“Brains Vs. Artificial Intelligence

Updated 2/11/2017

Artificial intelligence bot vs. the poker pros

By Noah Bierman

May 21, 2015, 3:00 a.m.

Rivers Casino in Pittsburgh
The Game. Texes Hold'em No Limit - Heads Up
14 days and 80,000 hands of no-limit Texas hold ‘em

Claudico, an AI from the same lab at Carnegie Mellon University that gave birth to Deep Blue, the computer that beat chess master Gary Kasparov.
The Pros: Jason Les, Dong Kim, Bjorn Li, and Doug Polk.

Its name, Claudico, means "I Limp" in Latin, a reference to the fact that it does not mind calling a bet in a fashion that many professional poker players believe to be weak and foolish.

The contest was part exhibition, part science experiment, and part test of humanity's limits. Lead scientist Tuomas Sandholm recruited four players recommended by top professionals to compete in a type of Texas hold 'em poker known as "heads-up, no-limit," a one-on-one game involving an especially complex array of betting strategies and choices.

The bot risked all its available chips on one hand while holding a 10 and a 5 of different suits — very bad cards — and bet big on another hand when the chances that its opponent could make a full house or a flush were great.

"It has a very sophisticated model," said Sandholm, the lead developer. "It just doesn't know that it's bluffing because it doesn't know the word 'bluff.'"
Unlike professionals, Claudico did not track its opponents' strategies. And its own game seemed random. For Brown and the other programmers, poker is the measuring stick, but not the goal.

They are really aiming to advance the field of artificial intelligence to fight cyberwars, perform negotiations and plan medical treatments, among other tasks that require complex decision-making with limited information.

Hold 'em poker, in this regard, offers a different challenge than chess or "Jeopardy!" because two cards are dealt facedown to each player; an opponent always has a large chunk of information missing. Five cards are then dealt face up for both players to use in forming their best potential poker hand.

The players beat the computer, but not by much.

Humans Out-Play an AI at Texas Hold ‘Em—For Now
http://www.wired.com/2015/05/humans-play-ai-texas-hold-em-now/
Claudico can only get close to Nash Equilibrium; it doesn’t react to the specific tendencies of individual opponents. The machine instead approximates ideal rational play, no matter the circumstances.

So the professionals adopted a constantly changing, exploitative strategy designed to locate and attack specific quirks in Claudico’s play. For example, it couldn’t process card removal—the way in which the cards in one’s own hand affect the likelihood of another player having specific card combinations. Les says that Claudico didn't factor that in, so the humans could tell when the AI was making big bets to disguise a weak hand, trying to force its opponent to fold.

That tell meant Les and his colleagues could pick off gigantic bluffs on the river by calculating that their hole cards made it unlikely Claudico had a hand as big as its bet would suggest. “It was writing a check it can’t quite cash,” says Les.

Claudico couldn't adjust to unusual bet sizing. That’s a big problem; it meant that the AI didn't always responding correctly. The humans capitalized on that. “Bjorn started using the most unusual bet sizes,” Les says. “He was falling in between the known sizes a lot, and was causing Claudico to have difficulties.”

When the final hand of the competition was completed, the players had wagered around $170 million (theoretically), and the team of humans professionals was ahead $732,713.

“While humans may still be ahead for now,” says Bowling, “it’s really just the beginning of the end.”

Poker has become one of the best ways to quantify the true power computers have in a way that is tangibly testable against a human opponent.

Unlike chess, poker is a game of incomplete information—no player has all the available data. An algorithm capable of determining optimal strategy for incomplete information scenarios could have applications for cybersecurity, medicine, and military strategy.

“Poker is now a benchmark for artificial intelligence research, just as chess once was,” said Sandholm. “It’s a game of exceeding complexity that requires a machine to make decisions based on incomplete and often misleading information, thanks to bluffing, slow play, and other decoys. And to win, the machine has to outsmart its human opponents.”


This was Heads UP poker!
How would it do at a full table or short handed 6 max or even with just two other players?

(Update)
OK, they did it again in February 2017. In the previous matchup, the pros won. The new computer named "Libratus", designed by Carnegie Mellon University, the same designers that built "Claudico". This time the computer beat (badly) 4 other professional poker players out of 1.8 million dollars (not real money though). Again, heads-up Texas Hold'em.

Let me know when it wins the main event at the WSOP against thousands of poker players.

I NEVER BLUFF

Any Hand Will Do?

Updated 2/11/2017

The Basics.
There are 1326 two card combinations in Texas Hold'em, including suits, 169, not counting suits. Seventy-eight are Pairs (6x13). 20 Broadway (A-10) cards and 16 of them are Suited Connectors.
You should get a pair, once every 17 hands or someone should be dealt a pair once every 17 hands, that's 16:1 that someone has a pocket pair, if you don't have one. The odds are 2.67:1 that your opponent also does not have a pocket pair.
If your two cards are not a pair, but suited, it's still 118:1 that you will not hit a flush on the flop.
You can not make a straight without a 5 or a 10. The 5 and 10 are KEY cards. It's still 76:1 against someone hitting a straight on the flop.

If your two cards are not a pair, you will hit a pair on the flop, 40% of the time or  it is 60% that your opponent did not hit a pair on the flop.

