Helping You Understand Bankroll Needs – Volatility

Here’s another guest article by Henry Tamburin, one that discusses a subject that weighs so heavily into your bankroll calculations – volatility.   Articles on this subject often make players eyes glaze over with their complicated “mathspeak” and complex  formulas but here Henry gives examples and charts and  “plain English” explanations that will help even the most  “non-mathematical” player.  Plus it is a good start for those who wish to dig deeper into the subject.

 

UNDERSTANDING VARIANCE

By Henry Tamburin

Astute video poker players know that the best games to play are those that have an ER (Expected theoretical return) 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 that’s 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, you’ll 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 at the per coin pay table below for 9/6 Jacks or Better (low volatility) and 10/6 Double Double Bonus (high volatility). I’ve 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 it’s 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, you’ll 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 4 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.

 

Here’s 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 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. You have only slightly more than a 1% chance of tapping out if you play the low-volatile 9/6 JOB but a whopping 25% of going broke when you play the more volatile 10/6 DDB. (That a sobering statistic … 1 out of every 4 two-hour sessions you will lose your $200 bankroll on average, even though the ER for 10/6 DDB is slightly over 100 percent when you play every hand perfectly.)

 

Game	Risk of Ruin
9/6 JOB	1.28%
10/6 DDB	25.12%

 

This is the reason that players who have modest bankrolls will most likely tap out when playing video poker games with a relatively high volatility. If you have a sufficient bankroll, then playing 10/6 DDB with a 100.07% ER is a great game. How much bankroll do you need? If you take the above example, to get the same risk of ruin as 9/6 JOB (1.28%), you would need a bankroll of $337 for your two-hour session (that’s 68% more bankroll compared to what you would need for the same risk as JOB). (This is what we mean when we say you need more bankroll when playing a game that is more volatile.)

The Table below lists the variance for a sampling of popular video poker games. As a guide, games that have a variance below 21 have low volatility, from 21-50 are medium volatility, and over 50 is a highly volatile game. (You can look up the variance for different video poker games in the book Video Poker for Winners by Bob Dancer, or by using either Video Poker for Winners or Optimum Video Poker software programs. The booklet The Frugal Video Poker Scouting Guide by Jean Scott and Viktor Nacht also summarizes the volatility of different video poker games. )

 

Game	Variance
9/6 Jacks   or Better	19.51
8/5 Bonus   Poker	20.90
8/5 Aces   and Faces	20.95
16/10 NSU   Deuces Wild	25.78
10/7 Double   Bonus	28.26
8/6 Bonus   Poker Deluxe	31.96
18/7/5   Joker Wild Kings or Better	33.09
8/5 Super   Double Bonus	38.64
10/6 Double   Double Bonus	42.18
15/10   Double Deuces Wild	50.93
8/5 Super   Aces Bonus	63.36
15/10 Loose   Deuces Wild	70.31
16/8/5   Joker Poker 5-of-a-Kind	70.41
9/6 Triple Double   Bonus Poker	100.11

 

Summary

1. Video poker games have different volatility.
2. Games that have a high volatility have a high variance.
3. When you play a game with a high variance,  your bankroll will experience higher peeks and lower valleys in your profits  and losses.
4. You’ll need more money if you  play a game with a high variance to prevent going broke.
5. Check the pay table of the game.   If it has higher payouts for hands at the top of the pay table and smaller payouts at the bottom of the pay table, the game is most likely very volatile.

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Henry Tamburin is the editor of Blackjack Insider, a newsletter that focuses on the game of blackjack.  However,  he often included articles specifically on VP and also  on many general gambling subjects that would be of interest to all casino visitors.  Look here for a link to a special subscription sign-up bonus.