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UNDERSTANDING VARIANCE WHEN YOU PLAY VIDEO POKER

by Henry Tamburin

Henry Tamburin is an expert on blackjack and video poker, the author of five books on casino gambling, featured blackjack and video poker writer for dozens of magazines and web sites, editor of the Blackjack Insider Newsletter, and host of www.smartgaming.com.

Astute video poker players know that the best games to play are those that have an ER close to, or slightly over, 100%, using perfect playing strategy. However, there is another characteristic of video poker games that is not so well known but just as important and thatís volatility.

A game that is volatile means your bankroll will experience some nasty up and down swings, and if you are not properly bankrolled, you can easily tap out. We can quantify volatility, and the term most frequently used in video poker circles to do this is variance per coin wagered. Simply put, the higher the variance, the more volatile the game.

Another way to look at variance is this: In the short term, a game that has a high variance means your expected results will more than likely be greater or lesser than the theoretical or expected results. This means a game that has a high variance will most likely result in bigger bankroll swings (both positive and negative); therefore, youíll need more bankroll to play a volatile game to avoid going broke. (Thus, players with small bankrolls should not be playing video poker games that are highly volatile.)

What makes one video poker game more volatile than another is the amount of the payoff for winning hands at the top of the pay schedule (the rarely hit hands) vs. the payoff for the hands at the bottom of the pay schedule (the more frequently hit hands). A game that is more volatile (i.e., has a high variance) generally pays more for hands at the top of the pay schedule whereas a game with a low volatility, pays more for hands located at the bottom of the pay schedule.

For example, look below at the per coin pay table below for 9/6 Jacks or Better (low volatility) and 10/6 Double Double Bonus (high volatility). Iíve also listed the contribution each hand makes to the overall ER of the game (column labeled % Return). Notice that the variance of 9/6 Jacks or Better (JOB) is 19.51 whereas for 10/6 Double Double Bonus (DDB), its 42.18 (meaning itís more volatile). The reason the latter is more volatile is that it pays more for 4-of-a-Kind hands (or quads) than JOB. If you get quads in JOB, you are paid 25 coins per coin wagered. With 10/6 DDB, youíll get paid more, from a high of 400 coins if you get four Aces with a 2, 3, or 4 kicker to a low of 50 coins for four 5s through Kings (see pay schedule for the payouts for all the quads). More importantly look at the contribution the quads make toward the overall ER for each game. In JOB, quads contribute 5.91% toward the overall 99.54% ER for the game, whereas in 10/6 DDB, the quads contribute 23.51%. The latter is a classic example of a highly volatile game. (Greater payouts in the less frequently hit hands at the top of the pay table). Moreover, look at the return for the more frequently hit two pairs at the bottom of the pay table. In 9/6 JOB, you get paid 2 for 1 for two pairs (contributing 25.86% return) whereas in 10/6 DDB, two pair pays only even money (with a corresponding 12.31% return). This is another reason why 9/6 JOB has low volatility and 10/6 DDB has high volatility.

 

9/6 Jacks or Better

Pay Table

% Return

Royal Flush

800*

1.98

Straight Flush

50

0.55

4-of-a-Kind

25

5.91

Full House

9

10.36

Flush

6

6.61

Straight

4

4.49

3-of-a-Kind

3

22.33

2 Pair

2

25.86

Jacks or Better

1

21.46

ER

99.54%

99.54

Variance

19.51

 

* Assuming max coin wagered.

10/6 Double Double Bonus

 

Pay Table

% Return

Royal Flush

800*

1.96

Straight Flush

50

.55

4 Aces with 2/3/4

400

2.46

4 Aces

160

2.29

4 2s, 3s, 4s with A/2/3/4

160

2.78

4 2s, 3s, 4s

80

3.08

4 5-Kings

50

8.15

Full House

10

10.86

Flush

6

6.78

Straight

4

5.10

3-of-a-Kind

3

22.59

Two Pair

1

12.31

Jacks or Better

1

21.15

ER

100.07%

100.07%

Variance

42.18

 

* Assuming max coins wagered.

Hereís a dollar-and-cents example of why you need more bankroll if you play a video poker game with a higher volatility. Suppose you want to play two hours (1000 hands) on a quarter-denomination video poker machine with a $200 bankroll. By using the Bankroll Function in Video Poker for Winners software, you can calculate what the chance is that you will lose your $200 bankroll (i.e., your risk of ruin) if you were to play the more volatile 10/6 DDB vs. the less volatile 9/6 JOB.

The table below summarizes your risk of ruin, or the percent of the time you will go broke in two hours, playing both games...

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