There are two types of hands in Texas Hold'em. A pair or better and a draw to a straight or flush. Every hand played after the flop is a contest between these two types of hands. The draws are broken down to connected cards, gapped cards, suited connectors and suited gaped cards. Anything else isn't worth looking at execpt when you are heads-up.

This is why aggression is so important in Poker, most players do not make their hand on the flop.

In a normal Cash/Ring game, you will most likely be dealt 30 to 40 hands per hour. In Tournament play, deep stack, you should be dealt 30 to 40 hands per hour in the early stages and 25 to 30 in the middle stages, with a full table. In the later stages it could average 30 to 40 hands per hour and up to 50 hands per hour short handed to 60 hands per hour with 3 or less players.

It helps to start with a good hand.

Top 5 hands: AA, KK, QQ, AKs, AQs (26 combinations) can be played from any position. AKs, AQs, usually need to bet 3xBB in early position, 2xBB to 3xBB in middle or late position.  AA, KK, may be best to reverse the betting process. The closer to the button, the more you bet, unless everyone is folding, as if you are trying to steal the blinds. Don't fall in love with AK or AQ, they are still only drawing hands. You will only flop an A or K 33% of the time, but an Ace, King, or Queen, about 50% of the time. You will flop a flush draw only about 10% of the time.
Group 2 hands: JJ, TT, AJs, KQs, AK (29 combinations) JJ, TT, Call in early position and middle position. Can raise in late position to steal the blinds or re-raise a small bet if everyone else has called. AJs, KQs, AK, will flop a straight, flush, or pair about 50% of the time. Call from early position or middle position, raise to steal the blinds or as a probe from late position or call raises if only one other person has raised before you.
Group 3 hands: ATs, KJs, QJs, JTs, AQ (25 combinations) Always see the flop, unless there are several raisers.
Group 4 hands: KTs, QTs, J9s, T9s, 98s, AJ, KQ (38 combinations)
Limp in unless you are on the button.
Middle Low Pocket Pairs: 99, 88, 77, 66 (16 combinations) Call in middle to late position or with less than 3 players.
Low Pocket Pairs: 55, 44, 33, 22 (16 combinations) Call in late position, or with only 2 or less players in the hand.

Trap hands

Use when you have a really strong hand and someone else has a lesser hand they can’t lay down. The trap is usually sprung by the flop. Any pre-flop 2 or 3 gaped middle cards; like 9-6, 8-5, or small pairs that have hit a set or better.  Only call small bets, if you don’t hit the flop, don’t bet unless in position, must always be played cheaply, fold if not hit on the flop.
Against good players, large bets like 6xBB to 2x pot or more, from late position, when all else have folded, may be a trap with AA,KK, otherwise it’s someone trying to steal the blinds with a weak hand.

Pre-FlopHands

High pairs: (AA, KK, QQ): vary from call to big raise (3x-5x); re-raise 3x the raiser,  re-raise the re-raiser.
KK will flop an over card about 20% of the time, QQ about 33%, each successive lower card about 12% greater than the last.
(AA,KK) Can slow play a tight table or against loose players, but always re-raise the raiser at least 2 times their raise.
(QQ) vary your raises; call, do not re-raise unless heads-up only or the raise was small
Middle pairs: (JJ,TT): Raise 2x,3x, do not call or slow play; raise only, do not re-raise, unless heads-up. TT will see more action and likely to flop possible straight draws, due to being a KEY card.
Mid-Low Pairs: (99, 88, 77, 66): Raise 1x-2x, call small raises, do not re-raise. Likely to flop straight draws.
Low Pairs: (55, 44, 33, 22) Raise 1x-2x in early position, call in Middle to Late Position; Fold large raises.
There is a 10% chance Pairs will make a SET by the river make, 16% for 2 Pair, 1% for a Full House, and about .25% for 4 of a Kind.
AK,AQ,AJ (suited or un-suited): Raise 2x-3x, call small to medium raises, fold to large raises except for heads-up, then call. Good hands to raise in the blinds, but only 1x BB.
AT-A6 (suited): Call all small bets, raise in early position 1x, fold all large bets, except when heads up.
AT-A6 (un-suited): Call all small bets, don't raise or re-raise, fold all large bets, except when heads up. Try to see the flop cheaply. Call in early position, can call small raises if less than 3 other players.
A5-A2 (suited & un-suited); Call all small bets, fold 2x+ raises and large bets, except when heads up. Suited has more options than un-suited. Call suited cards in early position, fold if raised.

Move up a group if someone raises or bets 3x or more before you, unless you are heads-up

KQ-KJ-KT-QJ-QT (suited); bet 2x-3x in any position, call any small bet, check any normal bet or if more than 3 remaining players.
KQ-KJ-KT-QJ-QT (not suited); bet 2x-3x in early position, bet 1x-2x in middle or late position, call any small bet, check any normal bet or if more than 3 remaining players. Fold any large bet.
Any other 19+ hand: (suited), bet 1x-2x if everyone checks, call small bets, fold large bets. (Points)
Any other 19+ hand: (not suited); call small bets, check if possible, fold to large bets
Middle suited connectors: check if possible, bet in late position, call small bets in middle position, fold to large bets. Likely to flop flush and straight draws.
Middle non-suited connectors: check if possible, call small bets in late position, fold large bets. Likely to flop straight draws.
Low suited and non-suited connectors: check if possible, bet in late or middle position, fold any bet if more than 2 remaining players. Likely to be middle or low pair. Great trap hand if a set is made on the river.
Gapped suited cards: Try to keep the gaps to 2 or less. The higher the lead card the better, K-2 can be bet in late position, best to check only; Q-2 check only, fold any other, unless heads-up, then call only small bets. Cards with 1 gap are more likely to hit a flush than a straight. The chance of hitting a straight with 1 gap is the same as any suited connector.
Gapped non-suited cards: Try to keep the gaps to 2 or less. Cards with 1 gap have the same chance of hitting the flop for a straight as any non-suited connector.

