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[I've been] thinking about the mysterious “Morton’s theorem,” which is often referenced but rarely explained. It was offered up as an RGP post several years ago by the late, great Andy Morton, who tragically died in a Motorcycle accident at age 34. No doubt Morton would have been a star in the poker world, as Lou Krieger, Abdul, and Izmet have all attested to.

Below is my attempt to explain Morton’s theorem, a very important concept not only for low-limit games, but for the general understanding of hold ‘em.

Morton’s Theorem

Andy Morton read a Mike Caro article in Card Player in 1996 which advocated never raising from early position in loose hold ‘em games: “The mistake is raising when many potential callers remain behind you, thus chasing away your profit.” Morton got to thinking about this, and argued against it in a post to RGP in 1997.

However, not raising when your hand is best violates Sklansky’s fundamental theorem of poker, which states:

“Every time you play a hand differently from the way you would have played it if you could see all your opponents’ cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.”

In other words, if you raise in early position with AA, and show your rockets, players in late position should not cold call their AT suited– you gain from their cold calling, and they lose.

But of course we’ve all seen rockets go down in multiway pots. Another version of the question could be stated as, “Do we want our opponents to chase with weak draws when we are betting the best hand?” So Morton got to thinking (and talking with Abdul), and made an effort to figure out why Caro was wrong about not raising with the best hand in low-limit games:

“What I’m going to tell you is that if you bet the best hand with more cards to come against two or more opponents, you will often make more money if some of them fold, *even if they are folding correctly, and would be making a mistake to call your bet.* Put another way, *you want your opponents to fold correctly, because their mistaken chasing you will cost you money in the long run.* I found this result very surprising to say the least. I’ve never seen it described correctly in any book or article, although at least a few posts to this newsgroup have concerned closely related topics.”

Thus, Morton found that there are times when the Fundamental Theorem of Poker is violated in multi-way pots. I’m not going to get into the details (see Andy’s original post for this), but Morton shows that there is a certain range of pot sizes for which it is correct for the chaser to fold (odds wise), but you make more money when he folds than when he incorrectly chases.

How can this be? Morton’s great insight is that in a multiway pot, the player with the best hand is no longer making 100% of the profit on the incorrect chasing by the fish. In a heads up situation, the player with the better hand takes 100% of the incorrect chaser’s bets, since there are only two players. But in a multi-way pot, the player with the current best hand is dividing up the incorrect calls with the player holding the best DRAW.

Let’s look at a simplified example:
You hold 77 in early position and the button holds AK hearts. You raise and 4 players (including the button) cold call. The flop is Qh Jh 7c. Assume that our set of sevens represents the current best hand. Obviously, the button has the best draw. Morton’s idea is that for every incorrect call the 3 players between us and the button make, the potential profit is divided between us and the player on the button. We can picture half of these calls going into our stack, and half of them going into the button’s stack.

Now let’s pretend that two of the players are colluding. Player C1 holds 98o and player C2 holds QJc. So Player C1 has a gutshot (4 outs) and Player C2 is drawing to the full house (4 outs, since another 7 gives us quads). With 5 BB in the pot on the flop, C1 (about 11:1) and C2 (about 7:1) individually are not getting the proper pot odds to draw (considering only the turn, for simplicity). However, together C1 and C2 have 8 outs, and are getting 4.7:1. So if these two fish play together, implicitly (implicit collusion) or explicitly (collusion), they are making the correct call.

This is the notion of “implicit collusion” and “the schooling of the fish.” Although individually, C1 and C2 are making the incorrect play, from your perspective, the 2 headed fish have enough outs that they are getting the proper odds to draw. To make things worse, their calls are divided between you and the button, who has the best draw. Morton’s Theorem says that we want the fish to fold in a multiway pot, even if they are getting the incorrect odds to draw out on us.

This “schooling” makes it very tough for the player with the best starting hand to win, and leads to the bad beats we see all the time at the lower limits. If 5 players at a table never fold, then together they have many, many outs.

[thanks to mike johnston and hdouble via cc]

What a Super B0wl! I bet not many people bet on the under for the Super Bowl, but that’s exactly what happened! Here’s a recap of the big storyline in the game, the battle of the two quarterbacks Drew Brees and Payton Manning and what it meant for the Super Bowl and for sportsbook betters. Much thanks to BetUS for their continued amazing support of the Super Bowl betting action! If you’re looking to bet on football, basketball, baseball, soccer or just about any sport, BetUS is a fantastic option.

