Bankroll Considerations
 

I'm just trying to seek confirmation on this.

Wonder if there is more to the picture. I think an example might illustrate my question better.

Lets say I place a bet 'b' on a game repeatedly.

And as per my average returns and variance(unknown at this stage), I have somehow magically determined that an appropriate bankroll for this kind of venture is 'BR'

However I dont have enough money to meet the bankroll requirement.(Again meeting the bankroll requirement is a pretty hazy term in itself). But hopefully we can take it at face value. And assume that it is a meaningful statement. Lets say, its something that gives me a 99% chance of not going broke ever.


Anyway my dilemna is that I only have an amount X, which is below BR

However I decide to take a chance that I wont go broke before I can turn a profit and decide to gamble anyway.

A few fine days later, I have managed to turn a profit and I now have the exact amount to meet the bankroll requirement.

Can I now feel better, assuming that I'm safe, as if I never played that game before and am making a fresh start with the appropriate bankroll.

Does the fact that I have had good days not mean that I'm probably going to have bad days soon, which would mean that I cannot really feel safe?

Now if we replace this "game" with
a) SNGs
a) Ring game at $blah buyin

etc etc

Does the independence of the result of each bet still hold??
Is independence a safe assumption, or are there reasons to believe there might be corelation.

Also assuming that I started with X, what is the probability that I bust out before I reach BR?

Re: Bankroll Considerations
 

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Can I now feel better, assuming that I'm safe, as if I never played that game before and am making a fresh start with the appropriate bankroll.

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Yes

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Does the fact that I have had good days not mean that I'm probably going to have bad days soon, which would mean that I cannot really feel safe?

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No. Past results do not influence future ones (except for psychological implication in games with decisions played against other humans. e.g. the fact that you have been running hot may cause your opponents to fear you and play worse.)

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Does the independence of the result of each bet still hold??
Is independence a safe assumption, or are there reasons to believe there might be corelation.



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Yes. Again, the only reason past results will influence the future is from a psychological standpoint. Another for instance, you may loosen up if you have been winning or an opponent may adjust to your style of play once he has played several hands against you. But as far as chance goes, every hand is independant.

Re: Bankroll Considerations
 

Thank You for the confirmation.

Now for the underlying question. When we try to fit the slightly more complex games, where external factors, including psychological and many others like people ajusting to you, or you adjusting to people bla bla
to this Normal distribution model, how far are we from the truth.

Have there been any empirical studies that suggest that the events are indeed IID?

Re: Bankroll Considerations
 

When your chance of going broke is calculated, an event that your bankroll will immediately go down and never reach a higher value has a certain probability. If this event happens, your chance of going broke increases. If the opposite happens, and your bankroll goes up, your chance of getting broke decreases.

Re: Bankroll Considerations
 

This OP is amusing in the way that he uses terms and jargon to imply that he has at least some minimal understanding of statistics and probability, then proceeds to type this:

"Does the fact that I have had good days not mean that I'm probably going to have bad days soon, which would mean that I cannot really feel safe?"

Yeah, man, you're DUE for some poor results.

I mean, if you need to ask a question like that, you'd better not be playing poker until you KNOW the answer. And not just think you know it, but really UNDERSTAND the answer. I hate to flame a guy for asking a question, but there's just something about the way this one was asked that struck me as ridiculous.

-w.a.

Re: Bankroll Considerations
 

The safe bankroll calculations assume averaged values for win rate and standard deviation and have no other parameters (besides bankroll safety factor), they cannot explicitly take into account an event such as people starting to play better against you as time goes on. One could probably guess a winrate as a more interesting function of time than a flat average, and do some complicated analysis. If one has a very very large database, one could analyze winrate vs average table VP$IP, table AF, table players to date number of hands against you, and many others. One could possibly extract some correlations, but it would be very complicated.
Certainly not a one line equation popular on these forums.

Re: Bankroll Considerations
 

If you want to eventually apply this to poker as opposed to coinflips that pay 1.1 to 1, you need to keep a couple of important things in mind there bro:

1)If you are not a winning player against your current set of opponents, your bankroll will never be large enough to protect you from going broke.

2)your winrate and standard deviation (from wich your risk of ruin and consequently your requisite bankroll requirements are derived) are statistics that will constantly be in flux as you go through the various stages of learning the game of poker.

Your winrate will go up as you plug various leaks and learn to value bet in the appropriate places and it will go down as you take on tougher opponents, tilt, and go though downswings.

Your SD will also move around as you adjust your game to your own knowledge, your differing opponents, your leaks, and your aggressiveness.

Since bankroll requirement calculations assume static winrate, sd, and bet sizes - your game and your opponents must become pretty consistent for this question to even relate to poker.

Here's my advice:

Start out at low limits, read, play, and learn the game until you can beat that limit and those opponents well enough to move up.

Take a few stabs at moving up before committing to a higher limit entirely.

Don't be afraid to move back down if your bankroll takes some serious hits due to better opponents/tilts/downswings.

rinse & repeat.

Remember: If you are not a winning player against your current set of opponents, your bankroll will never be large enough to protect you from going broke.

Re: Bankroll Considerations
 

Well that might have been uncalled for, but I'll accept your criticism.

I understand independence. I'm a CS buy with a decent mathematical background
What I was really trying to question was the independence assumption, and if it really holds. I wish I had used less jargon to come off as a rookie, and atleast get your sympathy [img]/images/graemlins/smile.gif[/img]

The question is just play with words to pose the question to a layman. I think you took it to literally. And if your answer is a blanket, it doesnt matter, you have blindly assumed the independence of events.

I'm just trying to question that, and was wondering if there is any similar situation, where such literature was already available, and could lead to more insightful answer to the puzzle.

Re: Bankroll Considerations
 

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The safe bankroll calculations assume averaged values for win rate and standard deviation and have no other parameters (besides bankroll safety factor), they cannot explicitly take into account an event such as people starting to play better against you as time goes on. One could probably guess a winrate as a more interesting function of time than a flat average, and do some complicated analysis. If one has a very very large database, one could analyze winrate vs average table VP$IP, table AF, table players to date number of hands against you, and many others. One could possibly extract some correlations, but it would be very complicated.
Certainly not a one line equation popular on these forums.

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Thank you for the reply.

I am not very familiar with the body of literature out there, and was hoping someone could point to another situation which is similar to the one we face here.

for example that we assume that the average expected pay off on the bet is a function of time t. Now is there a similar situation, possibly somewhere in economics.

I'm not looking for closed form solutions to the problem(which is admittedly complex), but certainly interesting insights that can be drawn by comparing two different situations.

I wouldnt mind reading a bunch of papers, only if someone can point the right resources.

Re: Bankroll Considerations
 

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If you want to eventually apply this to poker as opposed to coinflips that pay 1.1 to 1, you need to keep a couple of important things in mind there bro:

Remember: If you are not a winning player against your current set of opponents, your bankroll will never be large enough to protect you from going broke.

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Thank you very much for the kind advice. I'll keep it very much in mind.

But I was quite interested in the first part of your reply, where you said something about applying this to poker as opposed to coin flips.

I was wondering if you had any pertinent comment on that, besides general game play considerations. You seem to have caught the drift of the actual underlying questions.

poker sessions are not the same as coinflips that pay off certain odds. Or maybe they are. I do not know.

Just trying to learn as i go along. Just want to be aware of any patterns that might come along the way and throw a curveball.