Mental Exercise: Remember the last 3 flop textures. The probability is higher of a favorable flop hitting your hand if your hand is the opposite of the previous flops. (Gambler's Fallacy, but you will be surprised at how often it happens)

I NEVER BLUFF

Updated 2/11/2017

The Power of Isolation

The objective of an isolation play is to make a wager big enough that it gets other players to fold, so you can be heads-up against one opponent. An isolation play can be used to isolate a tight player, bluffer, maniac, or a player on a draw. At loose tables, play tighter. At tight tables, play looser. Know who are the other players using the same tactic.

Whether it’s a tournament game or a ring game, Isolation is the key to building your stack. The object is to attempt to limit the field with your premium hands. Loose players use it to bluff or semi-bluff, some overuse it. Playing the isolation game is dependent on the ratio of BIG BLINDS to your stack size. You can limit the field with almost anything other than AA or KK, but always make at least a small bet when in position with AA or KK. Slow playing AA or KK can lead to big losses. The optimal situation is to have at least 100 Big Blinds. 
Arnold Snyder uses a Competitive Stack Factor of 60 big blinds as a minimum stack size to be competitive.

The first person to bet has the power. Position can change with each street, until heads up.

An A or K or Q will hit the flop 50% of the time or hit by the river 50% of the time. If you don't have one, someone does. You can almost estimate 10% for each player at the table, including yourself. With 8 players, it’s at least 80% that someone has an Ace, King, or Queen in their hand.

Pre-Flop: About Position: You are either IN or OUT!

STACK SIZES:

Less than 100BB: You must play small ball and be cautious with most of your playable hands, don't gamble.

IN POSITION:

Play long ball (raises and re-raises) only with your top 10 hands. Try to Isolate one player, but don’t try to push around the chip leader unless you have the nuts.

AA KK QQ must be raised if you are in position, and don’t be afraid to go all-in, do not slow play. Later you can use this to put others all-in when you think you have the best of it or the flop is "B" or less. (see Flop Ratings)

OUT OF POSITION:

Play small ball when you are out of position.

AA KK QQ can be played for a for a hit and run pre-flop, with a check raise or small bet followed by a re-raise if you are raised, regardless of the number of players in the hand.

Less than 50BB: You must play Tight Aggressive. Don’t gamble, but make the other players gamble. Take away their odds. Make it unprofitable to call your bet.

IN POSITION:

Play long ball (raises and re-raises) only with your top 5 hands.

OUT OF POSITION:

Play small ball when you are out of position.

More than 100BB: Be aggressive, but only in relation to the ratio of other stacks to your stack and position.

If you are the chip leader, you should only bet according to the ratio of stack sizes, not pot size.

IN POSITION:

Always keep the pressure on when you have a playable hand and you are in position.

Switch between small ball and long ball depending on who is in the hand and if you think you are ahead or not.

OUT OF POSITION:

Play according the the pot size until you think you have the best of it, then switch to playing for stacks.

Switch between making probe bets and value bets to disguise your hand. You should only be trying to disguise your hand if you are in the lead and intend to keep it.

Post Flop: About Position: You are either IN or OUT!

3^rd Street (the Flop):

The old saying of "if it doesn't fit the flop, FOLD!"
Get in or get out. Let the gamblers gamble. If your hand is not good enough to make an isolation play, keep it small and fold to any raises where there are more than two players still in the hand. The more players in the hand, the more likely you will be beat at the river, if you don't force them out.

4^th Street:

The Power of Position reverses at 4th Street (the Turn). You are usually heads-up or three handed at this point.

Power is relevant to the size of your stack (your “Q”) compared to everyone else.

M ratio     Q ratio       Q Calculator

5^th Street:

You have what you have. If you weren't betting the best hand or able to control a weak player, you are toast.

I NEVER BLUFF

Poker outside the box.

Updated 2/11/2017

Poker pros are action freaks. The don't just play poker, they are so easily bored during the game that they have to play games within games. Side bets,  Proposition bets, insurance, running it twice, etc.

Double-flop Hold'em
An alternative to the traditional formats is, as the name suggests, to have two flops (and turns and rivers), now they call it "running it twice". In this game the pot is split between the winner according to each board, although it’s probable that someone somewhere has tried to play double flop hi-lo! The game can also be played with variations of hole card numbers and discards, which make things a lot more interesting. Two flops introduces key decisions like the choice between making an all-out attempt to win on one board (and perhaps scoop an opponent attempting to do the same) or trying to have some shot at both, or choosing between a combination of made hands and draws when you come to discard.

