Texas Holdem - Luck vs Variance

Texas Holdem Strategy Guide to Luck vs Variance

When's the last time you heard something about luck at the Texas holdem table?

The odds are the last time you played you heard someone talk about luck. If you're honest you probably either talked about luck or at least thought about it the last time you played.

Here's a list of common things about luck heard around the Texas holdem table:

  • That sure was a lucky break.
  • Talk about bad luck. She hit a four outer on the river to beat me.
  • I just need to hit a lucky streak to get back to even.
  • I'm the unluckiest poker player in the world.
  • It's lucky you hit your flush because I had the straight.

If you believe luck has anything to do with the results at the Texas holdem table it's time you learned the truth.

The truth is luck has nothing to do with anything that happens at the Texas holdem table.

It doesn't matter what you think or what you've heard or seen, everything that happens is a matter of mathematical probabilities and short term variance. Once you finish this page you'll realize this is true and you'll learn how to use this information against your opponents.

The best thing about learning the truth about luck and poker is it instantly makes you a better player. When you understand why luck has nothing to do with your results and how short term variance works you'll start looking at everything that happens while you're playing in a different way.

Once you learn about Texas holdem luck and variance you can see how they're directly related to odds, pot odds, and expected value. If you haven't read the pages covering those topics in this section yet make sure to check them out after reading this page.

How Short Term Variance Works

The reason luck doesn't have anything to do with Texas holdem is because you're using a deck of playing cards within a strict framework of rules. The deck of cards has a set number of cards, 52, and only a certain number of outcomes are possible in any situation.

Imagine the following scenario.

Before the river is dealt you have two pair and your opponent has a gut shot straight draw. When your opponent gets one of the four cards she needs to complete her straight it seems like good luck for her and bad luck for you.

Let's look at every possible outcome for this hand to see if luck has anything to do with it.

The board has four cards, your opponent has two cards, and you have two cards, for a total of eight known cards. This leaves a total of 44 unseen cards. Four of the cards complete a straight for your opponent and 40 of them don't. So every 44 times you're in this situation you'll win 40 and lose four.

While the percentages or odds are in your favor, the more times you're in this situation the closer the results will come to the correct percentages.

For example, if you're in this situation 1,000 times you'll win roughly 909 times and lose roughly 91 times.

The important number to consider is you have to lose roughly one out of every 11 times you're in this situation. It has nothing to do with luck and everything to do with simple mathematics.

You should actually rejoice when your opponent draws out on you in this situation because the average must come back to normal eventually and you've just put one on the negative side. This means in the long run you're one closer to the dominating numbers this situation requires.

Don't make the mistake of thinking you'll automatically win the next 10 times if you just lost a hand in this situation. While over the long term the averages always work out, the short term isn't guaranteed. You're not even guaranteed to win the next identical situation.

It's possible to lose two, three, or even more hands in a row in this situation, even as a huge favorite. It's not likely to happen, but it can.

If you simply put yourself in a positive situation like this over and over the numbers take care of themselves and force profit to you.

This outcome shows why what really happens is normal and if a result presents itself that isn't favored to happen it's simply short term variance.

In this example we assumed you knew the values of your hole cards as well as your opponents because of the way we set up the hand. In most hands you won't know the exact value of your opponent's cards but often you can generate a good guess. This doesn't change the lesson, simply the number of seen and unseen cards.

Here are a couple more examples. The example we just covered showed a hand where you were a huge favorite. Many players make the mistake of thinking they're a bigger favorite than they actually are in some hands. The next example covers one of these situations.

If you have a made hand after the turn and your opponent has four to a flush, you're a favorite to win the hand. But do you know how many times you'll win and lose on average? How big of a favorite do you think you are?

You know the value of eight cards, leaving 44 unseen cards. The deck has nine cards that complete your opponent's flush, so 35 cards make you the winner. Your opponent will hit their flush over 20% of the time. This means slightly over one out of every five times you're in this situation you lose.

This still makes you a big favorite, but you aren't so big of a favorite that you should expect to win on any single hand.

