I have a newly designed website and my blog is integrated with in it.

You can go to www.gambatria.com for the website or

www.gambatria.com/blog/ for the blog.

## Thursday, February 6, 2014

## Thursday, January 16, 2014

### Getting Ugly

For the past few weeks, I've been slowly walking through
the strategy table for full-pay jacks or better video poker. I'm about 2/3 of the way though and what's
left is well, just not pretty. The
expected values of the rest of the table are below 0.60. This means you can expect, on average, a
return of only 60% of your wager. But,
as I've explained the past few weeks, learning to play the ugly hands is at
least as important as learning how to play the good hands. It is also probably more difficult to learn these
hands as there are a lot of subtle nuances and a great deal of overlap. For example, one of the hands from last week
was the 2-Card Royal with no Aces or 10's.
This week's top hand is a 4-Card Inside Straight with 4 High Cards,
which is really a 4 High Card hand.
There is only one way this occurs -
J Q K A. But, if we compare this
to the 2-Card Royal we realize that if TWO of the J/Q/K are suited, we actually
go that route instead of the 4-Card Inside Straight.

Let's take a look at the next few entries and see what we
can learn from them:

· 4-Card Inside Straight with 4 High Cards

· 2-Card Royal with an Ace, but no 10

· 3-Card Double Inside Straight Flush with 1 High Card

· 4-Card Inside Straight with 3 High Cards

· 3-Card Inside Straight Flush with 0 High Cards

· 3 High Cards

Okay, so we've already covered a critical point of these
hands above. Adding to the complexity
however is the 2nd rule down when compared with the 1st. IF the 2 suited cards are an Ace and either
the Jack, Queen or King, THEN we keep the 4-Card Straight!

Next up is the 3-Card Double Inside Straight Flush with 1
High Card. So, a suited 8-9-Q would
cover this. This can't overlap with our
2-Card Royals, but can overlap with a 4-Card Inside Straight (8-9-Q suited with
a Jack off-suit). This would make it a
4-Card Inside Straight with 2 High Cards.
You'll note that the 4-Card Inside Straight with 3 High Cards is below
the 3-Card Double Inside Straight with 1 High Card, so surely the 2 High Card
version is even lower. In reality, we
won't find it on this strategy table at all as a 4-Card Inside Straight with 2
or less High Cards is NOT a playable hand in full-pay jacks or better. In this case we would keep the 3-Card
Straight Flush over the 4-Card Straight.

The next hand is the 3-Card Inside Straight Flush with 0
High Cards (i.e. 5-7-8 suited). If we
have a 6 off-suit this would be a 4-Card Straight with 0 High Cards which is
much higher in the table and thus would be played as the 4-Card Straight. If we have a 4 off-suit, then it is a 4-Card
Inside Straight with 0 High Cards. If
the 2 High Card version is not playable then for sure neither is the 0 High
Card Version. We would play the 3-Card
Straight Flush.

The 3 High Card hand is a critical hand to learn
about. It is frequently misplayed. There are four possible High Cards - Jack,
Queen, King and Ace. However, 3 High
Cards is a bit of a misnomer. In order
for the hand to be 3 High Cards, it MUST be J-Q-K. If we have J-Q-A we would discard the Ace
unless the Ace matches in suit to one of the other two then it would play as a
2-Card Royal. In similar fashion, we
would ONLY play J-Q-K if the three are of different suits. Otherwise we would again have a 2-Card Royal
(V3) and would play the hand that way.
The 2-Card Royals are frequently overlooked when there is a 3rd High
Card, but this is simply not the right way to play the hand.

There are only 5 more hands on our strategy table and I
will cover them next week. These five hands all have expected value below
0.50. Unfortunately, they account for
about 1/3 of all hands dealt - so they are critical to learn.