How does Insurance work?
Let's work with other numbers first just so I can be sure I'm doing all the math correctly. Let's say you're a 75% favorite. You win 75% of the time and lose 25% of the time, so you are a 75:25 favorite, or 3:1.

Let's make the insurance fully fair right now, so the rate will be 3:1 as well. We'll play for $10.

If you win the pot, which you will do often, you pay the $10. If you lose the pot, which you will do less often, you get paid 3 times that amount, or $30.

The way you can remember is that you pay the insurance the opposite of the pot -- win the pot, lose the insurance, but lose the pot and you win the insurance. If you're a favorite, you will win more than you lose, so you should pay the smaller amount when you win the pot. When you lose the pot in the rare situations, you then get a consolation prize that's bigger than what you would have paid. In other words, more frequent event involves less money and the less frequent event involves more money.

For 70%, it's 70:30, which is the same as 7:3, or (7/3):1, which is 2.33:1. It's just division. If you are giving insurance and are not in the pot, remember things are reversed from above. If the guy wins the pot, you get some of it. If he loses, you have to pay him. So, when you make money, it's the '1' in the ratio. When you pay out, it's the '2.33' in the ratio. To make it in your favor, just reduce your pay out, like give 2:1 odds.

Hold'em hi-lo
As you might imagine, in the search for different variations, hold’em games have often been played hi-lo as well. Crazy pineapple and Tahoe in particular allow for greater degrees of flexibility in going both ways. In the latter game A-A-2 is obviously the dream combination, although A-2-3 also allows for flexibility against being counterfeited for low. Since it is much harder to scoop by winning in both directions in variations of hold’em hi-lo which have a qualifier of 8 or better (i.e. the low hand must be five differently-valued cards of 8 or below), it is important to watch how the board develops. The board can make the difference between a chance to win everything or realizing you’re only playing for half and then playing accordingly.

Propositions for playing marginal hands like 72 and winning the pot outright or with a bluff. Propositions are bets outside the chips in the pot, something like an ante, but the money goes to the winner after the hand is done.

I NEVER BLUFF

POKER - The Liar's Game of 'Go Fish'.

Updated 2/11/2017

Remember the good old days as a kid and playing Go Fish with your brothers, sisters, friends and family?

Poker is the same game, but with a twist.

In the game of Go Fish, you are looking at cards in your hand and asking someone if they have one. If they do, they have to give all of them to you and if they don't then everyone else playing knows what you have in your hand and can ask for it. In the kids’ version of Go Fish, you could not lie. You could not ask for cards you did not have and they had to tell the truth. If they had some they would give them to you or tell you to "Go Fish".

Poker, on the other hand, is all about lying. The big difference is that you are not asking what specific cards someone is holding. Poker is a game where players play different ranges of cards. Loose players may play a large range of cards and tight players may play a narrow range of cards, all depending on how much they like to gamble, or how much risk their money's worth.

When you make a bet, you are actually asking a question of your opponents. If you are the first one to bet pre-flop, you are really asking the players if they can beat the range of cards you are representing. That's why poker players are fond of saying, "you don't play the cards, you play the player". No one knows what anyone else has. After a time they know pretty much which cards you like to play and how those cards may vary from position to position at the table.

If you are a tight player and everyone knows you are a tight player and you are the first to bet, you are basically telling them, "I have great cards so you had better have a monster hand to beat me".

If you are a loose player and every one knows you are a loose player, you a basically saying "I have cards I think have the potential to beat your cards, so you had better have a monster hand to beat me." You tell them this by the size of your bet and how much you believe it is the best hand or can become the best hand.

The game gets interesting according the various types of players you are playing against. Loose players gamble more and tight players gamble less, but both players have to lie from time to time. Loose players lie more, based on the fact that they are involved in lots of hands. But on a percentage basis, a tight player can actually be lying more just by playing slightly more hands.

It's even more interesting when you factor in the probability of hands into the number of liars playing a hand. If the fact that, at a full table, someone will get pocket pairs once every 16 hands, then when a normal 3 times the big blind bet is made and 2 call and one raises, then more than one person is representing that they have pocket pairs, which means that there is at least a better than 50% chance someone is lying.

Of course, poker players don't lie, they bluff! They can bluff meekly or they can be an extreme bluffer and bluff often.

After the flop is where the real art of the game comes into play. Each bet then is a series of questions about who has what and who believes what they are being told. If you believe the person who bet first had a good playable hand before the flop, is it still a winning hand after the flop?

Since the experts tell you that most hands miss the flop, then the question is which of those liars with pocket pairs will believe someone hit their hand and now their hand is beaten by a higher pair or a better made hand? And if they weren't lying, can you get them to believe you actually did hit your hand or that you really had a real pocket pair pre-flop and now you have a set or better?

The strength of the truth or lie will come in the strength of the question. And the strength of the question may be masked weakly, by a strong hand in order to get more money into the pot. The question can be asked strongly, by betting more than the other players are willing to risk and scoop up the pot now.

Of the two most common types of post flop bets, which is the truth and which is the lie? Is the PROBE BET, usually less than half the pot, really saying, "I have some of the flop, maybe not the top pair, but second pair or the nut straight or a flush draw", the truth? Is the VALUE BET, usually half the pot or more saying, "I think I have the top pair or better", the truth?

