BR disagreement/fallacy

[Oblivious]

Surely you arent arguing that there is no such thing as a 500bb downswing for winning players.

If we assume the probability distribution for streaks to be gaussian (a bell curve), we would see that the more extreme winning or losing streaks would be less probable. This probability distribution would be defined for all streaks, no matter how large. So if you play long enough, you will eventually encounter a losing streak of 500bb, 1000bb, and even 10000bb. Mind you, "long enough" might require hundreds of thousands of years... most of our careers dont last that long.

The fact that you brought up the qualification of "winning player" is strange to me. Even losing players have very large rushes upward. I agree with you that a winning player, starting with 500bb, would most likely never go broke if his earnings were added to his bankroll. This isnt the case for a losing player. But if a winning player starts a career with 500bb, and withdrawls money such that his bankroll is never over 500bb, he will eventually go broke provided his career is long enough.

Somewhere, the idea of convergence should be included in this argument, but Ive become a bit rusty since my course in Analysis.

[MicroBob]

I know it's more common in 6-max...but that's what I've been playing these days.

In the HUSH forum there was a thread where SEVERAL players posted their 300BB down-swings (and some were much larger than this).

Most were established winners.

Sthief said almost exactly what I was going to say.

If you have a 2% chance of a 300BB down-swing...then there is also a chance of catching those down-swings back to back.

It's exactly the same as losing to a 1-outer on consecutive hands.
If you play enough it will happen eventually.


Also - after the first 200-300BB's of your bankroll vanish you are CORRECT that you need to consider whether you are a winning player in the first place.
It is a big blow to one's confidence.
No matter how much you KNOW that such downswings CAN and WILL happen it also should occur to you that you are NOT playing winning poker anymore and that you have somehow developed some leaks into your game or just aren't concentrating appropraitely.

Stepping back in limits is an okay way to regain one's confidence, re-evaluate their game, AND protect one's bankroll when you start to get a little bit shorter than you are comfortable with.

[SCfuji]

you dont know how much of me wishes you were right.

[john kane]

the original poster has exactly the same thoughts as me. i agree with him.

you do not have 500BB if you are never going to use 300BB at the same level. you have 200BB at say 10-20 and 600BB at 5-10. That is the way you should be viewing your bankroll if you are going to move down limits when you lose 200BB of your 500BB. you are never going to be playing with the remaining 300BB at 10-20 so it is pointless viewing it as such.
Instead you should always be viewing your current level as risk money (in this example 200BB at 10-20) and if you lose it you can then drop down to 600BB at 5-10.

if you are saying you are going to move down whenever you lose a set amount, you do not have a bankroll, merely you are slowing the swings you experience.

for example, you could easily have a bankroll of $200 and play 2-4, ie 50BB. if you drop to $100 you move down to $1-2, if you drop again to $50 you play at $0.50-$1.

here you are playing with a 50BB bankroll and have a 0% risk of ruin as you will always have a bankroll. The reason for having such a large bankroll say 500BB is so you dont have to move down limits and constantly have swings, you want to be playing a set limit until you have won enough to move up.

players should either have a 50BB limit or a 1000BB limit imo. the 50BB bankroll means you are constantly going up and down, but have a 0% risk of ruin, the 1000BB means you never have to move down limit and can slowly progress.

[AustinDoug]

Was this bankroll strategy what led to the following post:

[ QUOTE ]
Since I'm taking a well needed break from playing poker, I am watching instead. What table limits are you watching and what are you looking for in the play of hands that might help your game?


[/ QUOTE ]

No, I'm back in school(changing careers)and I can't do well in school playing poker. I rather play poker instead so I'm taking a break in order to keep up with school. Was playing 20k hands/month this year. Been playing poker for many years now.

[ QUOTE ]
Surely you arent arguing that there is no such thing as a 500bb downswing for winning players.


Actually I was, sorry I assumed this. With that said, how in the world can anyone be a winning player then with that kind of losing streak(s)???


If we assume the probability distribution for streaks to be gaussian (a bell curve), we would see that the more extreme winning or losing streaks would be less probable. This probability distribution would be defined for all streaks, no matter how large. So if you play long enough, you will eventually encounter a losing streak of 500bb, 1000bb, and even 10000bb. Mind you, "long enough" might require hundreds of thousands of years... most of our careers dont last that long.


Now we're getting deep.