The Rise of Drew Brees

Heading in to the Super Bowl, I highly criticized the betting line of -4.5 for the Colts preaching that it was far too low for a team as strong as the Colts. I ignored all the hoopla surrounding the eventual Super Bowl XLIV champion Saints, refusing to tag them personally as a “team of destiny”.

The hardship of the city of New Orleans and the tremendous season of the Saints was lost to the wayside of what the Colts did in the 2009 NFL betting season and the deafening legacy of Peyton Manning. I hate admitting when I was wrong, but I have never enjoyed being wrong more than in Super Bowl XLIV.

A city mired in depression, catastrophe and destruction celebrated their very first Lombardi Trophy in style and it couldn’t come at a better time. With Mardi Gras just a week away from kicking off, the celebration in New Orleans will last forever. And to be honest, no city is more deserving.

Vindication had to be sweet for Drew Brees, especially winning in Miami. Brees was ironically jettisoned by the Chargers and thought about playing in Miami before coming to New Orleans, where he felt a cosmic calling luring him to one of the NFL’s worst teams. Returning to Miami with the Super Bowl trophy in play, Brees would not be denied. Throwing 32-of-39 passes for 288 yards and 2 touchdowns, Brees submitted one of the best Super Bowl performances by a quarterback in history.. He tied Tom Brady’s completion record and secured the second highest efficiency rating behind Phil Simms. On a team that has never won a Super Bowl, as a player that had been shunned by NFL franchises and in a situation where he was an underdog, Drew Brees emerged as the MVP of the biggest game of the season.

Peyton Manning, perhaps the best quarterback in NFL history, was picked off for the game clinching score and despite all his marvels this season, he wasn’t able to secure the victory. But I’m not about to lay the blame on Manning.

In fact, the reason the Colts lost the game was because his receivers simply couldn’t keep their hands on the ball. Reggie Wayne ended the game by letting a ball slip through his gloved hands in the fourth quarter. Austin Collie and Pierre Garcon were also unable to keep plays alive. Manning dropped a ball in to the hands of Dallas Clark in quadruple coverage, but that was the only spectacular play of the day for Peyton.

Nothing typified this game more than Collie lunging for the onside kick that opened the second half and having the ball bounce off his shoulder pads. First of all, players in those situations should never dive for a ball that doesn’t crest the 10-yard marker because it would be a foul in the first place. You can’t give a team like New Orleans momentum and that’s exactly what Collie did by diving for a ball that wasn’t in play in the first place.

That’s the end of my “the Colts should have won the game” rant. I can’t hate on a city, a team and a player like Drew Brees that is so deserving of a Super Bowl victory. In the wake of Hurricane Katrina, the subsequent mismanagement following the disaster, and all the continuing social difficulties that have followed since then, the Saints have given the city of New Orleans something to cheer for yet again.

I shouldn’t be surprised by the Saints victory. I really shouldn’t. But I am. I never once believed that Peyton Manning would let the Super Bowl slip from his hands. Yet I underestimated what it means for a team to play for a city that deserves the victory so much. And again, I seriously devalued just how good Drew Brees can be when everything is on the betting line. For the record, Brees romped past three future hall of famers in Favre, Warner and Manning to win Super Bowl XLIV.

Drew Brees will be remembered for a lot of things when his career ends. His meteoric numbers will jump out on the stat sheet. The story about the relationship he had with his mother will be highlighted. The fact he was jilted by the San Diego Chargers will certainly gain some steam. Yet nothing will stand out more than Brees substantiating hope to the city of New Orleans.

The Saints will march back home to a rousing applause from their fans, while Drew Brees can rest assured that he has accomplished more with a Super Bowl victory than most quarterbacks ever can. It’s one thing to keep a monkey off your back, or overcome the betting spread as an underdog. Validating the prayers and desires of a downtrodden city, Brees has emulated what a champion should be to the people behind him.

The Fall of Peyton Manning

The gushing love fest for Peyton Manning came to a screeching halt at Super Bowl XLIV when he failed to clear the Super Bowl spread and was run out of the building by the Saints. Now just 9-9 SU in the playoffs, Peyton Manning’s legend has returned to Earth to reside amongst the mortals. It’s not like losing the Super Bowl is going to make him any less eligible for the hall of fame when he retires, but people remember the times when a quarterback loses the Super Bowl. Just ask Dan Marino and Rich Gannon.

Manning was frustrated early on the by the Saints’ defense in the Super Bowl and with a pick-six that put the game out of hand, Manning was the one holding the bag when the Colts were upset by the team of destiny. Completing 31-of-45 passes for 333 yards and a touchdown, along with the pick, is subpar for Manning but he also had a bad day from three of his main receivers.