That's what makes poker so great. You get to ask the players what they have and they will tell you. It doesn't make any difference if it's the stoic old player that never talks or the brash young player that not only talks but animates the antics of an answer to the world. They do this by folding or betting. They do this by not saying a word, or by saying loudly, many words. But after the silence or the noise, comes the answer in the form of a bet or non-bet.

It usually isn't until you reach the river that you learn who bluffed or who lied and who didn't.

I think I'll start telling people to "Go Fish", more often, then make my bet or non-bet. Which will start to mean, “I have a great hand so let’s go to the river - ALL-IN"!

I NEVER BLUFF

FLOP RANKINGS

Updated 2/11/2017

Currently reading Every Hand Revealed by Gus Hanson.

If you have every watched poker on TV, you know they don't show every hand played. This makes it hard for new players to learn what hand to play and when to play them and how to play them. One of the chief reasons I think there are more aggressive players in the games than a few years ago. Gus Hanson takes you through most, not all, of the hands he was dealt when he won the Aussie Poker Millions tournament in 2007.

I'm about a third of the way through and it looks like Gus is really only playing in hands he thinks he can get heads up in, unless he has a top hand. Most of the hands he plays are played aggressively, from any position. The players appear to be less aggressive than you see on TV, which could be misleading, but may be due to not really knowing about the hands he is not in.

Still, it shows how aggression will win pots that would be lost if you didn't try to reduce the field and try to get heads up. Which leads to some thinking about reading the board again and what you are likely up against.

I like to rate the board, especially when I'm not in the hand, and see if I can figure out who has what. I rate flops from A+ to C, because even what some might consider a D type of nothing flop can lead to a monster on the end, but most players aren't going to go to the Turn or River without a hand that has the potential to win, unless you like to gamble or you're a Mental Midget.

FLOP RATINGS
A+
(usually hits someone - can lead to Big Pots)
Royal Flush, (Ace + K-Q-J) +/- gapped
Straight Flush (any) +/- gapped
Trips (any)
High Pair (AA-TT) + 1 Broadway card (A-T)

A
(usually hits someone - can lead to Big Pots)
3 Broadway Cards (AKQJT) +/- 2 are Suited or Gapped
2 Broadway Cards + Suited card less than a Ten
High Pair (AA-KK) - NO other Broadway Card
Ace Suited + 1 Broadway card, not suited

B+
(likely to hit more than one player - can lead to Big Pots - but may be 50/50 race)
High Pair (QQ-JJ-TT) - NO other Broadway Card
Middle Pairs (99-88-77-66) + Ace
3 Suited cards
Ace Suited with a card lower than a Ten
Ace non-Suited + 1 Broadway card
2 Broadway cards + 1 card less than a Ten

B
(hits limpers the most)
Middle Pair (99-88-77-66)  + K-Q-J - NO Ace
Ace + Low Pair (22-55)
Pair lower than a Ten + K-Q-J
Ace - non-Suited + Middle Connectors (9876)
J or T + 98 +/- 2 are Suited
3 middle connectors - (9876) +/- gap

B-
1 Broadway + 2 cards lower than a Ten
Low Pair (22-55) with NO Ace

C+
Low Straight (2345) +/- suited or gapped

C
anything else

The Turn and the River can change anything, but the right play on the Flop may cut out the draws that can win on the last two streets.

I NEVER BLUFF

RANKING HANDS AND POINT SYSTEMS

Updated 2/11/2017

Let's agree that an Ace is the highest card in the deck and is worth the highest points.
There are probably as many point systems for poker as there are poker games and the various ways to play them. I think it's best to keep it simple, so I rank the Ace the highest, by about 2 points and the rest at about face value. My point system adds for pairs, connectors and suited cards, since an AA or AK should have a higher value than AT or A9 or A4.

An Ace therefore would normally be worth 12 points and a K,Q,J,T would all be worth 10.
Since Kings outrank Jacks and Tens, it should really have a higher rank than 10. and giving a higher rank also to Jacks, so we should probably give a one point advantage of Jacks over Tens, which makes a Jack worth 11, Queen worth 12 and King worth 13.
Now the ACE should have that 2 point advantage, so I'll give it 15 points.

It's hard to put a value on a pair since 22 will win heads up about 55% of the time and only 12% against a full table and beats AK. Given that a deuce has about a 2 point rank and only 4 points counting both cards, based on face value, and AK would have a value of twenty-eight (15 for the Ace and 13 for the King), we should give a factor to pairs, suited cards and connectors.
We'll start a Pair off at 20 points and add a point for card value. We will also add one point for being connected and 2 points for being suited and 3 points if it's connected and suited.

So the lowest pair (22) would equal 22 points and a pair of threes (33) would equal 23 points and a pair of nines (99) would equal 29 points and add one point higher for each broadway card; TT=30 (20+10), JJ=31 (20+11), and QQ=32 (20+12), KK=33 (20+13), and AA=35 (20+15)

22 vs AKs;
AKs = 31 points [(15+13) +1 for the connector, +2 for being suited] vs the 2 deuces @ 22 points.

If you loosly equate it to odds, then AKs would be favored 31/22 or about 1.4:1. (actually 1.409, but a tenth of a point is really no consideration in betting or looking at odds of any kind, not a factor at all, so round it up) and KK vs AKs; KK would be favored 33/31 or 1.06:1.

