# Poker Variance Meaning

Variance is one of the characteristics that makes a big difference in the short term results between one game and another. Lets compare two popular machines. Below you have the pay tables for both full pay Jacks or Better (9/6) and a popular variety of Double Double Bonus (40/10/6). In poker, variance is the measure of uncertainty. A play that has high variance has a great deal of uncertainty. A play that has a relatively certain outcome has a low variance. The act of folding has a variance of zero. The two most popular statistical tools in use are the mean and standard deviation. They are the most common way in which large masses of data are summarized, but neither was developed with poker. Variance is a measure of how data points differ from the mean. According to Layman, a variance is a measure of how far a set of data (numbers) are spread out from their mean (average) value. Variance means to find the expected difference of deviation from actual value. Therefore, variance depends on the standard deviation of the given data set.

## What these terms mean to your video poker play

### By Jerry “Stickman” Stich

You might ask what difference volatility makes to the video poker player. Plenty! The higher the volatility, the higher – and lower – the bankroll swings.

Two factors that determine a player’s chances of winning or losing on a particular video poker game are the payback (sometimes called return) and variance (also called volatility) of the game.

Payback, or return, is the amount of money that is “paid back” or “returned” in the form of “winning” hands to players from all the money played through a video poker game. It is expressed in percentage terms. What this means is that by playing a game that has a 99.54 percent return, you can expect that in the long run you will get back \$99.54 for every \$100 of money played or coin-in for that game. If you are a dollar player that plays five dollars per hand, for every 20 hands played (\$100 in coin-in), you will have an average return of \$99.54 (payback) for each of those twenty hands over the long run.

Another way to talk about this concept is by referring to the house edge. The house edge is what the casino keeps from your video poker play – or any casino game for that matter. The house edge is the difference between the money bet or coin-in and what the game returns to the players. Using a 99.54 percent return like in the example above, the house edge is \$100 minus \$99.54. This equals 46 cents, or a house edge of .46 percent.

It is important to note how low that house edge is in comparison to other games on the casino floor. When you see signs advertising “Our slots pay back 97.3 percent!” remember that the house edge you are playing against is 2.7 percent! A house edge of .46 percent or a payback of 99.54 percent is the actual house edge and return percentage for the full pay version of Jacks or Better video poker with perfect play (commonly known as 9/6 JOB). I would venture to say there is not a standard slot machine in any major gaming market that has a house edge as low. That is one reason video poker is so popular.

Of course, not all video poker game returns are as high as 99.54 percent. Some go as low as 95 percent; and in some extremely bad situations, even lower. However, on the positive side, some returns are higher – even more than 100 percent! The player has to know how to find, recognize, and learn to play the good games, while avoiding the bad games. Fortunately, this information is readily available in magazines such as this one, as well as in books and on the Internet.

Remember earlier that I used the phrase “in the long run.” After 20 hands on a dollar game playing five dollars per hand, I guarantee you will NOT have \$99.54. You will have \$100, or \$105, or \$85, or any multiple of five dollars, since that is what the hands pay. You will have ups and downs during your playing session. Your credit balance will swing up and it will swing down. However, after thousands upon thousands of hands played, the average return paid will be very close to \$99.54 for every \$100 in coin-in you ran through this game.

The swings in bankroll that you experience are due to volatility or variance. Volatility is a generic term which refers to how high or low the bankroll swings. Variance is a mathematical term that puts a number on the volatility. It measures how far a set of values is spread out. The variance of video poker games runs from a low of about 12-15 to a high of nearly 200.

You might ask what difference volatility makes to the video poker player. Plenty! The higher the volatility, the higher – and lower – the bankroll swings. If you are fortunate enough to hit a large paying hand early in your session or video poker playing career, you will have plenty of money to continue playing. What if you don’t hit any large paying hands early on? In a high volatility game, the player loses at a much faster rate than they would on a low volatility game. The bankroll requirements for a high volatility game are much higher than for a low volatility game. Therefore, you must have enough cash, or bankroll, to ride through the losing streaks.

A future article will discuss bankroll requirements in more detail. For now, just be aware that multiple, high-paying hands on a game’s payback schedule come with a price. That price is steeper losing streaks and a correspondingly higher bankroll requirement.