Labels:
Double Inside Straight,
expected value,
High Cards,
Inside Straight,
strategy table,
Video Poker

## Thursday, December 26, 2013

### Distinguished Royals

I've spent the past few weeks walking through the
strategy table for full-pay jacks or better video poker. This week, we are in the heart of the table,
which is to say we are in the middle of the really bad hands. But, bad hands are the harder hands to play
correctly and are just as important as the good hands in achieving the
theoretical strategy of any particular game.
We finished up last week with the 4-Card Straights. From here the hands only get uglier. The next several entries are:

· 3-Card Double Inside Straight Flush with 2 High Cards

· 3-Card Inside Straight Flush with 1 High Card

· 3-Card Straight Flush with 0 High Cards

· 2-Card Royal Flush - "V3"

If you're relatively new to strategy tables, this part of
the table has problem just given you a doozy of a headache! The good news is that it is not nearly as
confusing as it might appear. Many of
the hands listed above cannot co-exist - meaning that you can't have more than
one in a particular hand. Thus, remembering
the exact order may not be as important as it might appear to be. For example, you can't have a 3-Card Double
Inside Straight Flush with 2 High Cards in the same hand as a 3-Card Straight
with 0 High Cards. You'd either have to
have at least 4 cards of one suit or have 2 sets of 3-Cards of different suits
- rather difficult with 5 cards.

There are still important things we can learn from this
section of the table. We separate the
hands the way we do because in some games the impact of the subtle differences
and the order of the hands will be different and thus become pertinent. The first thing you might notice is the
relationship of the top three hands. We
get a sense of the importance of a High Card.
A 3-Card Double Inside Straight Flush with 2 High Cards has a higher
expected value than a 3-Card Inside Straight Flush with only 1 High Card. Essentially, the value of the extra High Card
is greater than the value of the additional Straight Flushes (and Straights)
that may occur as a result of having an Open vs. Inside vs. Double Inside
Straight Flush. What this should also
tell us is that you shouldn't hold your breath for those Straight Flushes. They will occur, but not often. At the same time, I have written at length
over the years about how the Straight Flush is the forgotten hand of video
poker. Playing 3-Card Straight Flushes
correctly is very important to drawing them in proper abundance. While their pays are far short of the Royal,
they still pay double what Quads pays so their value should not be dismissed.

Next up is the 2-Card Royal Flush - "V3". 2-Card Royals are given 4 different
designation from "V0" to "V3". We
need to do this because the expected values of many of the hands in this part
of the table differ by only 0.01 or 0.02.
As not all 2-Card Royals have identical expected values, we need to
distinguish between them. V3 means that
the 2-Card Royal contains neither a 10 nor an Ace. An Ace in a 2-Card Royal essentially makes it
a Double Inside Royal. All 2-Card Royals
have the same number of ways to make a Royal - one. But, with the Ace, we eliminate all ways to
make a Straight Flush. While a '10'
doesn't have this problem, it does have the problem that it is not a High
Card. So, Aces are worth less than
Jacks, Queens and Kings and 10's are worth less than Aces. Thus, a 2-Card Royal with neither an Ace nor
a '10' is the one with the highest expected value. A V2 2-Card Royal means that the 2-Card Royal
has an Ace, but no 10. A V1 2-Card Royal
is one that has no Ace, but does have a 10.
Lastly, a V0 2-Card Royal consists of a 10 AND an Ace.

For the moment, I'll jump to below the strategy table -
to the V0 2-Card Royal. We are 'below'
the strategy table because this hand does not exist on the strategy table for full-pay
jacks or better. This means that we DO
NOT PLAY an A-10 2-Card Royal. Barring
the other three cards forming an otherwise playable hand, we would simply hold
the single Ace. More on that in a couple
of weeks.

The proper play of 2-Card Royals is critical to learning
how to master video poker strategy.
Unlike the prior 3 hands, 2-Card Royals overlap with EVERYTHING. You'll have 2-Card Royals with High Pairs,
Low Pairs, 4-Card Straights, 4-Card Flushes, 3-Card Straight Flushes, 3-Card
Inside Straight Flushes, etc... If you
blindly go after every 2-Card Royal, you'll hit more than your fair share of
Royals, but you'll lower the payback of your play. If you ignore 2-Card Royals, you'll miss you
fair share of Royals AND lower the payback of your play. The only answer is to play them when you are
supposed to. Based on the portion of the
strategy table shown, you can easily have a 3-Card Double Inside Straight Flush
with 2-High Cards AND a 2-Card Royal - V3.
For example, you could have 8-J-Q suited. From the strategy table, we learn that we
keep the 8 in this case. You might also
have a 3-card Straight Flush completely apart from a 2-card Royal. For example, 3H, 4H, 5H, JD, QD. In this case, we discard the 2-Card Royal in
favor of the 3-Card Straight Flush with 0 High Cards.

