When I was in high school – back in the middle of the last century – we had a home poker game that I hated. Everyone else seemed to love this game. But I thought there was something about it that made it antithetical to the natural rules of poker – everyone being for himself. The game was Anaconda.

Anaconda involved passing cards to other players – something I thought should never be allowed. It struck me as an invitation for collusion – or at the very least for punishing someone you didn’t like. Even so, I learned to put up with it. And now, like rock and roll that I also detested, I look back on it fondly – if only for nostalgic reasons.

Here’s how it’s played – or at least how we played. Different groups of players may have had slight variations.

The game was played high low declare.

The dealer dealt seven cards face down to each player. There was a round of betting. Then each player passed three of his cards to his left. There was another round of betting. Then each player passed two cards to his left. There was another round of betting. Finally, the last passing round, and each player passed a final card to his left.

We then added a “roll your own” feature. Each player would then arrange his cards as he wished them to be turned over. He would put his stack down in front of him. The order of the cards could no longer be changed. Each player would then turn over one card. The high hand showing would start the betting as they would in a stud game. There would be a round of betting following each up card that was turned up.

We rolled six cards face up and then we declared high, low, or high-low. Following the declare there was a final round of betting with the best declared high hand and the best declared low hand splitting the pot.

The game seemed wild and crazy. But here’s the kicker to it all. It was a game that greatly favored the conservative skilled poker player. The winning hand values were quite high, with the passing of cards back and forth. And the conservative player could fold all but the highest value hands. And then, with the seven additional rounds of betting after the cards were passed, he could soak his looser opponents.

The game also favored the player skilled in reading his opponent for high or low – since he could often sneak in for half the pot by manipulating his opponents with raises while reading the exposed cards. Also, if you were adept enough at poker to think about the cards that you were passed, you could often get a read on what your opponent was holding based on the cards he passed you.

Say, for example, that your opponent kept passing you high cards. It was a pretty good notion that he was trying to make a really good low. On the other hand, if he passed you low cards he might have either already made a really good low – or he might have been going for a big full house.

With good card memory you could also remember what remained in some of your opponent’s hand based on what you passed him. Think about it. If in the final passing round you passed the guy to your left the King of Spades and he had six cards showing at the end – but hadn’t exposed the King of Spades, then you knew with certainty what his unexposed card was. That could make a huge difference.

This game is great when your opponents are drunk or not paying attention but you are. It’s the perfect game to exploit the skill differential between you and other players. On retrospect, I think I love this game!

‘There is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world.’
-– Nicolai Lobachevsky

‘If you think the math isn’t important, you don’t know the right math.’
–Chris Ferguson.

A major factor attributing to poker’s worldwide appeal is the common belief that it is more a game about people than it is about anything else. With most decisions being situational in nature, the answer to many a procedural question is often “it depends.” Experts encourage one to play the man as opposed to his cards. But what if such conventional assumptions proved to be only partially true? This eventuality is addressed in the recently released The Mathematics of Poker. Authors Bill Chen and Jerrod Ankenman definitely state that it is the numerical reasoning behind our decisions that is more important than the searching for tells or the twitching of our guts.

Higher level mathematics is not a field in which the average poker pundit is generally well-versed, but this could never be said about Bill Chen. He holds a Ph.D. in mathematics, was a quantitative analyst by trade, and also has experience with software design. As for poker, his credentials are impeccable. Chen’s results from this year’s World Series of Poker were nothing short of astonishing. He left the annual event with a bracelet from the $2,500 Short Handed No Limit tournament and another from the $3,000 Limit Hold’ em contest. Overall, he cashed six times. Chen has been collaborating with Jerrod Ankenman since 2002, and their labor has been quite productive. As for Ankenman, he is a professional player who took second this year in a separate $3,000 Limit Hold’ em event at the 2006 World Series of Poker.