I suggest the following guidelines for deciding whether to play a video poker game based on its variance. From a bankroll safety point of view, if the variance is under 40, it is a fairly safe – albeit possibly boring – game to play. A variance of 40-80 means it may be an exciting ride, but think carefully about whether you have the bankroll and emotional will to play this game as there will be significant losing streaks. If the variance is over 80, seriously consider a different game. Unless you are certain you have a large enough bankroll and can emotionally endure potentially huge losing streaks, these games may not be for you.

You can use my advice above, or choose to ignore it. After all, it is just my opinion and it is your money you’re risking, not mine.

How Would You Play This Hand?

In the article above, I discussed variance and its effects on a player’s bankroll. Let’s take a look at a hand from a high variance game – Triple Double Bonus. The pay table is:

 Hand 5-Credits Pays Royal Flush 4000 Straight Flush 250 4 Aces w/2, 3, 4 4000 4 2s, 3s, 4, w/A, 2, 3, 4 2000 4 Aces 800 4 2s, 3s, 4s 400 4 5s thru Ks 250 Full House 45 Flush 35 Straight 20 3 of a Kind 10 2 Pair 10 Jacks or Better 5

The return on this game is 99.57 and the variance is 98.

With five credits played you are dealt the following hand:

Ah Js 5s 3d Ts

How would you play it?

Let’s examine the options. You have three of a flush (Js 5s Ts), two of a royal flush (Js Ts), a lone Ah, and possibly the Ah with the 3d kicker. You could also save the two high cards or just the Js.

What would you do?

If you choose to hold the Ah, you are absolutely correct! The Expected Value (EV) for this play is 2.346.

The EV for each of the other possible holds is as follows:

Three of the flush (Js 5s Ts) – EV 2.262

Two of a royal flush (Js Ts) – EV 2.186

Ah Js – EV 2.115

Lone Js – EV 1.964

Ah 3d – EV 1.750

Even though the kicker is an important card in Triple Double Bonus, it’s useless without the quads to go with it—and it can’t overcome the steady returns of a flush draw in the long run.

As a poker player you will have experienced times when you made the correct decision only to have the results make you want to punch the wall. Poker is a game with variance, meaning that things are going to happen that go against the odds of them happening (sometimes seeming like they defy all possibility). However, as long as you are making decisions that have a positive expected value (+EV), you will be profitable in the long run.

What exactly does expected value mean? Basically, if you were to flip a coin and someone offered you \$1 for every time you called heads or tails correctly and there were no penalty for guessing incorrectly, that would have a positive expected value. Since there is an even 50/50 chance of earning \$1 each flip, you can say that the EV of each flip of the coin is + \$0.50.

Now if you wagered \$0.50 each flip, it would be an even money bet. Half of the time, you would lose \$0.50 and you would profit \$0.50 the other half (\$1 of winnings minus the original \$0.50 wager).

Now let’s say you are given \$1 if you call a coin flip correctly, but you have to wager \$0.55 each time you flip the coin. You would not want to make this bet because it has a negative expected value (-EV). Over time, you would lose an average of \$0.05 on each flip.

## Playing Poker for the “Long Term”

Using the same coin flip analogy, in a sample size of 10 trials there are going to be times when heads comes up all 10 times. You know each time you flip the coin the odds of it coming up heads are 50%, but over the course of this relatively small number of flips the results seem to defy the odds. However, if you extend the number of flips to 100 or 1000 you will get closer to an accurate result of 50/50.

So that is what the “long term” is in poker. If you make the same play over an infinite number of trials, the resulting amount of chips you earn over time is either going to be positive or negative. Because the distribution of cards is random, there is rarely a guarantee that you will have the winning hand until all the cards are dealt. So in any given hand there is always a probability that the best hand can end up losing and the actual results deviate from the way the odds say they should. In hold’em, a pair of Aces is about an 80% favourite versus a pair of Kings pre-flop. That still means that 20% of the time the pair of Kings will win. But in the long run the Aces have a positive expectation to win.

## Getting the Most Value Out of Hands

Expected value is not just about a singular outcome (winning vs. losing), but it’s also about maximizing the value in every hand you play. This means squeezing the most value out of hands when you are ahead and losing the least when you are behind. It can also mean knowing how much to risk on a bluff where the percentage of times it will work and the value of the pot makes it profitable in the long run.

### How to Squeeze Maximum Value

Let’s look at a hand example to illustrate…

• No Limit Hold’em Tournament Play
• Blinds: 25/50
• You and your main opponent both have 3,000 in chips.

