Stroll Through the Strategy Table
/This week we continue our walk through a video poker strategy table.
Read More3-Card Straight Flushes and Deuces Wild
/
I love getting together with friends. Invariably, I get asked questions about
casino games that becomes fodder for a column.
This past week, I got several possible topics based on some questions I
was peppered with. One dealt with 3-Card
Straight Flushes. Another dealt with
which High Cards to hold and when.
Lastly, I was 'informed' that Deuces Wild is a bad game to play because
of poor payback. Admittedly, these came
from friends who will openly state that they are not expert Players. One of these friends also asked me what
benefit there was to the casino to offer games with a Player advantage. The simple answer to this is that so few
people play these games correctly, that they're willing to allow 1% or 0.1% or
maybe 0.01% of the people to make a few dollars at the expense of the other
99+%. The rest of the questions I was
asked only proves the point. If you
don't know when to hold a 3-Card Straight Flush or which High Cards to hold,
the odds are (no pun intended) is that you're not going to play the 100+% game
at 100+%.
So, I'll use this week's column to answer their questions
and hopefully educate some of you on how to move a few steps closer to Expert
Strategy. The first question dealt with
3-Card Straight Flushes. Normally,
Straight Flushes are the black sheep of hands.
They should occur every 9000+ hands, but because so many people ignore
the 3-Card Straight Flushes, they tend to be even more rare. The person who asked the question actually
spoke of how often he hit them, which was surprising. But, not after he told me that he tends to
throw Low Pairs in favor of 3-Card Straight Flushes. This is not such a good idea.
While 3-Card Straight Flushes tend to be forgotten, you
don't want to over value them either. A
Low Pair outranks EVERY 3-Card Straight Flush (NOT 3-Card Royals,
however). When you consider that in
jacks or better, every 3-Card Straight Flush, even Inside and Double Inside
ones are playable, this can lead to a lot of mistakes if you throw away the Low
Pair. When you consider that a large
percentage of 3-Card Straight Flushes are also Low Pairs, this error will prove
to be very costly to your bankroll. I
don't have the space here to list out all the strategy for 3-Card Straight
Flush, but for now, let's go with, they are below a Low Pair and every one of
them is playable. You also play 4-Card
Straights (not Inside) over the comparable 3-Card Straight Flush. The critical part is that you play even the
most awful looking 3-Card Straight Flush over a single High Card, except for
the Double Inside with 0 High Cards, which only outranks the Razgu.
Next up in the question bin was how to play High
Cards. Generally speaking, the goal is
to keep the suited High Cards. So, if
dealt 3 High Cards and 2 are the same suit, those are the two we play. If all 3 cards are of a different suit, but
one is an Ace, we play the 2 High Cards that are not an Ace. If it is J-Q-K all of different suits, we
hold all 3 cards. If you have 2
unsuited High Cards and one is an Ace, then you keep both. That describes which ones to keep. As for when to keep them, see the earlier
part of this article and you learn that we frequently keep a 3-Card Straight
Flush made up of 3 Low Cards over a High Card,
So, if dealt 3-4-5 suited and JQ (off suit), we hold the 3-4-5.
That brings us to the last question regarding Deuces
Wild. Should it be avoided due to low
payback. I'm not sure where my friend
got this notion. Perhaps he some bad
experiences playing it. If he tried to
use his jacks or better strategy on a Deuces Wild game, things would not be
pretty. In reality, Deuces Wild can
offer some of the highest paybacks in the casino. However, like all version of video poker, you
have to check the paytable. Sometimes,
different variations of video poker are given different unique names and
sometimes, they just scramble the paytable a bit and still call it Deuces
Wild. So, pay attention to the paytable
and make sure you are using the right strategy for that paytable.
While I do my best to give tips out in my column, the
only way you're really going to become an expert Player is by learning the
complete strategy for the games. I
continue to offer our 3 best selling video poker books for $5 each (includes
shipping and handling) to my loyal Gaming Today readers. You can choose from Expert Video Poker for
Las Vegas, which explains everything about the game from start to finish,
Winning Strategies for Video Poker, which contains the strategy tables for 60+
video poker variations or Video Poker: America's National Game of Chance, which
contains over 200 pages of my father's best columns, stories and quizzes. If you like to learn from anecdotal stories,
this is the book for you. Just send a
check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89134.