I've now covered about 2/3 of the strategy table for
jacks or better video poker. Next week,
we continue through the rest of the messy hands.

## Thursday, December 19, 2013

### Stroll Through the Strategy Table

This week we continue our walk through a video poker
strategy table. Specifically, the
strategy table for full-pay jacks or better video poker. Last week we left off at the 4-Card Flush
which was the last of the hands with an expected value of greater than
1.0. These are the hands that result in
net wins in the long run. The rest of
the strategy table have expected values below 1.0. This means that in the long run we will not
get back our entire wager. But, that
doesn't make them any less important.
When playing video poker, playing every hand correctly is critical if
you want to achieve the theoretical payback.

It could be argued that playing the hands below 1.0
correctly is more important than playing the ones above this line
correctly. First, the hands below make
up the lion's share of hands. Second,
the hands below are by far more complex than the ones above. You don't have to worry about confusing a
Two-Pair with a 4-Card Straight Flush as this is an impossibility. But a 4-Card Straight vs. a 3-Card Straight
Flush might leave you shaking your head.

Without further ado, here are the next batch of hands on
our strategy table:

· 4-Card Straight with 3 High Cards

· Low Pair

· 4-Card Straight with 2 High Cards

· 4-Card Straight with 1 High Card

· 3-Card Inside Straight Flush with 2 High Cards

· 3-Card Straight Flush with 1 High Card

· 4-Card Straight with 0 High Cards

The first thing you'll probably notice is that with the
exception of the Low Pair, the number of High Cards is specified. When the inventor of video poker decided to
pay on Jacks or better, he added an incredible layer of complexity to the
strategy. Simply put, in any hand
without a Pair or better, any card that is a Jack or higher is worth
considerably more than any other card. The
reason should be fairly obvious. We have
the opportunity to win with High Pairs.
For each High Card in the hand, we have three additional cards that we
can draw that will turn our hand into a winner.
These three cards add just over 0.06 to the expected value of the
hand.

Sometimes, this 0.06 means nothing and sometimes it means
everything. We just need to look at the
first three hands to see the impact. If
you have a 4-Card Straight with 3 High Cards and a Low Pair, you keep the
partial Straight. If you have a 4-Card
Straight with 2 High Cards and a Low Pair, you keep the Lower Pair. These hands are not very common, but they
illustrate the impact of the High Card.
So, if you have 10-10-J-Q-K (assuming no 3-Card Royal), then you keep
the Straight. If you have 9-10-10-J-Q
then you keep the Low Pair. Having a 9
instead of a King lowers the expected value so that it falls just below that of
the Low Pair.

If we keep moving down the chart, we find that the next
entry is the 4-Card Straight with 1 High Card.
As this is adjacent to the 2 High Card version, there really is no
impact in this case. We could lump these
two hands together if we want to remove 1 hand from the strategy table. We keep them separate because there are
versions of video poker where it is relevant and we want to make sure the
Player doesn't get 'lazy'.

In between a 4-Card Straight with 1 High Card and a
4-Card Straight with 0 High Cards we find 2 other hands. They are both variants of a 3-Card Straight
Flush. The first is an Inside Straight
Flush with 2 High Cards and the second is a 3-Card Straight Flush with 1 High
Card. This can start looking more
confusing than it really is. Most of
these hands CANNOT occur in a single hand.
It is not possible to have both a 3-Card Straight Flush with 1 High Card
and a 3-Card Inside Straight Flush with 2 High Cards. But, you can have a 4-Card Straight with 1
High Card with a 3-Card Straight Flush with 1 High Card. (8C 9D 10D JD 4H). We learn from the strategy table that the right
play is the 4-Card Straight.