Their book is not unwieldy but its pages are bloated with information. The work is broken down into five major parts; each of these support the central theme of maximizing average profit. By the second page of the Introduction—in which the common misconceptions of play are examined—readers will discern that there is no fluff in these 350+ pages. Parts II and III embody its intellectual core as they outline the mechanics of both exploitative and optimal play. Exploitative play is defined as maximizing expectation in lieu of your opponent’s strategy; whereas, optimal play makes use of fundamentally sound strategies which are independent from your opponent’s actions. While most players strive to be exploitative with their play, the better ones compete at a “near-optimal” level which is an evolutionary advancement over taking advantage of mistakes. Other than Roshambo [rock, paper, scissors] and the The Jam or Fold Game for no limit, many examples will not be familiar to the average person. A lack of familiarity is not a problem, however, because studying games like Clairvoyance, AKQ, Cops and Robbers, and Auction strengthen the mind and provide valuable perspective. Of course, novices should be forewarned to put off this purchase until they become fully grounded in the elementary facets of poker. This text does not address the majority of the decisions one makes at the table. In this way, Chen and Ankenman are more Plutarch than Sklansky by treating the mind as “a fire to be kindled, not a vessel to be filled.”

Prospective readers may wonder about the difficulty of the math presented, and whether the possession of serious quantitative skills is a prerequisite for extracting value from its pages. Not surprisingly, the answer is, “It depends.” Assuredly, most members of the book consuming poker public meet the author’s criteria in this area, which is the completion of eighth grade algebra. Although, what Chen and Ankenman may forget is that many of us no longer remember most of what we learned during those dark days of middle school. Understanding the proofs so prevalent in the narrative hinges on the retention of information that might have been long deleted from our memory banks. Furthermore, a rudimentary background in statistics is also necessary for apprehending the meaning behind the equations. Those with no knowledge of statistics and algebra will be slightly stunned by the extent of the quantitative detail on display. The math impaired might become slightly demoralized, but the good news is that some amazing ideas are presented above and below the ubiquitous expressions. The sections concerning bankrolls, backing agreements, and tournaments will be of value to everyone as will the chapters devoted to the Risk of Ruin model, the use of math to improve play, and a no limit hold ‘em case study used as the basis for justifying the precepts of game theory. With the exception of casino executives, who won’t cherish the conclusion, “risk of ruin is 100% for games with negative expectation,” this function will be universally appreciated. Luckily for the industry, millions of slots players are not troubled by the laws of probability.

Yes, this book is quite challenging, but self-improvement is rarely accomplished via easy endeavor. Beyond its application to the game, The Mathematics of Poker’s educational scope provides an independent rationale for its worth. Concepts in finance, economics, and psychology are explained and numerous theories are expanded upon for which poker players might otherwise never encounter. And even in regard to recognizable terms like Bayes’ Theorem and the Kelly Criterion, no source I’ve seen does a better job of illuminating their meaning than this one.

It is important to recall that this text is not an end point. Mountain ranges worth of mathematical information remain in need of interpretation. The Mathematics of Poker is a thorough introduction, and there is little doubt that future works will build upon its foundation. Chen and Ankenman offer something here that is totally unique due to its avoidance of felt level tactics and its emphasis on strategy—which is its essential virtue.

Tired of playing Hold ‘em or even Stud in your Dealer’s Choice game? Want to change things up? But you still want to have an edge over the rest of the field – without having to think too hard. I have the perfect “crazy” game for you. It’s my Christmas Present to you.

This game is crazy like a fox. It will interest the traditionalists in the room – and it is sufficiently bizarre to amuse everyone who plays it. It’s 5-card Draw (for the traditionalists) played hi lo, with a declare, and with the players rolling their own cards at the end, and betting on each card as it is rolled face up.

Each player gets five cards dealt face down as they do in regular 5-Card draw. Hand values remain exactly as they are in a standard hi-lo game. We played with the A2345 being the lowest possible hand. But you can call it any way you want. Some people like to discount straights and flushes – not allowing them to be low hands. For them, the best possible low is A2346, not of the same suit. Others always consider an Ace to be high, except in a straight, and so for them the best possible low is 23457.

In any event, for the deal and the draw, the game is exactly like 5-Card Draw hi-lo. But when the betting is completed on the draw there are still five more betting rounds. Let me explain.

After the bet on the drawing round, each remaining player arranges his cards to determine the order in which the cards will be revealed, one by one. Each player then puts his hand face down with the first card to be revealed on top of his stack, and each subsequent card to be revealed sequentially below it. He then turns over the top card. The high poker hand showing has the option of beginning the betting and players bet in turn as they would in a stud game. After this betting round is concluded each remaining player turns over his next card, followed by another betting round, and so forth until all but one card is revealed for the players remaining in the hand.

