Apparently I am a bit slow because I do not understand why you imply they should have different bankrolls in terms of big blinds, assuming the same win rate, standard deviation, and risk of ruin. Why do the stakes matter?

Are we all being trolled by the Top Dog?!?

I never said this.

No. What you need to understand is that expert gamblers think about things differently from most other people. The mathematical explanation for this is that instead of being in an infinite measure space you're now in a finite probabilistic measure space that can only go from 0 to 1, and that changes a number of things.

MM

All the math stuff is fine and dandy if people were robots unaffected by losing chucks of money that makes a difference in their life.

The truth is that everybody plays much worse than their expected win rate when they r in the midst of a 3 month downswing and there r bills to pay - unless they have so much that the swing is not psychologically impressive to them.

And the only way to avoid psychological effects of losing is to have a solid life roll. Have 6 months of expenses at least locked. Avoid debt. Keep the monthly nut reasonable. Don't surround yourself with parasites.

The 100 buyins is simply a construct used by pros to self discipline themselves into having an appropriate life roll.

I really enjoyed masons original posts in this thread but I'm totally lost and confused on his last 3-4 posts here....

No offense to Jonathan, but shouldn't this thread really be Mason on Bankroll Requirements?

Whatever, I'm happy with this thread. It makes me more confident with my 40 BI shot for $2/5 , though with the stipulation that if I drop to 30 BI, I go back to $1/2 and grind up 40 BI again for $2/5. If I'm a winning player at $2/5, then soon enough sets of 10 BI shots should help me "go infinite" as I like to say

One thing to keep in mind is that if you are considering moving up to double your previous stakes in order to win only slightly more per hour you need almost four times your previous required bankroll. That is yet another reason why most responsible pros are sitting on more than is mathematically necessary.

Hmmm it seems like there are two approaches here:

1.) Maybe we should pay attention to the consensus of the pros who actually MAKE A LIVING at this game and are strongly motivated to balance risk vs. reward in the real world.

Or... 2.) Maybe we should just make a ton of questionable assumptions and build a "model" to try to show how smart we are, and hide behind mathematical jargon to "prove" our position.

You don't need to be smart to know basic statistics. And as I just said, most pros who say they need a bigger a much bankroll than they actually would, given their claimed win rate, are saying that because they are exaggerating that rate and/or they need an excuse to not move up in stakes. (In the context of this thread, any good player who plays only 1-2 NLH with a 20K pure gambling bankroll should be ashamed of himself. He should be playing at least 2-4, especially since he is not forced to go broke at those stakes. Those who are correct to play this small with that bankroll are mediocre players who likely would not improve their income if they played higher.)

As for the high stakes players who need this much cushion, its off the original subject. They are doing the right thing but only because their edge is small. Thus they are conforming to the probability and statistics formulas that a 90 IQ could easily learn.

I think you've discovered for yourself why you can't use the SD results from your phone for plugging in to a risk of ruin formula. You're logging results by the session, which is fine for win rate but the SD it gives you will be on a per session basis, not a per hand basis which is what you want. I mean, imagine you played 3 monster length sessions of 1000 hands each and logged them. Would you expect an accurate SD calculation?

Hi SGspecial:

Again, going back to my Gambling Theory book and by using the maximum likelihood estimator of the standard deviation you can log in results by session and get either a per hand standard deviation or a standard deviation based on time (such as per hour of live play).

However, for the estimator to be reasonably accurate, I do recommend 30 to 40 sessions, so as you state, three sessions would not give you a good result, but not for the reason you give.

Best wishes,
Mason

Hi Everyone:

One interesting thing that this thread seems to point out is how unaware many of you are of the material that is in my book Gambling Theory and Other Topics even though this book was first published in 1987. It's the first book to talk about at any length the relationship of variance and expectation as related to gambling and a number of other topics such as bankroll requirements and the maximum likelihood estimator for the standard deviation as is being addressed here. (It even has the first example that I know of of the Independent Chip Model which is just a simple conditional probability problem [and I do not use the name Independent CHip Model -- that came later.])

