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Finding the best Video Poker games online
Video Poker, and casino games in general, can be characterized by
their expected return and risk. We have done so on numerous occasions.
For example, a classification of Blackjack, Video Poker, Baccarat,
Pai Gow Poker, Let It Ride, Caribbean Stud and Roulette, in terms
of expected return and risk can be found here.
Furthermore, a similar discussion on Deuces Wild video poker is available
here.
In this article we will first define expected return and risk in
layman terms. We will then proceed to explain why these two concepts
are *not* ideally suited to compare video poker games, and propose
a better indicator to do it. Finally, we will give you an example
how this new indicator works, by using it to compare almost all
Video Poker variants that are available online. We will *not* teach
you how to win at video poker, but you *will* learn which online
video poker games offer the best chances to win (under the
assumption you play optimally).
Expected return and House Edge
The expected return of a game is closely related to the house edge.
The higher the house edge (casino advantage) of a particular game,
the more money you will expect to lose in the long term. So expected
return is really nothing more than the house edge expressed from a
player's standpoint. Simply put:
Expected Return = - House Edge
Risk or Volatility
The risk or volatility of a game is often measured by it's variance
or standard deviation. A definition of variance or standard deviation
is beyond the scope of this article. All you need to know is that
these indices are both indicators of how much your *actual* return
will deviate from it's expected return. A high variance or standard
deviation indicates your bankroll will move up and down much more
than it would with a low variance or standard deviation.
A better way to compare video poker games?
Many players only look at the expected return of a video poker game
when deciding if it's a good game to play. The risk of a game is often
completely ignored, because this information is either not available,
or too technical to understand. And even if this information is available,
which game would *you* play: a game with a high expected return and
high risk, or a game with a slightly lower expected return, but also
with a much lower risk?
What is needed is an indicator that combines Expected Return, Volatility
as well as your Risk Aversion into one single number. For this purpose
we designed a new indicator, the Risk-Return Index (RRI), and we
will define it as follows:
RRI = Risk-Return Index = Expected Return - Relative Volatility*Risk
Aversion
The idea is to take the Expected Return of a game as a starting
point, and then decrease it when the Relative Volatility gets higher,
and the more so your Risk Aversion is higher. Relative Volatility
equals the Volatility of a game defined as a percentage of it's
Expected Return:
Relative Volatility = 100*(Standard Deviation/Expected Return)
Risk Aversion is defined as a variable between -1 and 1, which
expresses your attitude to risk. If it's zero you are risk
indifferent and the Risk-Return Index equals Expected Return. If
it's positive you are risk averse (you don't like risk),
and the Relative Volatility is fully subtracted from a game's Expected
Return. If it's negative you are risk tolerant.
-1<= Risk Aversion <= 1
The Risk-Return Index of a game can be used to compare Video Poker
games for all types of players, by simply varying the Risk Aversion
variable between -1 and 1. However, in the remainder of this article
we will assume you are moderate risk averse, with a Risk Aversion
of +0,5. Most people are risk averse, that is if they had to choose
between two video poker games with the same expected return, they
would choose the one with the lower volatility. Of course, nothing
stops you from repeating our calculations using your own estimate
of the Risk Aversion variable.
The best Video Poker online measured by the Risk-Return Index
(RRI)
In the final section of this article we will compare all video pokers
available online (but limited to Microgaming, Playtech, Boss Media,
Cryptologic and Real Time Gaming) in terms of their Risk-Return Index.
All video poker variants are listed in the table below, sorted by
their Risk-Return Index (better games are listed before worse games).