With the betting round concluded following four of the five cards showing, there is a simultaneous declare and then a final betting round. When that round is finished the players turn over their hands and the pot is awarded – with half the pot going to the highest of the hands declaring high and the other half going to the best hand declaring low. Obviously, if all of the remaining players declare in the same direction, then the pot is awarded to only one winner.

Here’s a sample hand. The game is $1 game but the limits double on each betting round: $1, 2, 4, 8, 16 etc. The wheel (A2345) is the best low hand. Straights and flushes don’t hurt a low. Five players: Abba, Barry, Carl, David, and Froida.

Abba: Ks Jd 3c 2s Ac
Barry: 7c 7s 6s 6c Kd
Carl: 9s 8c 7d 4c As
David: Qs Qd 5d 3d 2c
Froida: Tc 9c 6h 5s 4s

Abba is the first player to act and checks.

Barry bets $1

Carl calls $1

David calls $1

Froida folds.

Abba calls $1.

$4 in the pot

Draw round:

Abba draws two, discarding the K and J.
Barry draws one, discarding the K.
Carl draws one, discarding the T.
David draws three, discarding the 5, 3, and 2.

Abba is dealt the 3h and 5c for: 5c 3h 3c 2s Ac
Barry is dealt the Ah for: Ah 7c 7s 6s 6c
Carl is dealt the 3s for: 8c 7d 4c 3s As
David is dealt the 5d 5s and 2h for Qs Qd 5h 5s 2h

Abba bets $2. (He’s decided to run an expensive bluff)
Barry calls $2.
Carl calls $2.
David calls $2.

$12 in the pot.

First roll:
Abba rolls the: 5c (3h 3c 2s Ac are face down)
Barry rolls the: Ah (7c 7s 6s 6c are face down)
Carl rolls the: 3s (8c 7d 4c As are face down)
David rolls the: 2h (Qs Qd 5h 5s are face down)

Barry is high and acts first. He checks.

Carl bets $4.

David calls raises to $8

Abba raises to $12

Barry folds.

Carl calls the $8 raise.

David calls the $4 raise.

$48 in the pot.

Abba rolls the: 5c 3h (3c 2s Ac are face down)
Carl rolls the: 3s 4c (8c 7d As are face down)
David rolls the: 2h 5h (Qs Qd 5s are face down)

Abba is high and bets $8.
Carl calls the $8.
David raises to $16
Abba re-raises to $24.
Carl calls the $16 raise.
David raises to $32, capping the raising.
Abba calls the $8 raise.
Carl calls the $8 raise.

$144 in the pot.

Abba rolls the: 5c 3h 2s (3c Ac are face down)
Carl rolls the: 3s 4c As (8c 7d are face down)
David rolls the: 2h 5h 5s (Qs Qd are face down)

David is high and he bets $16
Abba raises to $32
Carl calls $32
David calls the $16 raise.
$238 in the pot.

Abba rolls the: 5c 3h 2s Ac (3c is face down)
Carl rolls the: 3s 4c As 7d (8c is face down)
David rolls the: 2h 5h 5s Qd (Qs is face down)

David is high and bets $32
Abba raises to $64
Carl calls.
David raises to $96
Abba calls the $32 raise.
Carl calls the $32 raise.

$526 in the pot.

Declare round:

They simultaneously declare as follows:

Abba declares low
Carl declares low
David declares high

David is the “lock” and has no competition. By house rules he may not initiate or escalate the betting. So the betting goes to the lower of the low hands to begin. That is Abba.

Abba bets $64.
Carl calls $64.
David calls $64.

The showdown:

Abba has the: 5c 3h 2s Ac 3c for a pair of 3s for low.
Carl rolls the: 3s 4c As 7d 8c for the winning low hand of an 8 low
David rolls the:2h 5h 5s Qd Qs — and is the uncontested winner for high with two pair

$718 is split between Carl and David, who win $359 each.