What most of you need to understand is that as a professional statistician when I first brought these subjects up in the 1980s virtually no one in poker had even heard the term standard deviation, and of those few who had, and this includes David Sklansky and Mark Weitzman, only a small number had any idea how to apply it.

And this brings us to today. Since the Gambling Theory book is more technical in places than other poker/gambling books, it was not the big seller that some of our other titles are (though the number sold is still about 14,000), but that doesn't stop people from talking about these subjects, as can be seen in my first post to start this thread, even though they know little as to what they are talking about and at times can make significant errors.

Anyway, if you're interested in this area which leads to a general approach as to how successful gambling should be attacked, most of you should find Gambling Theory and Other Topics quite helpful, and you should also find it far more readable that you might expect.

Best wishes,
Mason

Don't you think your third paragraph explains your first sentence? If it hasn't sold a lot of copies, then not a lot of people will know what is in it.

Also, I'm guessing that a lot of today's players who started after 2003 don't know any better and will feel the book is too old.

Hi Doc:

Well, 14,000 copies, while small compared to the sales of some of our other books, is still not a small number, plus, years ago I wrote many articles that appeared in various places where many of these ideas were addressed.

However, I think what has happened is that while many poker players are now familiar with these ideas, being familiar and understanding them are two different things. This is especially true given that probability theory can by very counter-intuitive, and an example, as has already been mentioned in this thread, is that a good player may need a smaller bankroll than a great player

I think this is absolutely correct even though the latest edition of Gambling Theory and Other Topics is 2004. While many things related to correct poker strategy do change over the years since players tend to change how they play the game in general, certain other things which are purely mathematical in general do not change, and that's what we have here.

Again, much that is in my book is as relevant today as it was almost 30 years ago when I first began to talk about these ideas with a few other people. What's interesting is that much of this unique material that appears in my Gambling Theory book really came right out of my work with the United States Census Bureau and then The Northrop Corporation. So it really wasn't that unique after all.

By the way, just as an example as to how little many so called experts in the gambling field understand this stuff is about 20 years ago I was attacked by none other than Stanford Wong. He accused me of making up the term "self-weighting" and put out a challenge to anyone to produce a math or statistic book that used this term. Fortunately, his challenge didn't last long since I called him immediately and gave him the name of two books on finite sampling statistics that used this term.

Best wishes,
Mason

Mason:

True, Gambling Theory and Other Topics (the book) came out in 1987.

But while hanging out at the "special collections" section (years ago) of the Las Vegas downtown branch of the Clark County Library I noticed very old copies of the Gambling Times magazine in which you had a column called "Gambling Theory and Other Topics".

Is it possible that the stuff in the book about "self-weighting", "standard deviation", and "variance" as they relate to gambling/poker was written about by you in articles for Gambling Times, hence, giving you credit for bringing them up even before 1987?

You were way ahead of your time based on the book (1987) but could you be even more ahead of your time as a result of the possibility (that can only be confirmed by you) if your articles about BR requirements were published even before that in articles?

Other authors should give you credit (about fluctuation and bankroll stuff) in their books, as well as to Sklansky for terms like "implied odds", "semi-bluffing", "effective odds" and other terms.

Hi gangnam holmes:

You're correct. Much of the pertinent material that appears Gambling Theory and Other Topics was first written in Gambling Times Magazine and also in my column in the old Poker Player Newspaper starting in 1983.

An interesting point. When first getting into poker/gambling in the early 1980s I found it surprising that essentially no competent statistician had come through gambling. Thus I got a lot of credit for doing things that many people in my field could have done.

By the way, I want to mention one book that was actually before my time and it's The Theory of Gambling and Statistical Logic by Richard Epstein, first published in 1977. However, it's very different from the book I wrote and is probably closer to The Mathematics of Poker by Bill Chen and Jerrod Ankenman than any other book out there in terms of its rigorous mathematical approach even though it's not a poker book in any sense.

