[Zetack]

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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?

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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