I won’t go into any strategy. But I will tell you that this game gives the skilled player perhaps the largest advantage of any home poker game. It provides seven rounds of betting – six after the hand is complete – for a player to exploit his advantage. And it provides the attentive dealer with many opportunities to gauge the strength of his opponents before he has to decide whether to bet and how to declare. I consider it, without question, to be the best game to call when calling dealer’s choice. And assuming you’re the only one in your home game to have read this article, you’ll be the only one to recognize all of the advantages in it for you! Isn’t that a nice Christmas Present.

I analyzed some of the necessary adjustments for those who are used to playing online, and who now also want to become successful playing live. Today, I will discuss those who move into the opposite direction, the people who have quite a bit of experience in brick and mortar cardrooms, and who now want this same kind of success playing online. For them, the following things are very important:

Be aware of the technical possibilities

Those who are new to Internet play are unlikely to get the most out of it immediately. While almost all good online players know how to get the most out of the lobby (to search for the most profitable tables and / or the worst opposition), the notes possibility (meaning they can quickly analyze one’s strengths and weaknesses, and attach this analysis to this specific player for future use), and also of excellent programs like Poker Tracker, where you can not only analyze your own game, but also that of all players you have ever played against – while experienced online players know how to do all this, those who are new often fail to use these kinds of features properly. It should be clear that when the opposition is getting the most out of things while you are not, that you are at a distinct disadvantage, and for quite a few players who are new to playing on the Net, it may take a very long time to get accustomed to all of these possibilities.

Be aware of the limitations as well

While an important part of the good players’ edge in live games comes from finding a good seat and from having good reads based upon a “feel” or upon tells that their opponents may give away, online these possibilities do not exist – or not to the same degree. In order to become successful online, you will have to try to play your hands well in general, and only make adjustments when your notes on, or your knowledge of, any specific player tells you that deviating from the usually correct strategy may now be recommended. While in live poker you would almost always base your decisions on strength that you feel in your opponent based upon what you see, online your read on opponents is simply a lot less reliable, meaning that deviations from the ‘normal’ proper play (that are a large part of the good players’ profit in live games) are less likely to have a positive effect on your results here.

Learn to adjust to the speed

This is a related subject. While in live games, the good players have all the time to focus on their opponents’ habits and tendencies (because the pace of the game is much slower, because people move in and out of games not nearly as often, and because you receive far less hands per hour than online), online things go much quicker. You get to play many more hands, people move in and out of the game at rapid pace, and with the large player base at most poker sites, it is hard to get to know every one of them – like you would in almost all but the very largest B&M cardrooms. As a new player, it is best to get accustomed to this new situation by starting out with playing on one table only, in order to make the transition as smoothly as possible. Once you feel comfortable with the new situation and know how to get the most out of things, then it may be time to try to improve your total hourly rate by adding a second or even a third table. What you should do is try to still make the best possible decisions despite the high speed and the inevitable loss of information that you will experience. Of course, the best way to do this is exactly the same as in live poker: through focus, discipline and complete dedication.

Some final words

As some of you may know, I have been going through this exact same process during the past couple of months. Even though I used to write for a lot of sites, I did not actually play much online: My main strength used to be playing the relatively large cash games in regular casinos. In the winter of 2004, I decided it was time to try to become the best possible player online too. So, I did the exact same things mentioned above. I started out slowly by playing in some very small games to get used to the graphics, the technical possibilities and the large number of hands per hour. When I proved successful in these small games, I started moving up gradually, and when I proved successful there too, I slowly started adding a second table. I still think that there’s lots of room for improvement left, and I am certain that it will take me at least one or two years to get the same kind of edge online that I have live. Having said that, I am simply giving things my all to get everything out of it what’s there – basically the same as I have always done playing live. Now, if you do things the same way I do, you will probably find that the transition is not nearly as hard as you thought it would be.

Whether it was at your Grandma’s kitchen table, in your neighbor’s smoky, beer-drenched basement, or behind the bleachers at St. Patrick Junior High School, 5 card draw was the first poker game most of us learned to play. Back when Chris Moneymaker and Daniel Negreanu were still in diapers, draw poker was the game du jour and Southern California’s card rooms were its thriving epicenter. These days, one is more likely to hear the phrase “draw is dead.” However, with the addition of 5 card draw ring games on Poker Stars and other rooms, this old-fashioned form of poker is gaining new life online.

