Wednesday, February 23, 2011

A Wild Ride on the Positive Side

            Frequently, people come up to me asking what is the best game to play in the casino and then answer it themselves by saying, “blackjack, right?”  By saying ‘best’, I usually assume they mean the best paying.  As table games go, they are essentially correct, although it may depend on the exact rules being used.  As for the best paying games (not just table games), the answer to that one is without a doubt video poker.  A decade ago, finding a video poker machine paying 99.6% or better in Las Vegas was easier than finding those little sheets of paper with semi-naked girls on them strewn on the strip.  Today, you have to search a little harder, but they are still there.

            While my father, Lenny Frome, added greatly to the popularity of video poker through his hundreds of articles and numerous books, he is also probably partly responsible for the disappearance of these ‘positive’ games.  Let’s be real.  The casinos don’t exactly purposefully put out games over 100% very often.  No one knows exactly why ANY were allowed to hit the casino floor.  We can only assume that because so many players played so poorly in the early days that the casinos never bothered to notice the few who might take advantage of the situation.

            Also, unlike a table game, which focuses more on a table minimum, video pokers focus on a machine maximum.  A $5 blackjack table allows the player to frequently play up to at least $500.  If that table were somehow created to allow a Player advantage, the Player could win a lot of money at $500 per hand.  With a mere 0.65% Player advantage and playing 30 hands per hour, a $500 blackjack Player could win $110 per hour.  Not a bad salary.  A 25-cent video poker machine allows for the Player to play $1.25 per hand.  At 800 hands per hour, this is still only $1000.  A machine paying 100.65% will afford the player a $6.50 per hour profit.  It beats losing, but tough to make a living off of it. 

            Why did I pick 0.65% as the Player advantage?  This happens to be the advantage for a relatively common form of video poker – Joker’s Wild (A-K).  When I say ‘common’, I don’t mean that you’ll find it at every casino.  I’m not sure you can find any 100+% payback machines along the mid-strip area of Las Vegas.  So long as the Players there are in awe of the marble statues while they play short-pay machines, there is no reason for the casino to offer anything but.  According to my friends at VPFREE, you can find these machines in about a half-dozen casinos in Las Vegas. 

            Now, before you go giving up your day job to go play these Player-friendly machines, I have to tell you that the highest denomination you’re going to find is a quarter machine – which will generate the $6+ per hour I mentioned earlier.  The casinos have figured out that a quarter machine will not attract the professional video poker Players and thus they don’t care much if a couple of people walk away a winner every now and then.  But as I said earlier, it beats losing.

            Learning Joker games can appear to be a bit challenging at first.  The strategy table has 50 entries on it which makes it rather long.  However, when you realize that the hands are broken down to Joker vs. Non-Joker, you realize that you actually have 2 relatively short tables to learn.  The fact that game pays for a Pair of Kings or Better (and not Jacks) means that the need to keep track of the number of High Cards is greatly diminished. 

            One of the toughest parts about playing a Joker’s Wild game is the volatility.  If you don’t get your Jokers frequently enough, you don’t stand much of a chance.  Joker hands account for just under 10% of the total number of hands.  The payback when you have a Joker is a whopping 286%!  For the other 90+% of the hands it is a mere 81.3%.  Expect to see wild swings in your bankroll with this one.

Tuesday, February 22, 2011

Happy Birthday to the Father of our Country!

Many years ago, I remarked to a high school classmate that I shared a birthday with George Washington. He looked at me and said, "you were born on the third Monday in February?". I just didn't know how to respond!

Today is the 279th anniversary of the birth of George Washington - and my 45th birthday. I'm trying not to think too much about being "mid 40's". I'd rather just go with you're only as old as you feel! Um, er...On second thought that may not be a good idea either. How about, you're only as old as your children make you feel? No, that doesn't work either - I have a teenager who keeps telling me how old I am. How about, you're only as old as your YOUNGEST child makes you feel? I like that one. My four-year old likes to jump on me like I'm still 20-something, so I'll stick with that one.