The Details Behind the Advice
/I’ve spent the last couple of weeks trying to get the beginners among you to make a relatively simple adjustment to your strategy. It involves four relatively common hands – high pair, 4-card flush, low pair and 4-card straight.
As I explained last week, they are played in this order because of their expected values. This week, I will walk through the calculation of the expected values for each of these hands.
HIGH PAIR
We start with the easy one first. It is easy because EVERY high pair has exactly the same Expected Value (EV). Since we already have a pair of jacks or better, we don’t have to worry about what are the specific cards discarded as they cannot help the hand nor interfere with other hands being formed.
When dealt a high pair, we will draw three cards. There are 16,215 combinations we can then draw from the remaining 47 cards in the deck (47 choose 3). Let’s look at the results of all of these draws:
45 will result in a four of a kind paying 25 each for a total of 1,125.
165 will result in a full house paying nine each for a total of 1,485.
1,854 will result in a three of a kind paying three each for a total of 5,562.
2,592 will result in a two pair paying two each for a total of 5,184.
11,559 will result in a high pair paying one each for a total of: 11,559.
The Grand Total is 24,915.
We divide the grand total by the number of combinations to arrive at the Expected Value of 1.5365. Every high pair has this exact EV. By itself, this number means relatively little in terms of our strategy.
Yes, it does tell us that we can expect to win about 1.5 units back when we have a high pair, on average, but it doesn’t tell us if we should play a 4-card flush or a high pair when we have both.
LOW PAIR
This will generate very similar results to our high pair. The only (and very BIG) difference is that all of those high pair hands at the end will now end up as low pairs and pay nothing. Thus, we will have a grand total of only 13,356, which when divided by 16,215 gives us an Expected Value of 0.8237.
4-CARD FLUSH / STRAIGHT
The 4-card flush and the 4-card straight each have 47 possible draws. The flush can result in nine flushes paying six each – for a total of 54.
The straight (NOT INSIDE) can result in eight possible straights paying four each for a total of 32. However, depending on how many high cards each has, it may be possible to wind up with a high pair as well.
For each high card that is in the 4-card flush or 4-card straight, three additional hands can wind up as a high pair instead of a losing hand. These additional three units when divided by 47 possible combinations means that each high card adds about 0.0638 to the Expected Value of our 4-card flush or 4-card straight.
So, a 4-card flush with zero high cards has an expected value of 1.15 (54 divided by 47). If there is one high card, we add .064 to this to get to about 1.21. With two high cards it climbs to about 1.28.
With three high cards – well, we would have a 3-card royal and that’s a whole different hand! So, a 4-card flush has an EV of somewhere between 1.15 and 1.28.
Since no other hand has an EV in between these two, we don’t bother separating these hands out on our strategy chart. Instead, we take the average of ALL 4-card flushes and say that its Expected Value is 1.22.
With regard to a 4-card straight, the Expected Value with zero high cards is a paltry 0.68. With one high card it goes up to 0.74. With two high cards it goes 0.81 and with three high cards to 0.87. Technically, a 4-card straight with 4-high cards is an inside straight (only one way to complete it) so its EV is much lower.
Because numerous other hands, including our low pair have an Expected Value in this same range, our strategy table shows each of these hands separated out.
So, when we look at all of these hands and rank them from high to low in terms of their Expected Values, we come up with the following:
High Pair: 1.54
4-Card Flush: 1.22
4-Card Straight with three high cards: 0.87
Low Pair: 0.82
4-Card Straight with two high cards: 0.81
4-Card Straight with one high card: 0.74
4-Card Straight with zero high cards: 0.68
It is based on these Expected Values that our strategy is derived. I’d like to raise two final important points. First, note that the 4-card straight with three high cards actually outranks the low pair – which is in conflict with the simple rule I gave two weeks ago.
While you should play this 4-card straight OVER the low pair, this particular combination is so rare that ignoring it while you work on learning the strategy will not cost you much. The ONLY way this hand can occur is 10-10-J-Q-K.
This leads to the second important point. For the purposes of this part of the strategy, ALL of our 4-card straights are outside – meaning they can be completed on either end. The other type of straight is an "inside," which has a gap in the middle or has an ace on one end or the other.
These can be completed only one way and have a much lower Expected Value. In Jacks or Better, most inside straights are not even playable.
I’d like to take this opportunity to wish everyone a Happy and healthy New Year and remind everyone to make their resolution to break the slot habit in 2012!
