The Mathematical Truth About Poker: Some Do Run Worse

Mike Matusow
Mike "The Mouth" Matusow: Is it really possible he runs worse than everyone?

This article constitutes a short dissertation on a banality. It'll seem stupid at first but bear with me; there are useful poker nuggets here.

The banality: You can't do anything about the cards you are dealt.

Now I know that everyone who has played even a little poker knows this is true - but few act like it.

Most players complain endlessly about their bad luck, cry about their rotten cards, agonize over the endless hours missing countless flops and getting sucked out on by bozos calling on a wing and a prayer.

You have to get over this if you have any hope of becoming a legit, long-term winner in this game.

You have cards; you have to play them; therefore you have to learn to play them in the most effective manner possible.

Get out when you know you're beat. Smile as pleasantly as possible when your opponent hits a two-outer for the third time that night.

And, of course, be gracious when you hit your hand.

Getting Your Share

Since this is so bloody obvious you're probably wondering why it merits a "strategy" article.

Well, I want to talk a bit about luck, about what it means to "get your share" of the cards and about what it means when aficionados of the game say wise things like "it all evens out in the long run."

Hansen: Likes his chances long term.

Gus Hansen was once asked by a reporter what role luck played in poker.

He responded that in any given session it probably accounted for about 90% of his outcomes. Over a month, he guessed it was about 10 or 15% and over a year it was down to around 2-5%.

In the ballpark, I'd say.

And it's true - all professional players of poker operate under the assumption luck will even out in the long run and skill will triumph. Otherwise there wouldn't be pros.

There aren't any professional craps shooters or baccarat players (no matter what some ill-conceived books and pamphlets may try to tell you).

There cannot be because of the mathematical nature of these games.

The Mathematical Truth

In all complex settings, the mathematical truth is considerably more complex and, in my opinion, more interesting.

The truth is there are certainly some people who have been luckier than most and some who have been unluckier than most.

I put have been in italics for a reason, which will become clear.

It is true that as the number of hands dealt increases the luck element shrinks, but it doesn't go away. In fact, it has to remain and to continue to play a role.

Think about it this way: Assume there is a distribution of the long-term expected value (EV) of every possible poker hand played from every position under all possible circumstances.

None of us have the time for distribution to even out.

It will be a wild and wonderful distribution full of all kinds of bizarre hands and outcomes and will be driven by a host of factors.

But it is a mathematical certainty that it will approximate a normal, bell-shaped curve.

The hands that have just awful long-term expectation will be relatively infrequent, mainly because they don't get played all that often, and will show up in the left-hand tail.

Those with the highest EV will also occur rarely (primarily because the situation has to be "just right" for them to get paid off). Those will appear on the far right of the curve.

Those with average outcomes will occur with greatest frequency and be at the peak in the center of the curve.

The so-called "computer hand" or break-even hand (Q-7o) emerged from simulations cranked out by a computer dealing gazillions of hands at random.

Everyone will be dealt hands from this distribution each time they sit down and, in theory, they will all be dealt the "same" hands.

In reality, of course, this sameness is only reached when an infinite number of hands have been dealt.

Frankly, I don't have time to wait for this and neither do you.

The Distribution of Luck

OK. Still with me? Here comes the fun part.

If you plot the distribution of the "luck" of each player (that is, the EVs of the hands they are actually dealt), you'll get another normal curve.

And when you plot it, you will discover that some players are below the mean, some above it - and a few are far below or far above it.

Ben Lamb
Some are flat out luckier.

Some folks are going to be flat out "luckier" than the norm and others "unluckier."

It has to be this way! If this seems nuts to you, just think about real life.

Some people get hit by trucks or lightning, or diagnosed with horrible diseases. Some people had the misfortune to live downwind from Mt. St. Helens or in the Ninth Ward of New Orleans.

Others stroll though life in perfect health, live in San Diego or bought a house on high ground.

The lottery has just awful odds; the worst EV of all gambles. But there are people who have hit jackpots of over $100,000 three times. Yes, three.

There have to be such "lucky" folks given the number of lottery drawings and the number of punters.

If you're one of these you've beaten the worst gamble in the civilized world and, unless you're a total nutball, you're going to go to your grave "lucky."

So, yes; you have to play the cards you're dealt and you've got to play them in the most advantageous manner.

You can't bitch about your lousy luck because there isn't anything you can do about it. In fact, if you do, it will hurt your game (more on this in a future column).

Cards Have No Memory

Allen Kessler
You can't bitch about your lousy luck.

The truth is some of you bemoaning your rotten luck, mystified because you never seem to hit your three-outer, nonplussed because you keep getting hammered by idiots making stupid calls, well, you know, you're right.

Reality bites. You have been unlucky.

Of course, you noticed the past tense in that last sentence. Cards have no memory and they don't know you've been smacked around the room by a random number generator for the past weeks or months.

Your expected "luck" for tonight's session is the statistical norm, the average outcome.

So go play your best game and don't sweat it. You can't do anything about the cards you're dealt.

More strategy articles from Arthur S. Reber:

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