Well, all over the country they have been having President's day sales this past weekend. The cool part about being the 'President' of a company is I get to have a President's day sale in my own honor! For this week only, we are offering our best-selling books at a very special price of $4.50 (for my 45th birthday!), which includes shipping and handling (in the U.S.). Pick from Winning Strategies for Video Poker, Video Poker: America's National Game of Chance or Expert Video Poker for Las Vegas. You can order one or as many as you'd like. Send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603. Please make sure it is postmarked by 3/1/11.

Friday, February 18, 2011

Overlapping Hands - a Jacks or Better Quiz

            We’ve all been there.  Up comes 5 cards.  You turn to your spouse or a friend or maybe a complete stranger and you say, ‘Which should I hold?  The Low Pair or the Straight?  The Low Pair or the Flush?  Should I go for the Royal?’

            The good news is that the overwhelming majority of Video Poker hands require very little decision making.  Once you realize you’re not playing Table Poker and there’s no reason to keep ace kickers, most hands are pretty obvious as to what to keep and what to throw. 

            There are, however, some frequently occurring hands that leave most novices and even many experienced players wondering.  It’s not necessarily because the choices are of nearly equal value as much as each hand looks so tempting.  In reality, there is usually little true decision making skill required for these hands.  Once you have made up your mind to let Expert Strategy be your guide, it simply comes down to knowing which play has the higher Expected Value. 

            So, let’s take a look at some common ‘overlapping’ hands.   Assuming we are playing Full-Pay (9/6) Jacks or Better, how would you play the following hands:

A)        10§     J¨        Jª        Q©      K§
B)        2¨       5¨       8¨       K¨      Kª
C)        2©       2§       3¨       4ª       5§
D)        10ª     10¨     J§        Q©      Kª
E)        10ª     10¨     J§        Q©      Aª
F)         2©       5©       5§       8©       10©

            The 4 card straight in Hand A has an EV of .85, while the High Pair has an EV of 1.54.   Playing anything but the High Pair would be a big mistake.  High Pairs beat ALL 4 Card Straights.   4 Card Straight FLUSHES beat ALL High pairs.

            The 4 card flush in Hand B has an EV of 1.19, while the EV of the High pair is again 1.54.  Once again, High Pairs beat ALL 4 card flushes.  The only types of hands we discard a High Pair for are 4 Card Straight Flushes (inside or outside) and 4 Card Royals.

            Hand C makes us choose between a Low Pair and a 4 Card Straight with no High Cards (STR4H0).  This type of straight has an EV of .68, while the Low Pair has an EV of .82.  A little closer than some of our other examples, but still a clear choice exists.  Play the Low Pair.

            Hand D is similar to Hand C, but the Straight now has 3 High Cards (STR4H3), which makes it the highest ranking 4 Card Straight.  Its EV is .87 which puts it ABOVE the Low Pair.   A 4-card Straight with 2 High Cards (STR4H2) would be a 9,10, J, Q has an EV of .81.  This is one of the more complex strategies to remember with regard to Low Pairs.  Play a Low Pair over ALL 4 Card Straights EXCEPT a Pair of 10’s versus a 10, J, Q, K straight.  In this ONE case, its preferable to play the straight.  It should be noted that there are only a few hundred (out of nearly 2.6 million possible hands) when this particular hand will show up.  While we can’t advocate playing the Low Pair against ALL 4 Card Straights, it won’t cost you a lot in the long run… about .001 of the total payback.  We do recognize the advantage of keeping the strategy table easier to remember.

Hand E is a choice between a Low Pair and a 4 Card INSIDE Straight with 3 High Cards.  The EV of this hand is a mere .53 and is the LOWEST playable 4 card straight.  Its EV is well below the EV of the Low Pair of .82 and thus we play the Low Pair.