KK vs 22, KK favored 33/22 or 1.5:1

What's all this mean?
Only that you shouldn't bet the farm. At best, heads up you are usually about 49/51, more likely about 60/40 and at worst only a 3:1 dog, using normal odds, and normal hands for All-In bets, and the point system would only show a slight advantage, since it all changes by the river, and you can throw any point system out the window.

Favorite-to-underdog matchup Probability Odds, discounting suitability

Pair vs. 2 undercards (AA vs KQ is only slightly better than 88 vs 34)
83% to 17% or 4.9 : 1

Pair vs. lower pair (AA vs KK about the same as 88 vs 33)
82% to 18% or 4.5 : 1 

Pair vs. 1 overcard, 1 undercard (KK vs AQ not much better than 88 vs 97)
71% to 29% or 2.5 : 1

2 overcards vs. 2 undercards (AK vs QJ about the same as 98 vs 76)
63% to 37% or 1.7 : 1

Pair vs. 2 overcards (QQ vs AK and 88 vs 9T)
55% to 45% or 1.2 : 1

Max points are 35 for the AA and minimum is 6 for the 23, 5 at face value, plus 1 for being connected. In a normal counting system, many people will play any hand with 2 cards totaling 18 or higher, which would be an 8 and 10, or any pair. Aggressive players like Daniel Negreanu, will add some connectors and suited cards to their range. Some say any cards that can be connected on the flop, like one or 2 gaps, or even 3 gaps, are connectors. and look for luck to help them with a miracle flop.

This point system adds up to 3 points which lets you reasonably increase your range of cards by giving an 89 a 18 point count because it's connected, or 19 points if suited, and 20 points if it's both.

In a normal count a KK would count the same as a TT, where this system gives a better value for KK at 33 points and significantly better than the 89 which is only 3 points lower the the normal KK of 20 points.

Now a hand like JJ at 31 points against the 18 to 20 points players normally use would be 31/18 or 1.72:1.

You can use this to help decide how much to bet or raise against a normal hand if you end up heads up and in position against the range of hands people play, depending on their position. It makes your hand look stronger, because it is.

Can you use it as a betting tool on the flop?
Look at it compared to the flop rating system: A+, A, B+, etc.
How about betting about 1.72 more than the normal bet? If the normal bet is 3 times the big blind, you could make it a little more than 4.5 times the big blind (3+1.72) if you have a 31 point hand vs a normal 20 point hand. Pro's seem to like to make normal bets look different, like a $325 bet when $300 is 3 times the big blind or $16,200 when a $15,000 bet is the normal bet.

I NEVER BLUFF

Bluff or Semi-Bluff in No Limit Holdem? (pt 3)

“Bluffing is a nice word for lying. The cards are going to even out in the end. In poker, the one who lies the best wins.” Chris Anderson

(Part 1) (Part 2)
Bluffing according to the flop

Most poker books say that players miss their hand on the flop. It's more likely that someone may have hit bottom pair or even more likely that a few people are on some kind of draw. Bluffing to represent a hand is easier as the lack of betting or weak betting progresses toward the button. Also the texture of the board may give someone the opportunity to represent a hand that may have missed most players.

Flops without an Ace

There is an 87% chance that at least one person at a full table has an Ace and a 76% chance that two players at a full table have an Ace. Actually there is an 87% chance that at least one person has any card you can name and 76% that two players have the same card. That being said, the lack of an Ace on the flop should mean that at least one person still in the hand has an Ace, as an overcard, because many players can not fold any Ace. As the betting moves around from early position players to late position players, a bluff can be represented that someone has paired the board and may have the Ace kicker. A single broadway card, King, Queen, Jack or Ten, can also be represented as many good players will already have mucked hands with high cards and low kickers. When the flop comes and it's 3 cards lower than a 10, if the opponent checks and you check, he is probably thinking you have an Ace, King, or Queen. If one comes, you should bet, even if you have low cards, if you think he will fold often enough for you to win.

Flops with an Ace

Knowing that there is an 87% chance that at least one person is holding an Ace and that there is a 76% chance that two people may have an Ace, as bets progress around the table toward the button, the lack of a bet gives more of an opportunity to represent the Ace that didn't hit someone's hand. Most good players aren't going to slow play even AK when the Ace hits, because there is that 76% chance someone else has an Ace and now may have 2 pair or an Ace high flush or straight draw. Everyone that has read any good poker book know the danger of allowing someone on a draw to get a free card, or even a cheap card, so there should be some betting going on, even a bluff.

Flops with a pair or better

There is only about a 2% chance that someone hit a set on the flop. Someone who did hit the set, may be slow playing the set, depending on how high it is and where they are in the betting sequence. Early position players are more likely to have hit a high set than a low set, so it's more likely they might slow play it. It's not likely that an early position player would represent a set by slow playing, more likely they could make an large bet to represent a bluff, if they have lots of chips. As the betting sequence moves around to the button, the lack of betting or weak bets could give someone the opportunity to represent the set.

There is less than a 1% chance that someone hit a straight or flush on the flop, this makes slow playing a made hand the optimal choice, unless someone has the low end. Here, a check raise, could be a good bluff against poor or weak players, or even good players if the bluff is made by a good player. Poor, weak, and tight players are not likely to make a check raise as a bluff.