Pierre Garcon dropped three surefire first-down catches. Austin Collie not only dropped a first-down pass, but he also lunged for an onside kick that hadn’t gone ten yards to begin with . Reggie Wayne allowed a touchdown pass to slip right through his fingers on the final drive of the game. It’s not like Manning didn’t come to play, and his receivers deserve as much of the blame for the loss as he does.

The injury to Dwight Freeney and the season ending loss of Bob Sanders also killed the Colts in Super Bowl XLIV betting. Even with those injuries, the Colts were able to hold the Saints to 24-points offensively and made the UNDER the bet to take.

That being said, Peyton will be the one to blame at the end of the day. He’s the quarterback and the league MVP. Touted as the greatest quarterback to ever walk the planet, and with the stats and broken records to prove it, he needs to assume the responsibility. That’s the unfortunate side of being the quarterback – when all is said and done, you’re the guy with fingers pointed in your direction when the dust settles.

In prop NFL betting, the Colts have opened the season as 6/1 favorites to win Superbowl XLV at Cowboys Stadium in 2011. They’re trailed in the AFC by the Chargers who have 8/1 odds despite the ongoing curiosity of LaDanian Tomlinson’s dramatic drop-off and the presence of Norv Turner. Holding pace are the Super Bowl champion Saints at 8/1 as well, and for now they’re the benchmark in the NFC. The Cowboys, Packers and Vikings are 12/1 to win Super Bowl XLV.

The kudos from the oddsmakers at BetUS notwithstanding, Peyton Manning has a massive mountain to climb in 2010 betting. After coming off a dazzling MVP season in which he went 16-1 SU as a full game presence, Manning must win a championship to validate all the hype surrounding him. It’s honestly an obstacle that he built himself, and we as fans love to scrutinize greatness in an effort to legitimize the history of the game. When all is said and done, Manning’s numbers will probably set the records across the board, but if his number of Super Bowl rings doesn’t match the other greats in history, then his place therein will be questionable.

Joe Montana and Terry Bradshaw both won four championships, leading all quarterbacks. Behind them, Tory Aikman and Tom Brady have three each as starters, while Steve Young earned two as a backup to Montana and one on his own.

For now the addiction to hyping up Peyton Manning has run in to a brick wall, and rightfully so. Manning did not just lose Super Bowl XLIV, but he also lost a fair chunk of the adulation that he’s enjoyed this season. Even I was quick to say that the Saints would only win if Peyton Manning let them, and maybe I was right because of the pick-six. I still place Manning as one of the greats no matter if he ends his career with one ring or multiple. But the greatest? That’s a question only Manning can answer and his quest for a holier grail than Super Bowl XLV starts on the road to Arlington.

I just got an email from a representative over at Full Tilt Poker and sent over this notice of a new type of poker game at Full Tilt called Rush Poker. Here are the details:

Warning: Rush Poker is extremely fast paced – prepare yourself for the most intense poker action in the world!

Available exclusively at Full Tilt Poker, Rush Poker is the ultimate high-speed poker experience.

This new poker format is designed to minimize your wait time between hands and keep you in the action. You’ll join a large player pool and face a different table of opponents every hand you play. When you fold your hand, you’ll be rushed to another table for a new hand right away.

To play even faster, use the Quick Fold button to move to a new table for the next hand immediately.

Here’s the official Rush Poker Frequently Asked Questions (FAQ) List:

What is Rush Poker?
Rush Poker is a new poker format available only at Full Tilt Poker. When you play Rush Poker, you’ll join a large player pool and face a different table of players every hand you play. As soon as you fold your hand, you’ll be moved to another table for your next hand.

What does the Quick Fold button do?
The Quick Fold button – located at the bottom of the Rush Poker* tables – moves you to another table for your next hand right away, even if the action hasn’t reached you yet. Players at your previous table will not see that you have folded until it’s your turn to act. You can use the Quick Fold button at any point in a hand, unless you have committed chips to the pot and are not facing a bet (including when you are the big blind), or you are all in. Beware – once you click the Quick Fold button, there is no taking that action back.

How do posting blinds and seating position work in a Rush Poker game?
You’ll post the big blind upon joining a Rush Poker game. After that, the big blind is assigned to the player who has gone the most hands without posting it. If there is a tie for who has gone the longest without posting, the big blind will be chosen randomly among the tied players. All other seating positions, including the small blind, are completely random from hand to hand.

