As most video poker players know, not all video poker is alike. There are different games, different pay tables for each game, games with few jackpot-sized winners and those with many jackpot-sized winning hands.
Each of these variations in the game affect that specific game’s variance – a measure of the size of swings, both up and down, in the player's bankroll.
This article explores the differences between high variance and low variance games.
Contents
1. Variance defined
According to investopedia.com, “The term variance refers to a statistical measurement of the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean (average), and thus from every other number in the set.”
In other words, it is a representation of how far things vary from one another.
2. Video poker game features that impact variance
In video poker, low variance means the pays for winning hands do not vary much. High variance means the pays for winning hands vary significantly.
A video poker game that has few or no very high-paying hands and many lower-paying hands tends to have a low variance.
On the other end of the spectrum, video poker games having several low-paying hands along with several very high-paying hands tend to have a high variance.
3. Characteristics of low variance video poker games
As stated in the previous section, low variance video poker games have few or no very high-paying hands and many lower-paying hands. This means that most of the paying hands pay about the same amount.
A good example of a low variance game is jacks or better. There are a total of nine winning hands. They are (from lowest to highest pay):
| Hand | Pays (on standard pay table) |
|
1-for-1 |
Notice that six of the hands pay relatively close to the same amount, and there is only one very high-paying hand (royal flush).
What winning hands pay is only part of the equation that determines variance. The frequency of occurrence and percent of total return must also be considered.
Frequency of winning hands and percent of total return:
| Hand | Freq. % | Cumm. % of Freq* | Cumm. | |
| Return | Return* | |||
|
47.2 28.4 16.4 2.5 2.4 2.5 0.5 0.02 0.005 |
47.2 75.6 92.0 94.5 96.9 99.45 99.97 99.99 100.00* |
21.56 47.54 22.43 4.51 6.64 10.41 5.94 0.55 1.99 |
21.56 47.54 59.97 74.48 81.12 91.53 97.47 98.02 100.01* |
* Totals may not appear properly due to rounding.
Over 99% of the total winning hands pay 9-for-1 or less. Less than one-half of 1% of winning hands pay more.
Also, the three top paying hands contribute about 2.5% of the total return. The rest contribute fairly evenly.
Because of this, the variance for a jacks or better game is low – 19.41 to be exact.
Low variance games have very few high-paying hands. The bankroll fluctuations are minor. These games are good for players who like to see steady results.
4. Characteristics of high variance video poker games
Now let us look at a high variance game – one with more of the winning amounts coming from higher paying hands.
One very popular higher variance game is double-double bonus. This game has 13 winning hands. They are (from lowest to highest paying):
| Hand | Pays (on standard pay table) |
|
1-for-1 1-for-1 3-for-1 4-for-1 6-for-1 9-for-1 50-for-1 80-for-1 160-for-1 160-for-1 400-for-1 50-for-1 800-for-1 (4,000-for-5) |
Notice the much higher payouts for the top several hands. Here is a list of frequency and percent of total return for these hands:
| Hand | Freq. % | Cumm. % of Freq* | Cumm. | |
| Return | Return* | |||
|
47.3 27.5 16.8 2.85 2.5 2.4 0.4 0.09 0.04 0.03 0.01 0.02 0.005 |
47.3 74.8 91.61 94.47 97.01 99.43 99.8 99.89 99.92 99.96 99.97 99.99 100.00* |
21.35 12.44 22.81 5.16 6.89 9.87 8.23 3.11 2.81 2.31 2.485 0.556 1.98 |
21.35 33.78 56.60 61.76 68.65 78.52 86.75 89.87 92.68 94.99 97.474 98.03 100.901* |
* Totals may not appear properly due to rounding.
The double-double bonus statistics show a different story. While the frequency of winning hands looks very similar to those for jacks or better, the percent of return is quite different.
The six lowest paying hands contribute less than 80% of the total return – not the better than 90% return in jacks or better.
The top paying hands contribute over 20% of the total return.
The concentration of over 20% of the return in the less than one percent of the frequency causes the variance to soar – to 41.98.
Adrenaline junkies tend to prefer high variance games.
High variance games have more of the total return concentrated in several high-paying hands. To pay for this, the pays for lower-paying hands are reduced. High variance games tend to have wild bankroll fluctuations. More frequent high paying hands shoot the bankroll up and reduced pays for other hands quickly drain the bankroll.
This fluctuation means a larger bankroll is required in order to ride out the losing streaks.
For more information on bankroll requirements, go here: Video Poker Bankroll Requirements
5. Summary
- Variance is low when most or all of the winning hands pay roughly the same amount.
- Variance is high when a larger portion of the total return is concentrated in fewer, higher paying hands.
- Low variance games require a smaller bankroll.
- High variance games are a wild ride.
- High variance means high bankroll requirements.