One last point that I should mention. All the 4-Card Straights to this point have
been Open Straight Flushes - meaning that they can be completed on both
ends. This means that as we have
completed about 60% of the strategy table, we have accounted for all Pairs and
for all 4-Card Straights (Open ended) and 4-Card Flushes. The remaining 40% of the strategy tables
contains very 'not pretty' hands. It is
a mish-mosh of 3-Card Straight Flushes, Inside Straight Flushes and even Double
Inside Straight Flushes, along with 2-Card Royals and hands with just High
Cards. To make matters worse, these 40%
of the entries account for nearly 50% of the hands.

Next week, we'll continue our stroll through the strategy
table.

Labels:
draw poker,
expected value,
High Cards,
jacks or better,
Low Pair,
Partial Straights,
strategy table,
Video Poker

## Thursday, December 12, 2013

### Get the Inside Scoop

Last week I began reviewing the strategy table for
full-pay jacks or better video poker. I
got about 20% of the way through the table by volume, but not very far in terms
of useful information. The top 8 hands were
mostly of the no-brainer category as they were the pat hands with the exception
of the 4-Card Royal. This week, I'll
keep moving down the table and provide some insight into the nuances of video
poker strategy. Please remember that
this particular strategy is applicable ONLY to full-pay jacks or better.

After a Straight, we find the following entries on our
table:

· 4-Card Straight Flush

· Two Pair

· 4-Card Inside Straight Flush

· High Pair

· 3-Card Royal Flush

· 4-Card Flush

The first thing you might notice about the above entries
is that we have two entries for a 4-Card Straight Flush and a 4-Card Inside
Straight Flush. There is a big
difference between the expected values for Straights that are open and those
that are Inside (or Double Inside). The
common definition of Inside Straight is when the opening is in the middle and
not on the ends (i.e. 5-6-7-9). However,
this leaves off some Inside Straights.
It is more accurate to define a 4-Card
Inside Straight as one that can only be filled ONE WAY. So, an A-2-3-4 can only be filled with a 5
and thus is an Inside Straight. With
this definition you can see that an Inside Straight can be completed with only
4 cards while a regular Straight can be completed with 8 cards. Straight Flushes are no different - except
they have the possibility of being turned into Flushes as well.

In this particular case, there is really no benefit to
splitting out the 4-Card Straight Flushes.
The one hand that lies between them can't possibly be a 4-Card Straight
Flush (Inside or not). We show them
separately because in some version of video poker, the hands that appear in
between may be able to overlap with them and we will find that in some cases we
will want to keep a 4-Card Straight Flush ONLY if it is not an Inside Straight
Flush. Also, as we will see as we move
down the table, this distinction becomes very important as we take a closer
look at 4-Card Straights.

The 4th entry on the table is a critical one - High
Pair. It is the 4th most common
hand. Thus, playing it correctly is very
important. Looking at the entries above
it and below it what we learn is that a High Pair is played OVER any 4-Card
Straights and 4-Card Flushes. We will,
however, play all 4-Card Straight Flushes over a High Pair. But, we will NOT play a 3-Card Royal over the
High Pair. So, if you have a suited
J-Q-K along with another Queen, you stick with the sure winner - the Pair of
Queens.

Below High Pair, we have a 3-Card Royal Flush and a
4-Card Flush. There is much to learn
here as well. The most obvious is that
if you have a 3-Card Royal and a 4-Card Flush, we hold the 3-Card Royal. This can be a tough choice because the
likelihood of hitting the Royal is still relatively small. But, by holding a 3-Card Royal we give
ourselves more chances for a Straight.
We might still hit a Flush and we have the longshot at the Royal. Also, with a 3-Card Royal, we leave ourselves
2-3 cards that can be matched up for a High Pair. The expected values are not really all that
close with a 1.41 for the 3-Card Royal and 1.22 for the 4-Card Flush. The decision is relatively clear.

From these entries we also learn that if the Player has a
3-Card Royal that is also a 4-Card Straight Flush (8-10-J-Q), we hold the
4-Card Straight Flush. With the 4-Card
Straight Flush, we still have many chances for Straights and Flushes so we
don't throw away the extra card even if it gives us a chance to get the Royal.

