Expected
Values of Video Poker Hands
Video
poker hands are paid based on the level of difficulty of making
the hand. How the
hands are paid off is disclosed on the face of the video poker
machine. By using
this payoff information and by knowing just how difficult it is
to make any particular hand, we can evaluate how to correctly
play any hand.
Let's
consider again the hand dealt us of:
5©6©7©8§8¨.
This hand is either a low pair, a four card straight, a
threecard straight flush or we could even discard all of the
cards and draw five new ones.
To
evaluate which hand to pursue, we must first know which version
of video poker we are playing.
Let's assume that we are playing a popular version of
video poker which pays on any pair of Jacks or Better and does
not use any wild cards. This
version (known as 96 Jacks or Better) offers the pay schedule
shown in Table 2.
This
version of video poker is one of the best around for both
longterm and shortterm play and is found throughout Nevada.
The "96" refers to the payoffs for Full Houses
and Flushes. Casinos
commonly "monkey around" with these payoffs.
Thus you will find 85 and 65 versions of the game,
where the payoffs on a Full House have been reduced from 9 for
one to 8 for one or 6 for one, and the payoffs on the flush
reduced from 6 for one to 5 for one.
These
may not seem like big reductions in payoffs, but they make a
huge difference in how beatable the game is.
We will go over the different versions of video poker in
a couple of chapters, but for now, let's just assume that we
have found a 96 Jacks or Better video poker machine and that it
has the following payback schedule:
Table
2. Pay Schedule for
96 Jacks or Better
Royal
Flush

800
per coin (usually shown as 4,000 for 5 coins)

Straight
Flush

50

Four
of a Kind

25

Full
House

9

Flush

6

Straight

4

Three
of a Kind

3

Two
Pair

2

Jacks
or Better

1

Any
winning poker hand in this version of video poker will pay off
in accordance with this pay schedule.
If we are dealt a high pair, say a pair of Kings, then
our payoff will equal the amount of money wagered.
Any other winning hand will be paid off in the same
manner. If we have
a straight, we will get 4 times our wager, a flush will pay 6
times our wager, and so on.
In
the case of winning hands, the value of the hand is simply the
amount shown on the machine's pay schedule.
To simplify matters, we will assume that the amount
wagered is one dollar and express all values in dollars.
Using this approach to valuing hands, a straight is worth
$4 and a flush $6.
To
obtain these values, we are really multiplying our possibility
of winning times and potential payoff.
With made hands, our possibility of winning is certain,
that is 100%, which is expressed mathematically as 1.0.
To determine the value of a hand, we multiply the
probability of making the hand times the payoff for making the
hand. Thus the
value of a made flush, such as 2©4©7©8©J©,
is 1.0 x 6 for a value of 6, which we will call $6.00.
With
hands that are not yet winners, we can use the same approach to
evaluate them. We
can multiple the probability of winning with that hand, times
the payoff if the hand wins.
This
approach to evaluating the value of different poker hands is
called calculating the Expected Value of the hand.
In calculating an expected value, we have a simple
way of comparing the value of one poker option with another.
Going
back to our hand of 5©6©7©8§8¨, we could evaluate all the possibilities of keeping the pair of eights
and drawing three cards by looking at all of the possible
combinations of hands.
There are 16,215 possible draws, which would include 4 of
a Kind  45 times, a Full House  165 times, 3 of a Kind  1,854
times, Two Pairs  2,592 times and no value hands  11,559
times.
To
convert this information into a form we can use for computing
the value of different options, we must multiply the frequency
of each hand times its possible payoff and compare these values
with the total number of draws.
Table 3 shows these calculations for discarding three
cards and drawing to a low pair.
Table 3.
Expected Value of Drawing to a Low Pair
Hand

Frequency of Hand

Payoff
of Hand

Frequency x Payoff

4
of a Kind

45

25

1,125

Full
House

165

9

1,485

3
of a Kind

1,854

3

5,562

2
Pairs

2,592

2

5,184

Total
Possible Draws with Payoffs

13,356

Total
Number of Possible Draws

16,215

Expected
Value (Possible Draws/Total Number of Draws)
13,356/16,215 =

.824

Before your eyes start to glaze, relax.
I am not going to make you do any calculations like this.
I just wanted to show you what's involved in computing
the expected value of a hand.
This
means that the value of keeping the low pair and drawing three
cards is $.82. Anything
less than a dollar means that our whole bet won't be returned.
So this hand is going to be a loser on the average.
But that doesn't mean that we shouldn't play the hand to
its highest potential. Let's
take a look at the other options of drawing to a 4card straight
or a 3card straight flush.
Computing
the expected values for these hands as well as the low pair, we
have:
Hand
Expected Value
Keep
Low Pair
$.82
Keep
4 Card Straight
.68
Keep
3 Card Straight
.58
When
faced with a decision like this, calculating the expected value
makes our decision of what to do easy.
Our basic rule of play is to always go for the hand
with the highest expected value.
In this case, we will keep the pair of eights and draw
three cards.
Let's
consider another hand of T©J©A©2©2¨. If we hold just the low
pair of twos, the value of this hand is $.82.
But what if we decide to go for the Royal Flush and hold
the T©J©A©
and draw two cards? The
expected value of this option in the 96 Jacks or Better version
of video poker is $1.32. But
there's still yet another option isn't there?
Let's
see what happens if we hold four Hearts and go for a flush.
The value of this option is $1.28.
Here's
a summary of our three options:
1.
Hold the low pair of Twos
$.82
2.
Hold the 10, Jack and Ace of Hearts
1.32
3.
Hold the four Hearts
1.28
The
calculations show us that the prudent course here is to keep the
T©J©A©
combination,
and discard the low pair. You
may think that it is the possibility of making a royal flush
that makes this option more viable, but the royal flush can only
be made one way with this draw.
There
are 1,081 combinations of two cards that can replace the pair of
Twos. These
include a pair of Jacks or Better  240 times; Two Pairs  27
times; Three of a Kind  9 times; a Straight  15 times; a Flush
 27 times and only one way of making a Royal Flush.
Adding up the values for each of these possibilities
gives us a value for the hand of $1.32 and tells us that
discarding the low pair is our best option.
Your
approach to playing video poker hands should now be obvious.
You should always play the hand with the highest rank or
value.
The
above information was taken from the Power Video Poker manual.
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