Hand F illustrates a 4-Card Flush with a Low Pair.  In this example, the 4-Card Flush has an EV of 1.15, well above the Low Pair’s EV of .82.  This 4-Card Flush has the lowest EV possible for a 4-Card Flush.  The more High Cards the Flush has, the higher the EV.  Of course, if a Flush has 3 High Cards, it becomes a 3-Card Royal and would outrank the 4-Card Flush. 

Let’s sum up what we’ve covered.  High Pairs outrank ALL 4-Card Straights and 4-Card Flushes, but do NOT outrank ANY 4-Card Straight Flushes.  Dealing with Low Pairs is a bit more complex.  Low Pairs are outranked by ALL 4-Card Flushes.  Low Pairs outrank ALL 4 Card INSIDE Straights, and ALMOST ALL 4-Card Straights.  The one exception is a 10, J, Q, K straight.

These rules apply based on this analysis ONLY for Jacks or Better Full Pay machines.  They may very well apply to other, if not MOST other pay tables, but it cannot be assumed that the strategy for one version of Video Poker will apply to other versions or other pay tables.  This is why it is suggested that you limit yourself to one or two versions of the game and become an expert at it before moving on to other versions.

Of course, these are not all the cases that make you turn to your friend and say “Which should I hold?’, but these are among the most commonly occurring and probably among the most commonly misplayed.  Nothing stated here can’t be easily determined by reading the Strategy Table for the particular pay table you’re interested in.  In a future column, I’ll review more common ‘overlapping’ hands.

Tuesday, February 15, 2011

It's Mathemagic!

          A couple of weeks ago, a colleague discussed with me the possibility of creating a simple three card sidebet for a game he was working on.  Essentially, it was no different than the Pair Plus wager for Three Card Poker. As a favor, I quickly gave him the frequencies for the hands and made sure there was a note that said that these applied ONLY to a standard 52-card deck.  The next day I received a frantic voice mail that stated that he wanted these numbers for a blackjack-style shoe and what did I mean that the numbers only applied to a single deck.  Since there is still the same number of cards of each type relative to the others, shouldn’t the frequencies stay the same?

          This led to a lengthy conversation in which I tried to explain why the frequencies change as the number of decks goes up.  Generally speaking, the frequency of sets (i.e. Pairs, Trips, etc…) goes up while the frequency of runs (Straights) goes down.  Below is a table that shows the frequencies of the winning hands in Pair Plus for both a single deck and a 6-deck shoe.

Mini Royal
Straight Flush
Three of a Kind

          The table clearly shows that which I just stated.  The frequency of a Three of a Kind more than doubles when we move to 6 decks.  A pair occurs about 15% more often.  Flushes occur about 20% more often.  In the meantime, Straights decrease by a mere 5%.  Our Royals and Straight Flushes decline slightly as well as they are a blend of Straights and Flushes.  The overall hit frequency goes up about 15% from 25.6% to 29.2%.  Is it any wonder that a paytable that works well for one deck would be a disaster (for the casino) with six decks?   If we were to take the standard Pair Plus paytable and apply it to a 6-deck version, the payback would go from just under 98% to nearly 115%!

          My colleague was having a tough time believing me, and I did my very best to try and explain it.  I used the Three of a Kind as an example.  Once the Player is dealt a Pair, he is looking for 1 of the 2 remaining matching cards with 50 remaining in the deck for a single deck game.  Thus he has a 4% chance of drawing the Three of a Kind at that point (2 out of 50).  When dealing from a 6-deck shoe, there are still 22 cards of that same rank left in the shoe out of 310 cards.  This gives the Player a better than 7% chance of drawing a Three of a Kind from a Pair.  With a single deck, the probability of drawing additional cards of the same rank decreases greatly as each card of that rank is dealt out.  Whereas, with a large shoe, the probability of drawing cards of the same rank does not decrease nearly as much as each was in used up.