I've stopped at this particular point in the Strategy
Table because the 14 hands I've listed (over the past 2 weeks) are the only
ones with an expected value greater than 1.0.
That means these hands are net winners in the long run. Some will be winners 100% of the time. Some will not. But in the long run, we can expect to get
more back than we wagered. These hands
make up about 40% of the table and about 25% of the total hands dealt. Beginning next week, we'll review the hands
with an expected value below 1.0. Even
though these are losers in the long run, it doesn't make them less
important. In fact, they may be more
important because they account for a larger percentage of hands dealt.

## Thursday, December 5, 2013

### Strategize

Every casino game that is more than pure luck has some
strategy associated with it. This goes
beyond the basic strategy that simply says you're better off not playing at
all. For many games, the strategy can be
summed up with a simple sentence or two.
For Three Card Poker, it is Play Q-6-4 or better. Four Card Poker has a two sentence strategy
that tells you when to fold and when to Raise.
Let It Ride's strategy takes a few sentences telling you when to pull
down the 1 and 2 wagers.

As strategy gets more complex, it is helpful to try and
put it into as easy as a format as possible to help a mere mortal to utilize
it. It is relatively easy to program a
computer to play a game perfectly. Very
few humans can take every game to this level.
Also, expending that much energy on memorizing a very complex strategy
can pretty much sap the fun right out of the game. Blackjack utilizes a relatively simple matrix
that crosses the Player's hand with the Dealer's upcard.

Creating a strategy for video poker is quite a
challenge. As said earlier, telling a
computer which one of the 32 ways to play a hand is relatively easy. But, there are 2,598,960 unique 5-card deals
from a standard deck. Coming up with a
way to group these together in a way that a Player can use is a whole different
story. I believe it was my father, Lenny
Frome, who was the first person who accomplished this. He grouped hands together in a way that
Players could easily understand and hopefully memorize.

A video poker strategy table consists of only two
columns. The first contains the hand
rank as it was categorized by my father.
The second contains the expected value of the hand. Ironically, this second column isn't even
needed to play video poker properly. It
is there just for reference. So, that
means the video poker strategy table consists of a single column - usually with
about 30-40 rows/entries in it. To play
video poker the correct way, you have to memorize the order of these
entries. This is not nearly as daunting
as it seems. About 10-15 of these
entries are more than a little obvious.
So, you're left with about 25 hand types that you need to learn.

Let's start at the top of the strategy table which
contain the most obvious hands:

· Royal Flush

· Straight Flush

· Four of a Kind

· 4- Card Royal

· Full House

· Flush

· Three of a Kind

· Straight

We'd be having a great night at video poker if these were
the only hands we were dealt. These are
all big winners, all with expected values of 4.00 or better. In fact, only one of these hands is not a
sure winner - the 4-Card Royal. This is
also the only hand that might overlap with any of the others, creating the only
strategy decision in the bunch. What do
you do if you are dealt a Straight (or a Flush) that is also a 4-card
Royal? Well, now you know the
answer. You have to throw away the sure
winner to go for the big winner. The
good news is that if you have a 4-Card Royal, you have a very good chance of
still winding up a winner. There are 47
possible draws, 1 of which will result in the Royal. Another will give you a Straight Flush. 6 or 7 more (depending on whether you threw
away a Straight or Flush) will result in a Flush. 5 or 6 will result in a Straight and a host
more will give you at least a High Pair which will seem like small consolation.

While this decision might be agonizing, mathematically,
it is very clearly the proper play. The
expected value of the 4-Card Royal is 18.66.
The expected value of the Flush is 6 and the Straight is 4. Of course, don't expect to see this hand
every hour. A 4-Card Royal will show up
once in about 2700 hands and only about a third of these will be a Straight or
a Flush. One other key point to
note. Do NOT throw away a Straight Flush
to go for the Royal. That Straight Flush
has an expected value of 50 which far exceeds the 18+ of the 4-Card Royal.

Next week, I'll move down the strategy table to the hands
that require a bit more thought.