Rules

Online 5 card draw games are played six-handed with a button, a small blind, and a big blind. Limit, pot-limit and no-limit structures are all available. Each player is dealt five down cards to start and may call, raise, or fold their hand. After the first betting round’s action is complete, each player, beginning with the small blind, may draw from one to five new cards. There is another post-draw round of betting, followed by a showdown. The player with the best five card high hand wins the pot.

Simple enough, right? Kind of like video poker? Wrong.

Basic Strategy/Starting Hands

The number one mistake 5 card draw players make is playing too many hands. Tight is right in this game. Playing small pairs and drawing hands will only bleed your bankroll. If you’re looking to blow off steam or let your inner poker maniac out, consider 2-7 triple draw or pot-limit Omaha. 5 card draw rewards patient players. But don’t worry – there are plenty of people out there playing that don’t even understand the basics. With one or two of them at the table, 5 card draw can be a surprisingly profitable endeavor.

Always consider your position when deciding to enter the pot. Think limit hold’em in the pre-draw round– if you’re the first one in the pot, come in for a raise and represent strength early. Limping invites more limping. Raise instead and narrow the field. From early position (UTG and UTG+1) you’re looking for at least a pair of aces or kings to open. In the cutoff, with the action folded to you, Q-Q or J-J become viable starting hands. On the button, add T-T and 9-9 if they come with decent kickers (T-T-A-J-8= good. 9-9-4-5-6= not so good). Two pair or trips are worth an open- raise from any position. Four to a straight or flush are not– avoid these drawing hands unless you’re playing from the blinds. Drawing to straights and flushes is another huge mistake players make in 5 card draw. You are almost never getting the right price to speculate on these hands in a six-handed game. Think about it– with one card to come you’re a 4-1 dog at best to make your hand and your opponents are likely to hold some of your outs.

Blind defense in 5 card draw is both dicey and opponent-dependent. In the small blind, open-raise with anything you would come in with from any other position (9-9 or better) and limp with weaker hands like big aces (A-Q-T-J-8) or a small pair (6-6-K-9-5). 8-8 and 7-7 are worth an open-raise as well from the small blind. If your hand in the small blind looks more like a good deuce-to-seven starting hand (2-2-4-5-7), just fold it and move on. In the big blind facing a raise, pay close attention to your opponent’s tendencies. For example, if you’re in the big blind with 9-9-K-5-4 facing a raise from an opponent in the cutoff who typically opens with J-J or better, you can safely fold. Also consider the size of the pot. If an early position player opens for a raise and gets two callers, a pair of tens or jacks might be worth a call from the big blind, while hands like a strong two pair (J-J-9-9-4) are worth a raise. Use that “notes” feature and keep close tabs on what hands your opponents are willing to enter a pot with.

So, you have a pair and it’s time for the draw. What cards do you dump? With a pair hand like A-A-J-8-7, draw three. Don’t try anything fancy like keeping the J kicker and trying to represent a set. A shocking number of players will try this. One exception might be if you’re reading an opponent for two pair and you have a high pair with an ace kicker. Then it’s possibly worth a gamble to try and catch an ace for a better two pair. Draw two to your trips, and one to your two pair. Save the fancy plays for when you have more specific reads to work off of.

With a new generation of online draw players emerging online, grandma’s penny-ante game never looked so profitable. Get on Poker Stars, play tight, and avoid the lure of pretty drawing hands. Not only will it improve your reading skills in other games, but it should put a nice chunk of change in your pocket.

I played a lot of poker in high school. That was back in the mid-1970s. Poker for high school students wasn’t like it is today. There was no Internet, no televised poker tournaments, and surely no legal poker rooms in New York where I grew up. For high school kids especially, poker was strictly an underground game – illegal, forbidden, and compelling. For us it was like smoking cigarettes or drinking beer or smoking pot or getting laid. You wanted to do it because it was forbidden. And it was fun.

A favorite variety of the game back then was guts. We generally played it in the senior room of the high school – a private room set aside only for seniors where we got away with playing poker because faculty didn’t enter (unless they smelled cigarettes or pot). Small fortunes changed hands over this game. And we were all on very short bankrolls. So it produced some bad feelings. I think Bob Crumstein still owes Mark Casper $223. To this day I get a shiver of nervousness when I think about it. Here’s how it’s played – at least how we played it.

