 bb/hr over this 100 hour period. This is my first 100 hour block of keeping statistics (I always used my br as a way of keeping statisics), and it made me think of some things, primarily that 300 bb bankroll is far too little.


When I computed my statistics(which I record every hour), I had 100 observations. My std deviation was 12.5 and my average was 1.8 bb/hr. I took my 100 observations, ranked them and wrote a small c program.


The program would randomly select a number between 0 and 99, index into my array of ranked wins/loses and accumulate a value. I figured this was a good way to simulate thousands of hours. Anyhow. I ran the simulation for 40,000 hours. I never let my bankroll grow beyond 300 big bets. My reasoning was, after 300 big bets I would spend the more(we do get to spend our winnings sometime, dont we?). Well, sure enough I went broke(not really fair to say broke, because I "spent" all money above 300 big bets) somewhere around 20k hands. In fact I went to -150, meaning my bankroll took a 450 big bet hit. This frightened me. My question is this...


Could my 100 hour statistics be abnormal and this simulation be unrealistic?


Could a 300 big bet bankroll be easily defeated if you are a winning player?


Does anyone else see these random beatings of 50+ big bets and still show a profit? Anyone see more than 1 per 100 hours regularly?


On a side note, a ran the simulation a second time using a perfect normal distribution centered on 1.2 bb/hr with a standard deviation of 10 and got the same results(a 300 bb bankroll was exhausted at some point over 100,000 hands this time).


-J

You are spending all of your winnings so of course you will go broke. Anything you spend goes against your winnings per hour, so you are playing an even money game with a 300 bb bankroll.

Whats the point of playing if you are not going to spend your winnings at some point? I have always heard that 300 big bets is a big enough insulation to take care of the inevitable tough run of cards you will run into, but upon my investigation, 300bb looks a little small. The only way I could see 300 BB its if you have a point where you switch to a lower limit to recoup. Just wondering where the 300 bb bankroll came from and wondering if someone has proven it statistically.

In REAL LIFE, ring games 300 big bets is not "insulation", against busting out. I have no knowledge of "simulations". However, in a real game scenario, you lose in increments, or "chunks". You make some comebacks, but those losing "increments" overtake that 300 big bets. After that, just look forward to getting ahead 150, 200 big bets, and your back on track to make some money. Basically, after losing 300 big bets, it's time to take off, and reflect on your game, your emotions, and where you have been playing.

With your hourly rate and standard deviation, 300 bb would allow you to play forever with less than a 0.1% chance of ever going broke, but this is based on never spending anything.


[(1-1.8/12.5)/(1+1.8/12.5)]^(300/12.5) = .001


If you always spend 1.8 bb/hr, then you have an hourly rate of 0, and you will go broke with a probability of 100%, though it may take a very long time. You could spend .8 bb/hr and you would still have a risk of ruin of 2%. If you only spend what you make in excess of 300 bb, then it still depends on your average net win per hour after spending, which I suspect should be close to 0 since you would normally be above 300 if you didn't spend.

BTW, don't think that losing 300 bets is anywhere near as likely as losing 70 bets. If losing 300 bets is 0.1%, losing 70 bets is

.001^(70/200) = 20% or 200 times less likely. If you lose 70 bets once in 100 hours, you will not lose 300 bets for 20,000 hours.

Make that .001^(70/300) = 20% or 200 times MORE likely. Gotta stop responding to my own posts...

Statistically you can calculate the bankroll you will need given your win rate and std deviation. You can use a 99% or 99.99% confidence interval to find out exactly how big your bankroll must be to insure you don't go broke. This information can be found in many books and is clearly and easily explained in Lou Krieger's Book Serious Poker.

I don't know how Lou Krieger does it, but if he uses the term "confidence interval", then I'm suspicious that he might be doing it wrong. It is a common mistake to say that because being broke represents a certain number of standard deviations below the mean after a certain number of hours, that this is your risk of ruin. The reason is that you can go broke before you ever reach this number of hours. This is not the way to do risk of ruin calculations. Use this formula to compute risk of ruin for a given bankroll:


r = [(1-u/sigma)/(1+u/sigma)]^(B/sigma)


u is hourly rate

sigma is hourly standard deviation

B is bankroll


This is correct, and comes from "Blackjack Attack" by Don Schlesinger. To get bankroll for a given risk of ruin, you can invert this equation or use:


B = [-sigma^2/(2B)]ln(r)

>u is hourly rate

>sigma is hourly standard deviation

>B is bankroll

> [snip]

> B = [-sigma^2/(2B)]ln(r)


I think you mean


B = [-sigma^2/(2u)]ln(r)