A flop with trips on the board, meaning someone may have quads, will usually mean everyone, including the person with quads, is checking or making the minimum bet and only calling. It's more likely that the bets will occur on the turn and river if someone has and Ace or a full house. Probably the one hand that shouldn't have a bluff going, but if you have enough chips and the betting checks to the river, a bluff could be made.

Flops with 3 high cards

Since everyone plays the Broadway cards, it's likely someone hit something. The bluff can be made when someone makes a weak bet, suggesting a hand that can be beat. If there is no Ace on the board, an Ace can easily be represented to suggest the Nut Straight. This is one of the most dangerous bluffs to be made because the board is ripe for a Full House.

Flops with 3 of the same suit

It's about 500 to 1 that someone will hit the flush on the flop. Playing for the flush draw with anything but the Nuts is dangerous, but that's where the bluff comes in. 3 suited cards on the flop is so scary that most bets will usually be minimal, except by the Nut draws. That's where a raise or check raise could win the pot before the turn.

Bluffing against player types

If you are against an opponent who almost always calls, then you shouldn't bluff at all. If you are against an opponent who folds too much, you should bluff frequently.

Aggression Factors (from I Hate Bluffing)

11 = Passive/Passive (CA = Calling Station)

12 = Passive/Aggressive (TA = Tight Aggressive),

21 = Aggressive/Passive (SA = Selective Aggressive)

22 = Aggressive/Aggressive (LA = Loose Aggressive).

3 = Maniac or Mental Midget (MM) How many maniacs are too many at a table?

http://ljblue.blogspot.com/2009/08/i-hate-bluffing.html

Passive Players

Generally the easiest to bluff, but the one you have to give in to if they raise back and sometimes if they even call. Weak tight players are not likely to continue with the hand if they are challenged. Calling Station players have to be bet off the hand with a big bet, if they call, you are going to have to make another large bet in the hopes the Calling Station will fold. Tight players play a tighter range of cards, so bluffing is actually easier, but tight players are easier to bluff. Don't go overboard on bluffing, you still have to pick your spots. Pure bluffs can be profitable against tight player, but have to be abandoned if called or raised. You will usually only be called by players that have a top hand. Aggressive players will be able to steal the blinds, but lose more when they have a good, but not great, hand. Don't play as many drawing hands agains tight players.

Aggressive Players

Aggressive players have to be met with aggression, but are harder to bluff. “In a balance of mutual terror, whoever acts first has the advantage!” The first to bet can sometimes take the pot, unless they are up against a loose aggressive or worse, a Mental Midget. Knowing who the loose aggressive players are and who the Mental Midget is gives the advantage to a Semi-bluff that catches a hand. Aggressive players tend to be poorer players, so a good player is rarely going to bluff an aggressive player. Tighten up on semi-bluffs and losen up on legitimate hands. Against aggressive players, play more drawing hands and do not play loose with marginal hands.

(Bluff or Semi-Bluff Part 1)

(Bluff or Semi-Bluff Part 2)

"The risk of never challenging is always greater than the risk of challenging"
Sun-Tzu's The Art of War.

I Never Bluff

Bluff or Semi-Bluff in No Limit Holdem? (pt 2)

Dan Harrington’s Law on Bluffing: "The probability someone is bluffing when he shoves a big bet into the pot is at least 10%", (until the final table)
(back to Part 1)

Bluffing Pre-flop

First of all, you should rarely bluff pre-flop, unless you are one of the blinds and only one other player has bet. The only other times to consider a bluff would be at the final table or heads up. Even AA should never be slow played pre-flop, especially since there is usually at least one loose aggressive player at a table and more than one selective aggressive player. It's when there are also one or more poor players that will hold on to top hands all the way to the river that someone with AA needs to make a reasonable bet or raise. Good players aren't going to gamble pre-flop against a full table, unless they are short stacked. AA only wins about 88% of the time heads up and against a full table it only wins about 36% of the time anyway. I love it when Mental Midgets go All-in, pre-flop, on the first hand. Even the Mental Midgets that win, because other Mental Midgets follow suit, tend not to last very long.

Bluffing by Table Type

Loose Tables

Loose tables tend to have many poor players so a good player is rarely going to bluff at a loose table. In loose games, tighten up on semi-bluffs and losen up on legitimate hands. In a loose game, play more drawing hands and do not play loose with marginal hands.

Tight Tables

Tight tables tend to have more good players, so bluffing is actually easier, but good players are going to pick and choose the best time to bluff. Good players are not going to go overboard on bluffing, but there will be better bluffs going on. Pure bluffs can be profitable at a tight table, but have to be abandoned if called or raised. You will usually only be called by players that have a top hand at a tight table. Aggressive players will be able to steal the blinds, but lose more when they have a good, but not great, hand. Don't play as many drawing hands in tight games.

Bluffing by Position

Early Position

Early position hands are just too vulnerable, even with good hands, to consider a semi-bluff, unless the table is weak and/or tight. That being said, the opportunity exists to represent a top hand against weak players and/or a tight table. Accepting that the range of hands for early position is mostly the top 5 to 6 hands, you might be able to consider a semi-bluff with some of the other top 10 to 15 hands.