Labels:
expected value,
Q-6-4,
Strategy,
strategy table,
Three Card Poker,
Video Poker

## Thursday, November 14, 2013

### Table your Hunches

Last week, I described how all casino game strategy is
based on expected values. You hit or
stick in blackjack not because you hope the next card is of a certain value,
but because there are certain probabilities as to what the next card will be
and how it will affect your hand and your chances of winning or losing. If
you're dealt two face cards, you don't give much thought to strategy. Hopefully, you're not one of those Players
who even thinks about splitting 10's!

But, if you are dealt a 16 and the Dealer has a 7, you
start giving thought to the strategy.
With a 16, you have 5 cards that will help you and 8 that will bust
you. The odds don't look to good and
this is why a lot of people stick on this hand, albeit incorrectly. You can stay put, but with a 16, the only way
you can win is if the Dealer busts, which will happen only 26% of the
time. So, your choices are a 61% chance
of busting right away or sticking and having a 74% chance of losing that
way. Of course, by hitting you also have
an opportunity improve your hand. All of
the 5 possibilities improve your hand.
If you pick up an Ace, you'll be most likely to push. Pick up a 5 and you'll win more than 92% of
the time. Don't get me wrong, it is not
a strong hand and the decision to hit is not an overwhelming one, but it is
still the right move. In the simplest
form, if you face this situation enough times - which you will if you play for
a few hundred hours, you'll find that you do better by hitting than by
sticking.

In blackjack, you don't have to memorize all of the math
behind the game. You don't have to
figure out how many cards will bust you or bust the Dealer. To learn to play blackjack, many Players use
a simple strategy table. It is a simple
little chart that shows every possible Player hand and each possible dealer
upcard. It then shows what to do - hit,
stick, double, split, surrender, etc..
Guys like me have already done all the number crunching for you.

Video poker is no different than blackjack except the
decision making process is far more complex.
In blackjack, the result is essentially binary - you win or you lose
(okay, you can tie also, so it is not really binary). In video poker, you can have 1 of many
results - ranging from a Royal Flush down to a High Pair or you can lose. Since each of the different winning hands
pays a different amount, the specific result must be taken into account. If someone invented a game of video poker in
which all hands above a certain rank paid a fixed amount, then we'd be able to
lump all the hands into win or lose.
But, we need to know the probability of each final outcome with a
different payout in order to appropriately determine the value of getting that
hand. Surely, it is more valuable to
wind up with a Straight Flush than just a Straight.

Video poker is also more complex than blackjack in that
there is more than just a handful of different possibilities for each
hand. The Player can hold all 5 cards or
discard all 5 cards or anything in between for 32 different possible
plays. Yes, most of these possibilities
will be quickly discarded, but they still must be considered from a
mathematical perspective. They are only
discarded because the human mind can quickly recognize possible draws that
would clearly not be the best strategy.

Despite the extra complexity of video poker, the
similarities are still stronger than the differences. In the end the decision still comes down to
the expected value. Like in blackjack,
you don't have sit there trying to figure out how many cards you need to
complete a Straight or the like. Again,
guys like me have already done the job.
We have looked at every possible deal, every possible draw for every
possible deal and summed up all of the final hands. Using this distribution, each possible draw
is assigned an expected value. Whichever
draw has the highest expected value is deemed the right play. The last step in the process is too try and
categorize the way each hand is played into a format that a human can use to
play the hands. We call this a strategy
table.

Unlike blackjack where the strategy is a matrix that
crosses Player hands with Dealer hands and tells you what to do, a video poker
strategy chart lists all the possible playable hands in order in a simple
table. The table usually contains the
expected value of each hand too, but this is just for information. To use the strategy table, you basically work
from the top and find the first hand that your dealt hand can make and that is
the way to play the hand. So, if you are
dealt a hand that is a 4-Card Straight and a Low Pair, you start at the top of
the table and work downward. If a 4-Card
Straight appears first, you play that.
If a Low Pair appears first, you play the hand that way. If you can't find any hand that matches the
hand you were dealt, then you fall to the bottom of the table and find a RAZGU
which means throw all five cards.

Next week, we'll begin breaking down a strategy table for
full-pay jacks or better. You'll be on
your way to becoming an Expert Player.

Labels:
Blackjack,
expected value,
Split 10s,
Strategy,
Surrender,
Video Poker

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