The Mathematical Truth About Poker: Some Do Run Worse

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.

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Most players complain endlessly about their bad luck. They cry about their rotten cards. Agonizing over the endless hours missing countless flops and getting sucked out on by bozos. You have to get over this if you have any hope of becoming a legit, long-term winner in poker. You have cards; you have to play them; therefore you have to learn how to play them in the most effective manner possible. Fold 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.

How Much Luck is in Poker?

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

poker math run bad

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."

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%; 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.

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The Mathematical Truth About Luck in Poker

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.

is poker luck

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

It's 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.

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.

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The Distribution of Luck in Poker Over Time

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.

poker luck

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.

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).

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Cards Have No Memory

poker downswings

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.

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Vegeta
2020-11-27 05:27:50

Please tell me how you had the Queen high straight flush and someone owned you with a king high straight flush Lmfaoo
That’s not even possible kid
You can have a king high straight flush over a Queen high smh
So yes all your crying about how bad you run is void and it’s clear you lie and most likely just a bad player😂

Paul
2020-11-26 06:05:16

I have had a bad run of cards FOR YEARS. I know that sounds absurd but I’m telling you it’s absolutely freaky. Just last session I lost 7 flush over flushes, 3 set over sets and in the last flush showdown I actually nailed a straight flush on the turn. In fact it was the Queen high straight flush 3rd highest possible hand. I shipped it, villain snaps and has the King high straight flush. And this is in a 6 max game.

And that is the TINIEST sample. I could literally name hundreds upon hundreds upon hundreds of almost exactly similar sessions I’ve had. I don’t know how to explain it but the probabilities seem so unbelievable that I would have to say some people are just unlucky

tiaan
2020-10-15 18:59:19

I ******* HATE LOSING WITH THE BEST HAND OVER AND OVER AGAIN.. but I wont give up

Tom Dynes
2017-05-05 19:55:39

100% agree, you are most definitely NOT a genious

Tisha Gipson
2017-04-07 10:17:55

He had more outs than the 2. If he had pocket 2’s and 2 comes out on the flop. That King, 9, or 7 would have given him a boat..still crushing your flush. Depending how much money he already had in the pot and how much he had behind him. Doesnt seem like a bad call.

Mel Finehout
2017-04-01 16:42:30

I’m sorry but I really doubt you turned 10K into a mil. Unless it was on Zynga.

There is a language of poker and you don’t speak it and I’ve never met a winning player who doesn’t.

Since there are far more internet trolls than Million dollar winners. Since there are numerous sites where people go to talk about poker. The odds that one winds up here, as there is little benefit from it, is low.

It’s not logical to believe you won a million. If you were an actual player youd know all these things.

Phakt
2017-03-31 08:43:19

I am very very new to hold’em. I thought I had the worst luck of all. I refuse to read books or watch videos. I don’t even watch tournaments. Over time, I turned 10k into 1 million. No, I am not a genious. I am a realist. I just play the odds. At large tables, I assume in most cases that one of my opponents has me beat unless the odds are GREATLY in my favor. I play super conservative and wait for the table to shrink, my odds then go up and I bet more loosely. It’s simple. I have gotten the shit kicked out of me when the odds seemed extremely in my favor. But then again, I kick the shit out of someone else ever so slightly more. Relax, It’s just money. Have fun. It’s fun watching everyone else loose their cool.
As a side note, I tried to change up my strategy after I got sick of seeing everyone else get great hands. Become more bold. I started loosing my ass so I went back!.

Phakt
2017-03-31 08:42:50

I am very very new to hold’em. I thought I had the worst luck of all. I refuse to read books or watch videos. I don’t even watch tournaments. Over time, I turned 10k into 1 million. No, I am not a genious. I am a realist. I just play the odds. At large tables, I assume in most cases that one of my opponents has me beat unless the odds are GREATLY in my favor. I play super conservative and wait for the table to shrink, my odds then go up and I bet more loosely. It’s simple. I have gotten the shit kicked out of me when the odds seemed extremely in my favor. But then again, I kick the shit out of someone else ever so slightly more. Relax, It’s just money. Have fun. It’s fun watching everyone else loose their cool.
As a side note, I tried to change up my strategy after I got sick of seeing everyone else get great hands. Become more bold. I started loosing my ass so I went back.

Smitcholin
2017-02-12 21:29:45

Any mathematicians know the chance of this happening? – My all in E.V for tournaments is 2,800 Big blinds. My real value is 600 over the course of about 10,200 hands. When translated to tournament chips it’s + 150,000 E.V but my real value is -300,000 over the same sample size.
Thank god these are only micros.

William s
2016-11-08 15:08:05

You cant always just think about the chances that someone hit a set, or a flush, straight, etc.
When a player bets strong you have to narrow his range to those better hands. Poker is all about ranges. When he folds his range is wide open, but when he calls or raises you have to narrow the range of hands he could have down to 3 of a kind or maybe top pair or a weaker flush draw which you beat. Learn to put players on a range of hands and then narrow that range based on his action and betting. Sometimes you can narrow his range to a few hands. Obviously u had the nut flush so u had to call or shove all in but even before u saw his hand u should have known that its at least a big pair or a set based on the betting. Learn pot odds and how to put players on a range and u will vastly improve your game. A great book is ‘professional no limit hold em’ by david sklansky

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