What if your opponent has an open end straight draw and a flush draw? This means she has 15 outs out of 44 unseen cards. This means she'll win roughly 34% of the time, or 34 out of every 100 times you play the situation.

Even in a hand with two starting hands close to the same value, luck doesn't come into play.

If you have a suited ace and king and your opponent has a pair of fives, the pair of fives will win just under 52% of the time heads up and the suited ace king will win 48% of the time. You'll actually tie a very small percentage of the time, which is covered in the slightly fewer than 52% of the time the pocket fives win. For ease of calculation we're using 52% and 48%.

When you play this situation 100 times the pocket fives hand wins 52 times and the suite ace king wins 48 times. This is close to a coin flip so you shouldn't be surprised at either outcome, no matter which side of the hand you're on.

How Understanding Variance Helps With Tilt

It's easy to get upset when an opponent does something stupid but wins anyway or when you trick your opponent and have a dominant hand only to get drawn out on. But now that you understand it doesn't have anything to do with luck you can use this information to avoid tilt.

When you go on tilt you start making plays based on your emotions, usually anger, instead of on sound playing decisions. Any time you make a play at the Texas holdem table that isn't based on the decision that makes the most money in the long run you're costing yourself long term profit. Tilt clearly falls into the category of playing decisions that aren't based on the correct decisions for long term profit.

Top Tip
The next time you lose in a situation where you're the heavy favorite remember what you learned in the last section. Simply understanding how the math works can be enough to help you remain calm and approach the next hand with a level head and clear thinking.

You can also consider commenting about how lucky your opponent was to try to get them to buy into how everything is based on luck. You can learn more about this in the next section.

Saying the Word Luck at the Table

As long as you never start believing that luck has anything to do with the results at the Texas holdem table you should spread the word around as much as possible.

You want as many of your opponents as possible to believe in luck and keep striving to turn their luck around. If your opponents believe everything that happens is based on luck they'll never learn how to improve their game. This helps you win more in the long run.

Developing your skills and abilities to become a winning Texas holdem player has a great deal to do with psychology. When you fall into the trap of thinking that luck plays a role you not only cost yourself money by basing your playing decisions on luck and feelings instead of math, percentages, and odds, you also run the risk of damaging the psychological way you play and view the game.

When you start believing luck helps or hurts players at the table instead of recognizing short term variance when you see it you stop making the correct plays.

You're making an excuse for poor play instead of taking responsibility for your mistakes and striving to correct them and increase your profits.

If you can help other players fall into the believing in luck trap you can help them damage their poker psychology. This in turn helps you in the long run.

Don't be afraid to tell everyone at the table how lucky you are when you win a hand or get a nice starting hand. Everyone gets dealt a pair of pocket aces or kings the same percentage of times in the long run, but it can seem lucky when you get them.

Some players can get irritated if you comment on how lucky they are on a hand, so you have to decide if you want to run the risk of irritating your opponents when they win a hand. Some players don't have a problem being confrontational, but if you do you might want to avoid starting the luck conversation. But if one of your opponents mentions it feel free to jump in.

Pros do it Too

You don't even have to be an amateur poker player to fall into the luck trap. Recently a televised poker game was on with Mike Matusow. He was in a hand as a favorite and was considering making an offer to run the hand twice but didn't.

He ended up losing the hand and started whining about how no one knew how bad he ran at poker. This is another way of saying he always has bad luck. And he's been a pro long enough to know better.

If you're not familiar with running a hand twice, in big cash games sometimes the players agree to run a situation twice. If they get all in pre flop with an ace and a king against a pair of sevens they could run it twice, dealing the flop, turn, and river and then dealing it again.

It's a way to average out situations when playing for high stakes. The only place you generally see it is at the highest level tables.


Now that you know the difference between luck and short term variance at the Texas holdem poker tables you can start using what you've learned. The next time you're on the short end of the variance stick quietly rejoice because you've got one of the losing draws out of the way. It always brings you one step closer to winning in the long run.

Now you never need to worry about going on tilt again. Since there's no such thing as a bad beat you can stop getting upset at the poker table. Just keep getting your money in when you're the favorite and let the math take care of everything else.



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