Do I have the same amount of time to act in a Rush Poker game as I do in a standard ring game?
Your amount of time to act and your time bank in a Rush Poker* game are the same as in a standard ring game, with the following exceptions:

• During pre-flop play, if it is your turn to act and no players have raised in front of you, you will have a shortened decision time and will not have the option to activate your time bank; if there is a raise in front of you, you will have the standard decision time and the option to activate your time bank.
• Your time bank will be fully replenished at the start of each hand.

How do I play more than one table in a Rush Poker game?
You can multi-table the same Rush Poker game by clicking the Join Now button in the Rush Poker lobby more than once. Each seat you take in a Rush Poker game is considered a different entry into the game – you can have up to four entries. Rush Poker is designed to make certain that your multiple entries will never be seated at the same table.

Are there any rules in place to ensure the integrity and fairness of a Rush Poker game?
Yes, the following rules apply to Rush Poker:

1. A player who uses the Quick Fold option cannot be seated at his next table with any players still in the hand at the time of the Quick Fold. This prevents players who have more than one entry in a Rush Poker game from taking advantage of other players.

• For example: Player A has one entry in a Rush Poker* game, while Player B has two. Player A is at the same table as one of Player B’s entries and Quick Folds before the action reaches Player B. At his next table, Player A cannot be seated with Player B’s other entry because Player B would gain an unfair advantage knowing that Player A folded out of turn at the previous table.
• Continuing from the example above: if Player B Quick Folds after Player A does, Player B will be allowed to sit at Player A’s next table as there is no longer any advantage to be gained.

2. A player with multiple entries in a Rush Poker* game cannot have any of his entries moved to a table with another player who used the Quick Fold option at a table where one of his other entries had yet to act.

• For example: Player A has one entry in a Rush Poker* game, while Player B has two. Player A is at the same table as one of Player B’s entries and Quick Folds before the action reaches Player B. At a different table, Player B’s second entry folds his hand. Player B’s second entry cannot be seated at the same table as Player A because Player B would gain an unfair advantage knowing that Player A folded out of turn at the previous table.

Why can’t I observe a Rush Poker game?
Every time a player in a Rush Poker game folds or finishes a hand, they are “moved” to a new table. There are no consistent tables to observe and every player has a unique view of their own action. The best way to experience Rush Poker* is to try it out!

Do I earn Full Tilt Points by playing a Rush Poker game?
Yes, Full Tilt Points are awarded in the same manner as a standard ring game. For every Rush Poker hand that you are dealt cards in, you’ll receive the standard one Full Tilt Point per dollar raked from the pot. See the Full Tilt Points page for a detailed explanation of earning Full Tilt Points. Please note that you will still receive Full Tilt Points for a Rush Poker hand where you use the Quick Fold option. Provided that there is rake taken from the pot in that hand, you will receive points even if you move to another table before the hand is finished. Happy Hour bonus Full Tilt Points are also awarded for Rush Poker games during standard ring game Happy Hours. See the Happy Hour page for more details on earning bonus Full Tilt Points.

The reopening of the historic Hialeah Park Race Track on November 28, eight years after owner John Brunetti closed it to the public, drew a huge overflow crowd of 26,874; in the next two days, however, that number thinned to a mere 4,305 and then 1,193. But the declining crowds did not bother Brunetti, who said the resumption of racing at Hialeah was just “the means to an end”, the end being permission from the state to open a casino. Such permission is a privilege doled out to South Florida’s struggling parimutuels, which have withered in the face of competition from other forms of gambling in the state such as the Florida Lottery, Indian-run casinos and the increasingly popular Internet poker sites. The question is: can Vegas-style slots casinos really reverse the parimutuels’ declining fortunes? Various tracks and frontons are betting that they can.

The latest parimutuel to take the plunge is the Calder Race Course, which had been rushing to complete an $85 million casino in time for the Super Bowl, which kicked off on February 7 at the adjacent Sun Life Stadium (formerly known as Joe Robbie Stadium and Dolphins Stadium). But other establishments that have already jumped in ahead of Calder and Hialeah are reporting mixed results, calling into question the familiar adage: ‘the house always wins’. Some of the parimutuels have already scaled back their plans to build lavish gambling palaces.

The Opening of Magic City Casino

The November 10 formal opening of the Magic City Casino, owned by Flagler Dog Track, brought Miami’s movers and shakers out in force, evoking the glamour of the days when members of the Rat Pack – Frank, Sammy, Dean et al – visited the track. Speaking before a cheering crowd, newly-elected Miami Mayor Tomás Regalado crowed about the 500 new jobs the casino created with “no public funds!” Unfortunately, the euphoria has subsided since then; while gamblers still flock to the new slots, income per machine has dropped by half since Magic City’s soft opening in October.