It's important to note that we assumed your attitude to risk is expressed
by a Risk Aversion of +0,5. Both expected return and variance of each
video poker variant were calculated using "Bob Dancer
Presents WinPoker" by Zamzow
Software.
| Video Poker Variant |
Software |
Expected Return |
Variance |
Risk-Return Index |
| Full pay Deuces Wild |
|
100,7620 |
25,83462 |
98,24 |
| Pick 'em Poker |
RTG |
99,4466 |
14,90929 |
97,51 |
| Jacks or Better |
Microgaming |
99,5439 |
19,51468 |
97,33 |
| Jacks or Better |
Playtech |
99,5439 |
19,51468 |
97,33 |
| Full pay Jacks or Better |
|
99,5439 |
19,51468 |
97,33 |
| Double Bonus |
Cryptologic |
99,9367 |
31,98543 |
97,11 |
| Double Jackpot |
RTG |
99,3953 |
21,76472 |
97,05 |
| All American |
RTG |
99,5979 |
26,46673 |
97,02 |
| Aces & Faces |
Microgaming |
99,2555 |
20,95179 |
96,95 |
| Aces & Faces |
Playtech |
99,2555 |
20,95179 |
96,95 |
| Tens or Better |
Microgaming |
99,1388 |
19,50156 |
96,91 |
| Tens or Better |
Boss Media |
98,3998 |
8,80674 |
96,89 |
| Bonus Poker |
RTG |
99,0618 |
20,75425 |
96,76 |
| Double Bonus Poker |
RTG |
99,3693 |
27,50922 |
96,73 |
| Double Double Jackpot |
RTG |
99,3359 |
33,43641 |
96,43 |
| Deuces Wild Power Poker |
Microgaming |
99,3747 |
35,03345 |
96,4 |
| Deuces Wild |
Playtech |
98,9131 |
25,61744 |
96,35 |
| Deuces Wild |
RTG |
98,9131 |
25,61744 |
96,35 |
| Aces & Eights |
RTG |
98,6303 |
21,57253 |
96,28 |
| Sevens Wild |
RTG |
98,7988 |
26,55395 |
96,19 |
| Bonus Deuces Wild |
RTG |
99,0625 |
32,75408 |
96,17 |
| Jacks or Better |
Cryptologic |
98,2534 |
18,91092 |
96,04 |
| All American |
Cryptologic |
98,1100 |
21,05036 |
95,77 |
| Tens or Better |
Cryptologic |
97,9598 |
18,98287 |
95,74 |
| Tens or Better |
Playtech |
97,9598 |
18,98287 |
95,74 |
| Double Joker |
Microgaming |
98,1005 |
21,81212 |
95,72 |
| Deuces & Joker |
Microgaming |
99,0675 |
45,58855 |
95,66 |
| Joker Poker |
Playtech |
98,5987 |
35,91720 |
95,56 |
| Joker Poker |
Microgaming |
98,5987 |
35,91720 |
95,56 |
| Deuces Wild |
Cryptologic |
97,9716 |
24,98064 |
95,42 |
| Deuces Wild (1 hand) |
Microgaming |
97,9563 |
25,21670 |
95,39 |
| Joker Poker |
Cryptologic |
97,9469 |
25,35133 |
95,38 |
| Double Double Bonus Poker |
RTG |
98,4888 |
38,41116 |
95,34 |
| Jacks or Better |
RTG |
97,2984 |
19,32326 |
95,04 |
| Loose Deuces |
RTG |
99,0722 |
70,87180 |
94,82 |
| Bonus Poker Deluxe |
RTG |
97,5908 |
30,67764 |
94,75 |
| Jacks or Better |
Boss Media |
95,4828 |
30,49747 |
92,59 |
Suggested reading
Video Poker - Optimum Play, Dan Paymar,
1998-2003, ISBN 1-886070-11-3, ConJelCo LLC (page 27)
Also take a look at Dan Paymar's video
poker website.
Dan Paymar defines the Attractiveness Quotient (AQ) of a game as (Expected
Return - 100) x (1000/Standard Deviation). AQ can be used to compare
positive expectation games, but doesn't work for negative expectation
games. This was the motivation for us to come up with a new indicator,
which we called the Risk-Return Index (RRI), and defined above. Like
AQ, the Risk-Return Index takes into account both expected return
and volatility of a video poker game, but unlike AQ it also works
for negative expectation games, and furthermore takes into account
your attitude to risk, by using a Risk Aversion variable.
BTW, thanks to TomSki , the author of VP
Strategy Master, who suggested the name Risk-Return Index.
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