### Pre-Flop

The following hand example will demonstrate how to squeeze maximum value against a player on a suspected drawing hand. Importantly, you already know that this player likes to play suited cards and likes to chase draws. Before the flop, your opponent in middle position limps and you elect to call from the button with . The small blind completes and the big blind checks.

### The Flop

The flop is dealt and everyone checks to you, as shown in figure 1 below:

Figure 1

Jackpot, a set! But wait – what if someone has a flush draw?! Should you be afraid of someone drawing to another heart and try and shut the hand down right now by putting in a big bet? No, you shouldn’t. This is a very common mistake. Many players see the potential flush draw and overbet the pot or push all-in to “protect their hand”. Protection is incorrect thinking because it doesn’t maximize your expected value. If you try to shut the hand down now with a big bet you will lose money in the long run. Does this mean you should slow play by only betting a small amount or even checking? No, it doesn’t. It means that you should bet the maximum amount that you think someone will call to draw to their hand and make an incorrect decision.

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For someone to correctly draw to the flush with one card to come, they need 4-to-1 odds. So in this case, the pot is 200. If you bet 50 trying to slow play, the pot will now have 250 and it will cost them 50 to call giving them 5-to-1 odds (250/50 = 5/1). This would be a correct decision for them to call and would be –EV for you because they will hit their draw better than the 5-to-1 odds you are giving them. So, what is the correct amount to bet? This depends on your opponent. If you know someone likes to chase draws, you should consider betting around the size of the pot. If you know they will only call a reasonable sized bet, then you should bet enough to give them about 3-to-1 odds. This would be an incorrect call on their part.

### Poker Variance Meaning Example

There are additional factors of implied odds to consider here, but that is for another lesson. In this case, you know at least one of your three opponents likes to chase draws, but you can’t be sure he has one now. I would bet around 100. This will make the size of the pot 300 and will give someone 3-to-1 odds to call. The guy in middle position who likes to chase, calls.

### Poker Variance Meaning Examples

The turn is a ten of spades and our opponent checks:

Figure 2

How much should you bet here on the turn to maximize EV? Well, you can be pretty confident that your opponent doesn’t have a King because they would have likely bet the flop against three opponents. While they could have a straight draw if they had a hand like 45 or 34, the most likely hand your opponent has contains two hearts including AX and connectors such as or . If he does have , he now has a pretty big draw and is unlikely to consider folding. But we don’t know that for sure, so we have to bet an amount that maximizes our EV against a range of drawing hands. The pot is now 400 and our opponent has 2,850 left. Based on our opponents tendencies, I would bet around the size of the pot, so let’s make it 350. Our opponent calls.

### The River

The river is a beautiful . If our opponent was on the flush draw, he just hit, but it also gives us a full house. The size of the pot is 1,100 and our opponent bets out 600:

Figure 3

His bet lets us know that he likely has the flush. He could also have a King, but it’s not likely based on his previous actions. Either way, we’re in a great situation.

Now, how do we get the most out of this hand? After his bet of 600, there would be 1,700 in the pot and it leaves him with 1,900. Many beginning players will raise the minimum here because they are afraid of making their opponent fold. But that is leaving money on the table.

Players who often chase draws will not fold when they make their hand. They feel emotionally attached because they have already spent a lot of their stack to get there. Also, we have 1,900 left and if we just raise the minimum to 1,200 we are committing most of our stack which looks like we have a huge hand. I would think for a few seconds and then push all-in. Our hand is pretty concealed and it looks like we have a King, so it’s highly likely we’ll get called here. Our opponent calls showing and we rake in a monster pot.

## Don’t be Results Focused

Since you cannot control the final outcome of any given hand, the goal in poker is not to win every hand, but to make decisions that have a profitable expected value. Sometimes luck is in your favour and sometimes it’s against you, but if you are making +EV decisions that is what makes you money in the long run. It is important not to let negative results get you down or hurt your confidence in your abilities. Just remind yourself that you wanted that donkey to call you down with bottom pair because even though he spiked two-pair on the river this time, he is your personal ATM if he keeps making that play.

A firm grasp of the concept of expected value will serve you well. In our next lesson, calculating EV, we’ll take things a step further and discuss the additional criteria that must be incorporated into your decisions. We’ll also look at some common EV spots in both cash games and tournament poker – all with the intention of positively affecting the long-term profitability of your decisions.

### Related Lessons

By Donovan Panone

Donovan started playing poker in 2004 and is an experienced tournament and cash game player who has a passion for teaching and helping others improve their game.

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