Marc Dunbar, an instructor in parimutuel law at Florida State who is also an expert in gambling, said that while new casinos would enjoy flashy openings, “the reality of the marketplace” would soon bring them down to earth. And the reality is that competition in the gaming market is fiercer than ever, with the Seminole Tribe’s hugely successful casino operation in the Hollywood reservation going head to head with parimutuels/casinos operating in the Miami/Dade and Broward area.

Adrian Segredo, 33, a gambler unwinding over a cocktail at Magic City on Friday night, commented that the Seminole Hard Rock had live entertainment, “where this [Magic City] doesn’t have it.” What Flagler does have is in-the-neighborhood convenience – and of course, dogs. By law, greyhound racing must continue to be held at the parimutuels in order to justify their gambling license, although the crowds continuing to attend such races are sparse. Still, management claims that while they have no exact figures, the coming of the slots has filled more grandstand seats. Some patrons also prefer to take in the races from the comfort of the air-conditioned casino, where a window offers a railbird’s view of the track.

Flagler is also hoping to entice patrons into placing a bet or two with various promotions, including Thursday Doggie Dinner Theater, which features dancing waitresses and food specials, as well as offering giveaways, and Tuesday Doggie Bingo, where patrons connect the results of the day’s races on a free bingo card in hopes of scoring a winning bingo.

Still, it remains uncertain if slots can lift the fading fortunes of a racetrack and its workforce. Horsemen employed at Pompano Park raised a $100,000 campaign to help win approval from voters in 2004 for ‘racinos’, only to claim afterwards that the racing track reneged on its promise to increase measly purses.

There have been no similar protests at Magic City since Vice President Isadore Havenick said that the overall operation is profitable. And yet, there are indications that all is not well. The casino has indefinitely postponed its planned $90 million second phase – which would have featured a nightclub, multiple restaurants and an amphitheater. Instead, Magic City is opting for a smaller expansion which would simply add an additional 150 to 200 new slot machines. Havenick attributed the second phase’s delay to the high tax rate the state levies on slots – which amounts to half of every dollar made.

While Florida legislators attempted to cut down the rate to 35% earlier in the year, such moves were stalled after the legislature, the Seminole tribe, and the governor, failed to come to terms on an Indian gaming compact. The stalemate also threatened Hialeah Park’s large-scale redevelopment.

The Redevelopment of Hialeah Park Race Track

Brunetti said that the park’s future survival as a racing venue hinges on lawmakers allowing stocks and thoroughbred racing – as opposed to the quarter-horse sprint-style races that are currently permitted at the track. He hopes to use revenues from slots to fund a massive redevelopment of Hialeah that would encompass a two-story casino, a hotel, and non-gambling establishments such as a multiplex cinema and bowling alley. The project would take seven to ten years to complete and cost one billion dollars; Brunetti said the redevelopment would funnel substantial amounts of money into the local economy, likening it to “building Hoover Dam during the Depression”. And indeed, casinos are just about the only things still being built in a moribund economy where most other construction projects in South Florida are at a standstill.

“We put hundreds of people to work,” Calder spokesperson Michele Blanco said. “That’s a good-news story.”

Magic City Casino is found at 450 NW 37th Avenue in Miami, Florida USA and Hialeah Park Race Track is found at 2200 E 4th Ave in Hialeah, Florida USA.

Some random poker thoughts on “I Put You All-In” and Finding the Perfect Playing Card:

The “I Put You All-In” Phrase

How did the phrase, “I put you all-in” get started? This has to be, without a doubt, one of the dumbest poker trends I’ve seen in a long time. How can anybody put me all-in? Don’t I still have the right to fold?

While I still think it’s stupid for people to say this with multiple players left in the hand, it’s even common for players to utter the phrase when there are only two players left in the hand. Is “I put you all-in” even a legal bet? Why not just say, “I’m all-in”?

Some will argue it’s an intimidation thing, but I don’t buy it. Maybe it’s just me, but I figure if this type of statement intimidates you, you won’t be playing poker for long. What are the odds you just happen to hit the newbie who can be intimidated before he ends up quitting the game all together? I’m guessing slim and none and slim is walking to the door.

The Perfect Playing Card

Why can’t I find the perfect playing card?

All I want is:

• Bridge-size cards
• Poker peek (corner) index
• White cards
• Bright colors
• Colorful back
• Easy to shuffle, control, and pitch

Is that too much to ask?

[thanks to kroska and kc via cc]