          Taking this to the extreme, imagine a game where 4 cards are dealt and you are trying to draw a Four of a Kind.  In a single deck game there is are only 13 ways to do this.  By the time you have been dealt Three of a Kind, you have only a 1 in 49 chance of being dealt the fourth card of the same rank.  In a 6-deck version, you would a 21 in 309 chance – which gives you a 3 times greater chance of hitting it from that point.  In total, you would have 13/270,725 (0.0048%) probability of getting a Four of a Kind from a single deck vs. a 0.0357% probability from 6 decks.  This translates to nearly 7 ½ times as likely to get it using six decks.

          There are many lessons that can be learned from all this.  The first is a simplistic lesson in why casinos like large shoes for games like blackjack.  It is much harder for a Player to count cards and trying to figure out what is coming up.  Just because a few small cards have been dealt doesn’t mean large cards are that much more likely than normal to show.  With a single deck, just a few small cards means the probability of large cards increases by a far larger margin.

          The second lesson is that it is not always that easy to compare paytables from one game to another.  If a casino were to offer a Pair Plus type wager from a large shoe, they would have no choice but to offer lower payouts than they do for a single-deck game.  However, that would not necessarily mean that the overall payback is lower.  You need to make sure that you are always compare apples to apples.  A game dealing 7 cards can’t offer the same payouts as one dealing 6 for like poker hands, but you can’t just look at the payouts and say that one is ‘worse’ than the other.  You have to look at the actual frequencies of each winning hand and determine the true overall payback.

Friday, February 11, 2011

To Comp or Not To Comp

          This past week I read a new story about how the Las Vegas Sands was greatly reducing their comps program.  (see:  When I first read the title, I shuddered a bit.  Over the past couple of years while Las Vegas has struggled, I have received numerous e-mails from readers (mostly locals) who have watched their comps all but disappear.  It seemed to be happening yet again!

          Comps are the casinos ‘frequent shopper’ reward program.  Many years ago, if you spent enough hours gambling at a high enough denomination, the casino was eager to throw you a buffet, a room, show tickets or any other freebie that they could.  Back then, it was fairly subjective.  There were no electronic cards to throw into the machines, so most slot and video poker Players were not offered any comps.  At the tables, you’d ask to be rated.  You wouldn’t get a reward you didn’t want.  The pit boss would ask you if you’d like a room for the night.  Or you’d casually mention that you were hungry and he’d hand you a ticket for the buffet.

          The idea was to keep the Player happy and in the casino!  The casinos considered the profit center to be the casino itself.  Most of the rest existed only to serve the Player for the rare times he didn’t want to gamble.  Also, comps were an incredible marketing tool.  You appear to be giving the Player something worth far more than the actual cost.  After all, how much does it REALLY cost to feed one more person at the buffet?  How much does it cost to give two tickets to a show that isn’t sold out?  Most of all, you hand the guy a room with a sign in it that says the suite goes for $500 a night, when in reality that is the rack rate and it hasn’t been rented out at the price EVER, and it was going to be empty that night, anyhow.

          Until the huge boom in Las Vegas of the 1990’s, Las Vegas was known as a place where a relatively low-roller could get comped pretty nicely.  Just being a $5 blackjack Player could get you some free stuff.  Here on the East Coast in places like Atlantic City and Connecticut, $5 won’t even get you a place at the table, with minimums frequently being $15 - $25!  Also, as the technology changed, the whole concept of comps changed as well.  Players were given ‘Player reward’ cards to put into the machines and were awarded points based specifically on how much they played.  These points where then directly translated into casino cash that could be spent for items in the casino – from food to shows to rooms to stuff in the gift shop.  Some casinos went further and started giving ‘cashback’ – they sent actual checks to Players that could be used in the casino for a limited amount of time.  This became a critical part of cultivating regular Players – especially locals who could come back in the timeframe allotted. 

