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:

About Arthur Reber

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Oliver 2014-07-29 18:21:33

i prefer chess.

lee 2014-07-14 02:02:27

lol...reality bites. nothing realistic about an RNG.

Etrain 2013-11-06 00:20:49

Have been playing poker for years and believe its 95% luck. Nobody gets more unlucky then me in this game. I play tight and only go all-in when I have the best hand. However, I get sucked out on EVERY time. People will think I'm making this up but have not had 1 winning day in two months due to these all-in suck outs. Meanwhile, my friend seemingly always hits the perfect card no matter what the odds. He, of course attributes this to skill but hitting the river card against huge odds has nothing to do with skill. I hate how people think they are somehow good poker players when they are just lucky.

Awejn 2013-11-04 11:40:32

I guess it's not easy for the human mind to accept that there's something you simply CANNOT control, hence the need to put the whole luck-factor in some sort of context, to try and make sense of it somehow. "Why me?" would be a typical indicator for that - taking something personal that's absolutely impersonal, arbitrary and out of our hands.

Here's an idea for a different approach: Keep a record of both unlucky AND lucky situations over a significant amount of time and see what comes out of it. Cause I suspect that "us unlucky" players usually don't celebrate our luck as much as we complain about the bad luck. Maybe we don't even realize that luck-wise we're actually "break-even"? So taking a look at how we deal with the lucky streaks might help to put things a little more in perspective. (I for one sometimes find myself thinking that I somehow "deserved" that lucky river card since I'd barely gotten any hands for the past hour, or the guy I sucked out on already had his share of luck for the night anyways ... But do I ever deserve that UNlucky river card? - And there you go.)

ream 2013-10-26 01:28:35

nice words Joe. Yes, everything what happens in life is luck. Who we are, where we're born, which tournaments we win and which we don't.

I can tell you I play better than most people who made it to the WSOP final table. Joe Cada, a winner of the main event, is a losing play online.

Bill Gates is where he is thanks to luck. Many don't understand that. In fact, almost nobody understands that.

"Fooled by Randomness" is a good book I'd recomment, it's a bestseller.

Joe Anastasi 2013-08-13 00:37:43

Wow! Finally someone who tells it like it is. He said the four letter word: luck. I have always said that among players of equal skill, luck is both the short and long term factor. And luck can come in so many ways in poker, not just getting good cards. Yes, players might get the same cards, but the scenarios in which they get them can be very different. Now there is no question that a good player will beat a bad player with good luck in the long run. But in some cases that can be a very long run. Still, in does little good to bitch about your bad luck, and does much good to improve your skills. However, the winning player who never sees his good fortune as luck is just as delusionary as the bad player who thinks all his misfortune is a product of bad luck.

Bob Suruncle 2013-07-31 10:45:43

You say at the beginning that the short term game is 90% luck and later you say that cards have no memory. If the cards and the math has no memory then every session is a short term game and therefore luck falling to 2-3% long term is an invalid statement. I agree they some people are extremely lucky and others unlucky. That holds for long term as well as your example of the three time lottery winners states.

CS 2012-05-20 03:06:06

Article is good and spot on. Could have gone in a little more detail about why randomness creates this, and just how far it can be either way, but at least this article admits it straight up that even over a huge sample, some people will run worse than others and it can be extreme. I'm sick of the same old articles saying it's selective memory or happens to everyone etc. Fact is, 3 year, well over a million hands+ super bad runs don't happen to everyone. Weekly? Monthly? Sure. I have it documented and it's not pretty. More than 3 standard deviations from the mean, over a huge sample and the ever-sobering fact is that just like it doesn't have to continue and can change at any time, it also doesnt have to change and can stay under for my lifetime.

However, going through this I have noted that I've ran "above" in other aspects outside of the game, like life and health. I've been very fortunate health wise. Not that it's a trade off, or that I'm unlucky in one thing because I'm lucky in another. It doesn't have to be anything and probability is only that, probable, nothing is absolute.

Kudos to the author for having the balls and grace to actually tell it like it is. I understand why most articles don't say this, it's because most poker players complain about their luck regardless of fact. However, although not many, there are a select few that will suffer lifetime and it's nice to have an article like this for them.

Also, it's not just hands/weather your pair over pair wins 4/5 or better or worse. Timing can have everything to do with everything. A decent generalized analogy I've used before is TJ Cloutier and Chris Ferguson, both good tournament players in their own right. However, a simplistic example is Chris hit a 9 on the river (AQ vs A9) for his WSOP main event win over TJ. Chris went on to fortunes and glory, and TJ wound up pawning one of his bracelets. Had the 3 outter not come, things could be much different.

Now just imagine this on broader terms and even smaller sublets. We could even say the guy who busted in 367th would have won had he not busted. It also works for many other samples. It is especially true in tournament poker though, but cash is not fully exempt.

Anyway, as a guy who's played 20 yrs and gone through this, shall I say, "improbable" run in the last 3, I could go on and on about this. I'll leave it be though and again give kudos to the author.

peter burrell 2011-11-19 08:32:51

wow...ok first i want to say that i think this is a fantastic article and it just helped me extinguish one of my biggest "leaks." Arthur i really dont know what you mean by q 6 as he said, he says q 7 and arty he says, which is exactly what ive always known and used as a very helpful fact. It allows me to know its pretty much an even money shot or 50/50 that i have the best hand if everyone folds to me if im on the button or in the small blind. All if this is meaningless anyways Reber i enjoyed your article a lot and love how you explained a question i have been wondering which is the question of luck vs skill in poker and i loved the gus hansen quote. well done.

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