Many players played at one time. We usually had 10 or more at a long cafeteria table in the room. Everyone got dealt three cards face down. Everyone put in $.25 each. This was the initial pot. It would be matched by players losing the hand, as I’ll describe. When the pot was matched there was no ante.

Beginning to the immediate left of the dealer each player in turn declared “guts” or “no guts”. If he declared “guts” it meant that he was in the hand. If he had the highest three-card poker hand of all the players declaring “guts” – straights and flushes not counting – then he won the pot. If, on the other hand, he declared “guts” and was beaten by another hand held by a player who declared “guts” then he lost the hand. As a penalty for losing he had to put into the pot an amount equal to the pot at the start of the hand. He had to match the pot. If more than one person who declared guts lost then each had to match the pot.

The size of the pot could become very large. Here’s a typical run of hands for you to consider.

Imagine the game starting with ten players. Three players declare “guts”. The first player reveals two aces, a very strong hand in this game and usually a winner. The second player reveals two kings – also a very strong hand and usually a winner – but not this time. The third player who declared guts turns over three 6s. It is better than any pair. So he wins and the first player’s aces lose. After the player with trip 6s takes in the $2.50 pot, the two losers must match it by putting in $2.50 each, making the pot on the next hand $5.00.

On the next hand, an early decision maker figures he may steal the $5.00, hoping that other players will be too nervous about matching the relatively large $5.00 pot. So he declares “guts” as a bluff of sort, with only a pair of 7s. Unfortunately for him, the very next player has a pair of Queens – a hand that dictates a guts call for all but the most timid player. So he declares guts as well. And then, fantastically, the next three players and the dealer all declare guts as well. They have, in order, trip 9s, a pair of Kings, trip 5s and a pair of Jacks. The dealer, declaring guts with the pair of Jacks, made a bad move – even for this game. It might have made sense to make this call with one or two players already in the hand. But with all of the other folks declaring guts in front of him it was a very bad move. But most high school players back then were awful. .

The player with the trip 9s won the $5.00. Then the six losers put in $5.00, making the pot for the next hand the astronomical (by high school standards in the 1970s) $30.00.

The game continues. The next hand four players declare guts. Trip Kings beat out three other strong hands. Three players put in $30 each. That produced a pot of $90.

The next hand everyone declares “no guts” up until the player in front of the dealer. If he declares “no guts” then the hand is dead (we didn’t let the dealer win if no one else had called guts in front of him). So, effectively, the player right before the dealer is the last person to make a decision about whether to open the hand at all.

He looks down and sees A54 – an Ace high. Ace high is generally a borderline hand in late position like this. It’s a little better than 50:50 to beat a random hand. Still, it’s quite a risk. Since it loses to any pair. And the dealer will almost surely suspect weakness because of the late position and the huge pot.

The player in next to last position is generally aggressive. So he takes his chances and says “guts”. The dealer looks down and sees “229″ – normally not a hand to risk the princely sum of $90 on. But it is a pair, and he knows the other guy is pretty wild. So he reluctantly says “guts”.

He wins $90 and his opponent must match the pot.

We usually played without cash – both to make detection of our gambling more difficult and also because we often played for money we didn’t have on us. It was an easy game to keep track of on paper – since the bets we simple and only involved an ante or a pot-sized match. We developed convoluted IOU structures to keep track of who owed whom how much.

Unfortunately, because we played “on paper”, collection became a real problem. Ethical players like myself always paid up. But some didn’t. It became unfair, with many bad feelings. I stopped playing when someone announced that all debts were being reduced by one decimal place. Instead of Joe Tessatore owing me $107, he now owed me $10.70. I wouldn’t have minded except that I had just paid up my loss of $27 to someone. Instead of being more than $70 to the good I was going to be $17 in the hole.

But the game did produce a lot of action. It can be a great home game too I imagine. I’d tend to suggest that there be some limit on the size of the matched pot. But even so, my shivering memories of putting more money than I had in all the world on the line still causes me to decline when asked if I’d like to play at home. But who knows, maybe some day I’ll find the spine to play a few rounds of guts again.