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."

IMG8376
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.

Oldurrrr
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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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

William s 2016-11-08 14:59:17

The 1/4000 odds of hitting 4 of a kind that u mentioned may be true with a random hand. But once u flop a set your chance of making quads is obviously better since 1 card out of the remaining 30-40 cards makes quads. U have 1 out to make quads and 2 chances to hit it so its 4%....which is much better than 1/4000. After the flop u multiply your number of outs (1) by 4 and this gives u your percent chance of winning. (Not exact but super super close) That formula helps determine your percent chance of improving quickly at a table. So google "odds of hitting quads after flopping a set" rather than "odds of hitting quads" because the latter gives you the odds with any random starting hand rather than when you already have 3 of a kind...and obviously i didnt count the cards that pair the board to give him a full house which make his percent chance if winning go up. Conaider that if you play the hand after the you make your flush against his 3of a kind 1,000 times you will win like 70% of time (i didnt do the exact math) so u win in the long run. And when bad players get lucky it keeps them coming back to play. Otherwise they would always lose and all poker tables would be full of wizards and none of us would have any significant advantage

Ethor 2016-11-07 21:19:37

2-5 game at Harrahs in Cincinnati. I've been playing snug. I look down at two aces...AA v KJ. Flop: 9-2-j rainbow, 3 players and 110 in the pot, I bet out 75, I'm raised to 200 by "the rookie" KJ...I go all in 375 more. King on the turn. Awesome! Next hand I buy in for $500 more (Once again this happened consecutively) I look down at KK, this must be a joke, I three bet to 90 get 4 callers. 5-8-10 flop. Rainbow. I'm first to act, I check because I want one person to bet out and kill the draws with a check raise all in. (It's borderline, probably should just go all in but this table was loose and a check raise usually gets most idiots' attention) HOWEVER, everyone checks. Turn is a king, the nuts!!! I go all in and I get called by Q-9 ?? Gut shot only, no flush... Jack on the river. I say outloud "you call an over pot size bet on a gut shot straight, when I'm all in and you get zero implied odds???? Wtf!" Ok, next hand JJ, I already know I am going to lose. Now I know this is a cruel joke. 4-9-j flop rainbow. This time I don't bother with a slow play. There's 5 to the flop with my 30 raise, 157 in the pot including the folded blinds. I'm seriously tilted and don't care. I bet out $400, get called by j-9, 10-Q and 10-8... Turn is a 2. "Please GOD please, I will actually be up if I win this (80% river card for a win) hand." 7 hits. I already know. The guy with the nuts bets something like $75 into this $2000 pot. I really considered flipping the table over and pondered if I had enough to bail out of jail....I walked out, I should have died on my racing drive away through the rain going 9o in a 45... Anyway, I HATE POKER and after winning a lot in early 2015, have lost all but once since the Cincy bad beat for the ages ... 1 for 25. I can't psychologically recover and have decided to quit. Did I mention I hate poker?!!!

Delicious Points 2016-11-01 23:25:48

Listen, I had an epiphany earlier today. I found out I was one of the unluckiest players every single time because each time I go in with a better hand pre-flop, I suck out; Scarily, this happens to me around a shocking 75-80% of the time. The answer is not to leave in disgust, just rebuy and if you don't tilt and continue to play well, I end up with my money back and then some.

In other words, be patient and understand that bad beats will eventually happen to you. Just more for some people than others, I am unfortunately the former.

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