A Little Advice
/ Last week's column was a gambling related philosophical debate about perfect vs. good enough. This week, I'm going to the other end of the spectrum. It is nearly impossible to define a 'bad' strategy as there really is no end to how bad a Player can play most games. Playing every hand in Three Card Poker would probably meet the definition of a bad strategy, but is it worse than Folding every hand below a Pair? Probably not, and I'm not going to waste my time to try to find out.
This is not to say that every strategy that isn't perfect or as per last week's column 'good enough' would necessarily meet the definition of 'bad'. I don't consider playing Three Card Poker with the strategy of Play any hand with a Queen to be good enough, but I can't really call it a bad strategy either. With a game like Three Card Poker, there isn't really much to learn so you draw your line in the sand where you do and that's how you play it.
A game like video poker is far different. For anyone that doesn't use Expert Strategy, you might be hard pressed to find two people who used identical strategies. In reality, they may be TRYING to use Expert Strategy (or some other particular strategy) but due to its complexity, they make a variety of errors along the way. Then there are the multitudes of Players who just play by the seat of their pants, pretty much oblivious to the math that should be guiding them. To these Players, getting them to even good enough will be quite a challenge.
But, no matter what level they play at, if they just learn a few simple strategy points that might help them get a little closer to Expert Strategy then at least it is a step in the right direction. So, today's column is for these Players. I would like you all to consider learning just this small part of the strategy and trying to implement it. You may still be a long ways away from playing Expertly, but hopefully, we can save you just a few bucks along the way and add to your enjoyment too.
Here goes:
1) High Pair
2) 4-Card Flush
3) Low Pair
4) 4-Card Straight
This strategy only means something on the hands that are either a 4-Card Straight or a 4-Card Flush and are also a Pair. Approximately 25% of all 4-Card Straights and Flushes fall into this category, so these hands are fairly common. This is why it is imperative that these hands be played correctly. Let's take a closer look at why you should play the hands as described above and learn how these are NOT close calls.
The High Pair is the only sure winner in the bunch, but this is NOT the reason it is at the top of the chart. The determining factor is always the expected value of the hand, which is the average amount we expect to win with that hand over the long run. Sometimes, the sure winner is not the right answer, but in this case it is. The expected value of our High Pair is 1.54 which reflects the opportunities to turn this into Two Pair, Trips, Full House and Quads.
Next up is the 4-Card Flush which will win for us in the long run. This is NOT to say that we will have more winning hands than losing hands. With 9 opportunities to complete a Flush and perhaps a few more to complete a High Pair (depending on the exact makeup of the 4-Card Flush), we can expect to win with this hand only 20-30% of the time. But since many of these will win with a Flush, the wins will be significant. The expected value of a 4-Card Flush is 1.22. It will be a smidge higher if you have 1 or 2 High cards and a bit lower if you have none. If you have 3 High Cards, you have a 3-Card Royal and that takes precedence over the 4-Card Flush, but not the High Pair.
While the Low Pair has the exact same probabilities as the High Pair of winding up as Two Pair, Trips, Full House or Quads, the fact that it starts as a losing hand is enough to bring its expected value all the way down to 0.82. That means in the long run, this is a losing hand. It is the second strongest losing hand (behind the relatively rare 10-J-Q-K Straight, which is also the ONLY exception to the rule I'm presenting here as you hold this 4-Card Straight over a Low Pair, which can only happen with a Pair of 10's). The Low Pair is also BY FAR the most common hand in video poker, accounting for nearly 30% of all hands.
Lastly, we have the 4-Card Straights. While a 4-Card Straight with 2 High Cards ranks only slightly below the Low Pair with an expected value 0.81, it is still below it. It only gets worse with 4-Card Straights with 1 High Card or 0 High Cards with expected value of 0.74 and 0.68, respectively. These may not seem like big differences, but they will eat at your bankroll over time.
It would still be far better for anyone reading this to become a truly Expert Player, but any improvements in your strategy are still better than none. To help you on your way, we continue with our holiday special. We are offering Winning Strategies for Video Poker, Video Poker: America's National Game of Chance and Expert Video Poker for Las Vegas for $5 each, which includes postage and handling. Feel free to order as many as you'd like as they make great stocking stuffers! Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133. We'll do our best to get them to you before the holidays.