I agree completely, and I sometimes wonder how many people even understand that concepts like "semi-bluffing" and "implied odds" were first defined by David and how much that moved the science of poker forward.

Best wishes,
Mason

After discussions in this topic, I went out and bought gambling theory and other topics, it arrived this morning. Can't comment on the book as a whole as I skipped straight to the topic 'computing your standard deviation' and maximum likelihood calculator.

My results are stated earlier in this thread, using a sample size of 45 sessions (2 months play for me) and the formula in Mason's book for calculating maximum likelihood, I come to a bankroll requirement of 3,543bb's or 35BI's.

That 'feels' about right to me based on my knowledge of the game I play in. And is obviously very different from the 4.7BI's I get from just using the Standard Deviation from my phone app.

Hopefully there is other good material in the book, but regardless of the rest of the content, the book is a valuable purchase for me as a predominately live player as I now have an accurate way to calculate BR requirements.

Do I smell a 2+2 poker calculator app in the near future??

Mason,

I am still confused as to why you say a good player (with a 3bb/hour win rate at $1/$2) may need a smaller bankroll in terms of big blinds compared to an excellent player (with a 3bb/hour win rate at $25/$50), assuming both players have the same standard deviation and want to have the same risk of ruin. If you are simply saying that a good player can win more in terms of big blinds and have a lower standard deviation versus awful players at 1/2 compared to an excellent player versus good players at 25/50, is that not common sense to everyone?

You will be happy to know that when I started learning the game 12 years ago, I studied every 2+2 book available diligently, including yours. I even read your books on craps.

The main problem I have with following strict mathematical bankroll requirements is that I realize that most players (especially the audience of amateur poker players who are trying to improve) have a difficult time quantifying their win rate (they almost always over-estimate). They are also plagued with thought-process issues. When they lose a decent chunk of their bankroll, they get sad and have unhappy lives. I have found through coaching countless players that they have way less emotional turmoil when they lose if they have a gigantic bankroll compared to if they have a "mathematically standard" bankroll. I confidently suggest that most players keep a gigantic bankroll because, at least for most amateurs, they would rather remain sane than grow their bankroll as fast as possible. I teach people to win, not robots.

In the initial quote you pulled from CardPlayer, I was asked "I hate losing. What can I do about that?" Clearly this question is from an amateur player who cares about losing (meaning he is not a robot). While I gave a few suggestions besides the one you decided to post, I am somewhat sure that if this player keeps a larger bankroll than he currently does, he will hate losing a bit less. My answer also states that most professionals (at least the biggest winners in the game who I associate with) keep a proper bankroll of 100 buy-ins. Obviously this is an overly simplistic statement. I thoroughly discuss taking shots/moving up aggressively in my books, training videos, and articles. While using the term "proper" when defining a professional's bankroll was perhaps inaccurate, the fact that almost every professional I know keeps a gigantic bankroll is accurate.

There seems to be something going on here underneath the surface and non of has to do with bankroll

Your error is extrapolating from that fact that small stakes pros should do the same. Anyone who does well at 1-2 is hurting himself if he doesn't move up to bigger stakes well before his gambling bankroll hits 20K.

What's going on is that when a decision has a clear cut answer based on math you don't defer to supposed experts if they disagree with it. Bunts and punts used to be done too much even when the mathematicians showed it to be wrong. At first people tried to claim that the actual practitioners should be believed over the math guys. Until, that is the few coaches who were willing to listen started outdoing those who wouldn't.

Is there a difference in a $1/$2 player moving up to $2/$5 and a $20/$40 player moving to $50/$100 if both of their win rates get cut by the same percentage?

Do you assume that the vast majority of amateur poker players who my huge bankroll concept was directed to can act as emotionally rational as the best sports coaches in the world?

I never said this.

MM