          As we all know, in 2008 the economy collapsed.  Many casinos, looking for ways to cut costs began cutting comps and cashback.  Many Players reacted very negatively to this – which should be no surprise.  Cutting out these items was akin to taking money right out of their pockets.  The buffet comp that cost the casino $5, but was worth $10 to the Player wound up costing many of these casinos far more than the $5.  Local players starting shopping around for better deals.  If Casino A wasn’t going to give them a free meal, maybe Casino B would!  Some of the casinos that catered to locals have been hurt by the economy, but some of it has been their own poor decision making in this regard.  They thought that their Players would stay loyal to them even if they didn’t reciprocate.  They were wrong – very wrong.

          So, that brings me back to the case of the Las Vegas Sands cutting back on its comps.  I think we’d all agree that the Venetian is not really trying to attract the locals.  It is a big beautiful place, but it was built to attract the tourists.  The hotel was not built as a place for the casual Player to crash for a few hours before hitting the tables again.  It was built to be a luxury hotel that people would WANT to stay at so they could say they stayed there.  If giving away rooms for free means that people who are willing to pay don’t have rooms, then reducing these comps makes a bit more sense.  

          As the article did not make it very clear as to exactly what they are reducing - are they all but eliminating a ‘reward’ program for the average Player? – I can’t exactly condone their actions.  At the same time, it’s not in the same category as when one of the off-strip properties catering to locals decides that the couple that plays 2-3 hours most every night will no longer get a free buffet every couple of weeks.

          Tell me what you think!

Wednesday, February 9, 2011

Double Bonus Video Poker Quiz

Double Bonus Video Poker Quiz

Is it any wonder we call Las Vegas, Video Poker Heaven? With this pay table widely available even on quarter machines, we can squeeze 100.1% out of this liberal game, plus the benefits of slot clubs, which put an additional 0.4- 0.7% return on the table.

Pay Schedule
Royal Flush4,000
Straight Flush250
Four Aces800
Four 2-3-4's400
Four 5-K's250
Full House50
3 of a Kind15
Two Pairs5
Pair Jacks or Better5

But it won't happen unless you learn the nuances of the strategy, which is more complex than what you would use on Draw Poker. To see how proficient you are, take this test and find the answers below. If you can get 5 or 6 right, you are ready to take on this challenging game.

Which cards would you hold?
Hand Card A Card B Card C Card D Card E
1 3s 6s 9s Kd 8h
2 4c 7c 2h 3s 9c
3 5s 6s 7s 8s 9c
4 7s Js Qs As Kc
5 9d Jh Qc Kh 8d
6 4d 6c 7c 8s 2c

Hand Cards Explanation
1 D A 3-card flush is playable but one high card is better
2 A,B and E Much better than drawing 5 new cards
3 A,B,C,D and E Paying 5 the straight is the play.
4 A, B,C and D Hold the 4 Card Flush; Try for the Royal only if the
Royal pays 960 coins
5 A,B,C and D Those high cards make it the play
6 A,B,C and D Even a poor inside straight plays in this game

Tuesday, February 8, 2011

The Year of the Rabbit

            Happy Chinese New Year!  2011 is the year of the Rabbit on the Chinese calendar.  I think the folks at Shuffle Master are hoping it’s the year of the Rabbit too!  In the last few months, one of their latest table games, Rabbit Hunter launched at two casinos in California – Pala Casino and Jackson Rancheria.  I wrote about this game back in November in a lead in to the game being on display at the Global Gaming Expo (G2E) in Las Vegas.  I had the pleasure of working with Roger Snow, Executive VP at Shuffle Master in developing the math for the game.

            Rabbit Hunter is very unique in its betting structure and rules of play.  I don’t know of another game in which you have the opportunity to literally buy an extra card, and as a result, play six cards to the Dealer’s five.  Let me review the basics of the game and then I’ll go into more detail about buying a card.

            To begin play, the Player makes an Ante wager and an optional Bonus bet.  While this Bonus bet is ‘optional’, I will tell you that the strategy makes this wager all but mandatory.  The Player and Dealer are each dealt five cards face down.  The Dealer will also deal a 6th card to each Player FACE DOWN in a separate spot.  The Player may look at his 5-card hand and then he has to make a choice as to how to play the hand.