Middle Position

In my opinion, middle position is the worst position at the table. Middle position players are usually sandwiched between the early position top 5 or 6 hand ranges and the late position's pure strength of their position. That does give a good oppertunity to exploit a weakness shown by an early position weak bet and represent a top hand against weak late position players. Against good late position players it may be a good place to occasionally try to steal the blinds.

Late Position

First of all, you have to Semi-bluff less often if you are the last to act and have to opportunity to get a free card, because it's still about the Semi-bluff. Secondly, someone could be sandbagging. It's all about how many are still in the hand and the strength of their bets. Against weak bets, it's a good place to make a play, but analyze who is making the bet. Against weak timid players, it's a good place to test their metal. Against good players, it's representing a hand that can beat the board. With 3 or more players still in the hand, someone is sure to have a good hand, but how good. Late position is probably the best place to try Arnold Snyder's "Rochambeau" style or Blair Rodman and Lee Nelson's "Kill Phil" style. Although the button is the place where poor players try to steal the blinds, the cutoff seat just before it and the real stealing position just before the cutoff position, are where the good player try to steal the blinds and/or take down the pot.

(Bluff or Semi-Bluff pt 1)

I Never Bluff

Bluff or Semi-Bluff in No Limit Holdem? Part 1

Re-reading "The Theory of Poker" by David Sklansky.

OK, I still hate to bluff, but found out that what I really hate is the 'pure' bluff. A pure bluff is a bet, which if called, has no chance of winning in a showdown. A semi-bluff is a bet with more cards to come. A semi-bluff, when called, may not be the best hand, but has a reasonable chance of becoming the best hand. The main thing to eliminate from your game is the gamble factor, don't be a Mental Midget. There is no semi-bluff you can make on the river, with no cards to come, it's a pure bluff. Pros look for the best opportunity to maximize the value of their hand. That's why a good player is easier to bluff against than a poor player. A good player can recognize when someone may be bluffing, but because a good player will usually only semi-bluff, they can more easily represent a good hand and make it believable. A poor player will just play to the river without realizing that their hand may not be the best, but can't let it go, where a good player can fold when a reasonable bluff has been made. We need to re-evaluate when to make the semi-bluff. Playing too tight by not bluffing at some time in the game only makes your strong hands worth less in pot equity. Don't semi-bluff if you are sure you are going to be called. Betting for value is clearly incorrect when you put more money in the pot with a hand you know to be the underdog. If you think your chances of getting away with the bluff are greater than the pot odds, you should go for it. You should bet if you know the opponent will fold with enough frequency, to make the bluff profitable. It's important that bluffs are random, don't always bluff just because of the pot odds. The weaker you think your opponents hand is, the more likely your bluff will work. The stronger your opponent thinks your hand is, the more likely your bluff will work. The larger the pot, the more likely a bluff will be called.

Randomizing bluffs allows a tight player to take the thought out of the bluff. It also allows both tight players and loose aggressive players to appear to be selective aggressive players. Opponents might be able to outguess a player because they remember patterns of play. Randomizing bluffs forces them to try to outguess an uncontrolled action, which is impossible. Sklansky suggests using a card, like the King of spades as the random trigger. The normal bluffs, combined with a random bluff, are more deceptive. Sklansky even goes farther by using 5 cards which includes all four Jacks. The game he played in this example was lo-ball, like Razz, in which those high cards are generally no good to win with. Using a card in Hold'em that generally doesn't help anyone, may be a good choice. The cards would be added to the number of outs to make the hand look better to an opponent. When the random card appears on the flop, you would bet, even if it didn't help your hand. If the hand fit the board, like for a straight or flush draw, it would appear that it helped your hand. Harrington suggests using a watch with a second hand. When the second hand is between 10 and 12, you could bluff. On a digital watch you could bluff when the last second is a 9 or when it matched one of the flopped cards, duece to nine. Again, only bluff good players who may fold to a bluff and it increases your odds of winning. Even if you lose, your odds are better on the hands that do win, because you are more likely to be called by the second best hand. The opponent can never tell when you are bluffing, because it's random.

In deciding to bluff, first determine the odds of making your hand. Then determine the odds your opponent is getting on the bet. Then you must randomly bluff in such a way that the odds against your bluffing are identical to your opponent's pot odds. If you have a 20% chance of making your hand and your opponent is getting 5 to 1 odds, the ratio of your good hands, 20%, to your bluffs, should be 5 to 1. 20/5 = 4. You should bluff 4% of the time, a ratio of 20% to 4% would equal 5 to 1. If there are 10 outs, you would pick 2 unseen cards as the random bluff, to give you the 5 to 1 odds needed. It doesn't have to be exact, but the closer you are to the exact ratio the better. In game theory, when you bluff this way, you take optimum advantage of the situation.

Bluffing against 2 or more players

It's rarely correct to bluff 2 or more players when all the cards are out. The chances the bluff will succeed decrease geometrically with each player in the pot. In most bluffing situations against more than one players the probablilties that each player will fold are not independant. Position and player types have to be factored in because players who might fold in one position might not fold in another. Betting to reduce the field is not a bluff. When there is a caller ahead of you, the caller and the original bettor cannot both be bluffing. When you have a minimum to near-minimum raising hand and the player before you, who has the same standards as you, raises, then his hand is probably better than yours. It takes a better hand to call a raise than to raise a call.

(Bluff or Semi-Bluff Part 2)

I Never Bluff