If you get sucked in by this fallacy and make or call bets based on it, you're going to seriously hurt your game. See the previous article for the full explanation.

This week, I'd like to shift gears and discuss another statistical/psychological principle known as regression to the mean. To the casual eye it may look like a fallacy, but it isn't. Like the gambler's fallacy, it is an important aspect of bankroll management.

Let's start with an imaginary situation that may seem totally off the wall. It isn't.

Suppose you're a tall man, well above average. Let's make you 6'2" (North American average is about 5'10"). Let's give you a wife who's 5'8" (which is also about 4 inches above the norm).

What would the best estimate for the height of your male children as adults?

(a) 6'2"

(b) 5'10"

(c) between 6'2" and 5'8"

(d) between 6'2" and 5'10"

If you're like most folks, you just picked either (a) or (c). The standard argument for (a) is that it's your height and since those are your genes your kid is most likely to be about your height.

Best estimate for the height of Greg Mueller's children: 11'7".

It's wrong.

The rationale most often given for (c) is that your son should be some kind of "blend" of the heights of the two parents.

This is also wrong. The correct answer is (d).

I could lecture about genes and how they operate in these situations but the reason (d) is correct is based on statistical analysis, and holds no matter what the conditions are.

If both parents are above average in height, then their son is most likely to be between them and the mean height for the kid's sex. If both are below average, their kid will most likely be taller than them but below the mean.

Put simply, you're most likely to see "regression to the mean."

Here's the basic reasoning: The mean (or "average" if you prefer) is the most common outcome in any situation. If you're betting on what's going to happen next, your best bet will be the mean.

If I ask you to guess the height on the next man to walk in the room, you'd maximize winning by picking 5'10". Any event that is different from the mean is less likely to occur.If the next guy who walks in is 6'2", that's unusual and unlikely.

So having a 6'2" dad is unusual and having a 6'2" son is unusual. It's more likely that he'd be closer to the mean, but since Dad does carry some "tall" genes, he's most likely to a bit shorter than Dad but taller than average.

Does not carry the tall genes.

Now, back to poker. Let's assume you're a solid, winning poker player (hey, if you regularly come to PokerListings, you almost certainly are). You've been averaging +5BB/hour in your $2/$5 NL game for a couple of years.

Now suppose you have a good five-hour session and rack up a $1,500 win (i.e., 60BB/hour). What is the most likely outcome the next time you play?

(a) a win of 60 BB/hour

(b) a win between 5 and 60 BB/hour

(c) a break-even session

(d) a loss slightly less than 60 BB/hour

Those who say (a) believe that what happened in the past is most likely to continue. This is wrong. It is like assuming that the kid in the above example will grow to the same height as his father.

If you're averaging 5BB/hour, a 60BB win is big - and rare. Repeating it is unlikely. Remember, the cards are pieces of plastic; they don't know what you won or lost last time out.

Those who chose (c) usually argue that since breaking even is the default for the game, this is the most likely result.

That's wrong for two reasons. One, poker is actually a negative-sum game, because the rake has to be factored in. Two, you're a long-time winning player, so you're less likely to break even in any given session than you are to register a small win.

Those who choose (d) are committing one version of the gambler's fallacy, assuming that things have to "even out" in the long run and that the big win has to be balanced against a big loss.

The correct answer is (b), simply because it is the outcome that is between this last session and your average result which, we know, is the most likely outcome. In short, you're most likely to see "regression to the mean."

What's the poker lesson here? A big win doesn't mean you're the next Phil Ivey.

What's the poker lesson here? Scale down your expectations. Racking up a big win is unlikely. Unlikely events are, well, unlikely.

In fact, if we had enough data we could calculate not only the mean outcome of each session you play, we could calculate your standard deviation. This number, which is a measure of how variable your play is, will tell us exactly how likely any arbitrary outcome is for any session of any length.

For example, if your mean of 5BB/hour is accompanied by a standard deviation of 30BB/hour, we know that the probability of that 60BB win is only about 2.5%, or 1 in 40. And, of course, you're just as likely to have a wretched night at the tables where you lose 55BB.

Don't get too excited by a big win. It doesn't mean you're the next Phil Ivey. It doesn't mean that you're now taking control of your table. If you've been losing, it doesn't mean that you've turned any special corner.

Stay cool and appreciate that all our results tend toward the mean of the relevant distribution - whether we're talking about how tall our kids are likely to be or how much cash we're going to take out of the cardroom with us next trip.

Author Bio:

Arthur Reber has been a poker player and serious handicapper of thoroughbred horses for four decades. He is the author of The New Gambler's Bible and coauthor of Gambling for Dummies. Formerly a regular columnist for Poker Pro Magazine and Fun 'N' Games magazine, he has also contributed to Card Player (with Lou Krieger), Poker Digest, Casino Player, Strictly Slots and Titan Poker. He outlined a new framework for evaluating the ethical and moral issues that emerge in gambling for an invited address to the International Conference of Gaming and Risk Taking.

Until recently he was the Broeklundian Professor of Psychology at The Graduate Center, City University of New York. Among his various visiting professorships was a Fulbright fellowship at the University of Innsbruck, Austria. Now semi-retired, Reber is a visiting scholar at the University of British Columbia in Vancouver, Canada

More strategy articles from Arthur S. Reber:

• The Gambler's Fallacy
• Living the Good Life
• The Best Book Ever Written About Poker
• Mix Your Game Up by Mixing Your Game Up