He can Fold, forfeiting his Ante and Bonus wager.  He can make an additional wager (Play wager) equal to his Ante which will allow him to go head to head against the Dealer OR, he may make that Play wager AND buy the 6th card for an amount equal to his Ante wager.  Note, that the Player CANNOT only buy the card without also making the Play wager.  If you choose to buy the card, the money you pay goes right to the casino.  This extra card can help you win more on your other wagers, but the money you pay is gone. 

Assuming the Player does not Fold, his five (or six) card hand will go head-to-head against the Dealer’s five card hand.  His hand will also be used to determine if he wins the Bonus wager.  In both cases, if he bought the 6th card, he may use any five of the six to make his hand.  If the Dealer’s hand is not at least an Ace High, the Player’s Ante Wager is a push and the Play bet will be paid even money if the Player’s hand outranks the Dealer’s hand.  If the Dealer’s hand qualifies with an Ace High or better, then both the Ante and Play wagers will pay even money if the Player’s hand outranks the Dealer’s hand.  If the Dealer’s hand outranks the Player’s hand, the Play wager is lost. 

            I have little doubt that many Player’s will sit down to play Rabbit Hunter and find the notion of buying a card rather distasteful.  That said, the analysis takes this fully into account, and the paytable in use at the two casinos has a payback of 99.35% which is more than a little competitive.  It is one of the highest for any table game anywhere and just a smidge below Blackjack.

            The strategy for Rabbit Hunter may seem a bit odd at first.  Buying the additional card is mostly for the benefit of the Bonus bet.  While it can have some residual impact to the play against the Dealer, this benefit is limited to low ranking hands or partial hands improving.  For example, if you buy a card with Two Pair and it turns into a Full House, your Bonus pay goes from 2 to 30 – well worth the expense.  But, the impact to beating the Dealer is much smaller.  With a Two Pair you’ll beat the Dealer 92+% of the time vs. 99.9% for a Full House.  The extra 7% is nice, but would not be worth buying the extra card on its own.

            As a result, we find that there are certain High Pairs which are not worth buying the card for.  The improvement from a High Pair to a Two Pair or Trips is simply not enough to warrant buying the card.   Whereas when a Low Pair improves to a Two or Trips, we find that it does pay to buy the card because we turn the Bonus bet from a loser into a winner while ALSO improving our hand.

            When all is said and done, this is the complete strategy for Rabbit Hunter for the paytable in use currently.  I should point out that there are a couple of minor exceptions, but we’re talking about 0.01% or 0.02% of payback as a result. 

Play and Buy the Card when:
-          Player has a Straight Flush that is a 4-Card Royal
-          Player has a Flush that is a 4-Card Straight Flush or 4-Card Inside Straight Flush
-          Player has a Straight that is a 4-Card Straight Flush or 4-Card Inside Straight Flush
-          Player has Three of a Kind
-          Player has Two Pair
-          Player has a High Pair that is a 4-Card Straight Flush, 4-Card Inside Straight Flush or Flush
-          Player has a Pair of 10,J, Q that is a 4-Card Straight or 4-Card Inside Straight
-          Player has a Pair of K that is a 4-Card Straight
-          Player has a Low Pair
-          Player has nothing, but a 4-Card Straight Flush, 4-Card Inside Straight Flush, 4-Card Flush, 4-Card Straight or 4-Card Inside Straight

Fold when:
-          Player has A-8 or less and is not a Play/Buy hand

Play and not Buy when:
-          Any other hand

            With this strategy you will Fold 23% of the time and Buy the Card about 47% of the time.  When you buy and miss, it will hurt.  When you buy and get that Rabbit, it will pay off big time!
            Shuffle Master has 8 additional casinos lined up for Rabbit Hunter, including the Las Vegas trial at the Luxor.  Stay tuned for more information on it.  As Elmer Fudd would say, “Here’s to the year of the wabbit. Hehehehehe.”