The fact that you brought up the qualification of "winning player" is strange to me. Even losing players have very large rushes upward. I agree with you that a winning player, starting with 500bb, would most likely never go broke if his earnings were added to his bankroll. This isnt the case for a losing player. But if a winning player starts a career with 500bb, and withdrawls money such that his bankroll is never over 500bb, he will eventually go broke provided his career is long enough.


Why is it strange? I made the statement to fit the BR for never going broke. If your comfortable at a level and making good money, why not cash out down to your BR limit? Isn't that the whole idea? I'm not saying your BR is your life savings, sorry if you thought that.


Somewhere, the idea of convergence should be included in this argument, but Ive become a bit rusty since my course in Analysis.

[/ QUOTE ]

[AustinDoug]

If there was internet poker when I went through school I would have never graduated.

Yeah, it's horrible, I love poker. Even being a railbird takes up time but at least I don't have to stress about anything.

[Zetack]

[ QUOTE ]
I hear from everyone if your BR gets too low then it's time to play lower stakes. I disagree with this "if your at least a break even player or better". Here is why, you have a BR of 500BB, with that kind of player and BR means you should never go broke, EVER! This will handle any and all variances in your game. So what if you get down even 200BB, you have the BR for that reason and you will get even again. IMO if one has to play lower stakes then they were never a break even player at the stakes in the first place. Can someone explain to me why this wrong?

[/ QUOTE ]

You are confusing two concepts, I think. The first is that our results over time are an accumulation of a number of independent events. Over a long enough time, if we have a true winrate then we can can predict with very good accuracy what our results will be.

In this respect, if you could keep playing at the same limit no matter what happened to your bankroll (i.e you could loan money interest free to your bankroll) you would never move down if you were a winning player because even if your bankroll moved into the negative numbers eventually it would move up into positive numbers. Of course for most of us, our bankroll really is our bankroll and we can't just add to it at will.

The second concept that you need to follow here, is that each hand is completely independent of every other. Likewise your future performance is completely independent of your past results.

What does this mean? It means that there is absolutely no difference from a future results standpoint between starting out with a 200 BB bankroll and having a bankroll that used to be 500 BB's but has shrunk to 200 BB's because of a vicious losing streak.

Lets say that you have two a winning player with a "true" winrate of 1.5 BB/100 and a SD of 16. With a 200 BB bankroll you can calculate the risk of ruin for both those players. And it will be exactly the same. If player A just scrounged together 200 BB's from outside sources and that's his starting Bankroll, and Player B used to have 500 BB's and has lost 300 BB's, it makes no difference. Their risk of ruin is exactly the same.


Assuming that each player is risk averse to exactly the osexactly the same degree, if the risk of ruin is too high for Player A, it will be too High for player B. Both of them should move to a lower limit.

I see what you want to say. Player B has just suffered a terrible run, losing 300 BB's. For him to go broke he will have to have suffered a 500 BB losing streak and for a winning player that's such a tremendously unlikely streak that it doesn't make sense for him to drop down.

Unfortunately, it just doesn't work that way. At 200 BB's he isn't somehow magically protected from dropping another 200 BB's just because he's lost 300 BB's. His risk of ruin is exactly the same as any other player with his winrate and standard deviation and CURRENT bankroll. Your future results are completely independent of past results.

Lets look at it another way, since you want to look at the overall accumulation of independent results (hands). Which player is more likely to have a 500 BB losing streak--The winning player with a 500 BB bankroll, or the player with the exact same wr and sd who has just dropped 300 BB's?

Looked at one more way. What is the liklihood that a player with a certain winrate and sd who has just gone on a 300 BB losing streak, will now immediately go on a 200 BB losing streak? It is exactly the same at that moment as at any other given point in his poker playing carreer. It has exactly the same liklihood as it would if you choose a point where he's just gone on a 1000BB heater, or a 20,000 hand breakeven streak, or whatever.

If you agree that it is possible for a winning player to have a 200 BB downswing, and if you further agree that 200 BB's is thus too small a Bankroll to start playing a given limit, then it follows necessarily that it is to small a bankroll for a player to continue to play that limit, no matter what their immediately preceeding results have been, including a 300 BB downswing.

Ok, one last crack at it. Because your future results are independent of your past results, there is simply no difference between a five hundred BB downsing and five 100 BB downswings back to back to back to back to back. I hope you agree that even great players can have 100 BB downswings.

--Zetack