Poker is getting tougher and a lot of top players are turning to game theory to help get an edge or, at least, eliminate their opponents’ edge.  You can find a lot of articles about game theory in top poker magazines like CardPlayer and on top training sites like CardRunner.  It’s great advice and it works great in tough poker games but it’s not a magic bullet.  In fact, if misapplied, it can hurt your game rather than help it.

CardPlayer is Costing You Money

And they’re not the only ones. Bluff Magazine, CardRunners, LeggoPoker, DeucesCrack, all of them are costing you money.  It’s not their fault.  They’re all great sources of information but you’re misapplying the information.

Have you noticed that you tend to lose money after your watch your favorite pro give a lecture on how to apply game theory in poker?  You balance your raises and 3-bets.  You float dry flops and you three-barrel bluff.  You do everything thing your idol tells you to do and you wind up spewing money all over the felt.  The question is – why?

Hawks and Doves

Before we go deeper into poker game theory, we need to have a better idea of how game theory works and for that we’ll use a simple game called Hawks and Doves.

Richard Dawkins talked about the Hawks and Doves game in his book The Selfish Gene but the game was originally proposed by J. Maynard Smith, a 20^th century evolutionary biologist.  According to Smith, the rules of the game are as follows:

Hawks will always attack when it confronts another Hawk or Dove and will only retreat if seriously injured.

If a Hawk and Dove engage, the Hawk will attack and the Dove will fly away unharmed.

If two Hawks engage, they will fight until one is seriously injured or dead.

If two Doves engage, they will threaten each other until one tires of the contest and flies away.

A bird doesn’t know if it’s facing a Hawk or a Dove until they have a conflict.

The contestants are arbitrarily awarded 50 points for a win, 0 points for a loss, -100 points for getting seriously injured or killed and -10 points for wasting time in a long contest.

As it turns out Hawks have the advantage when there are a large number of Doves in the populations and Doves have the advantage when there are a large number of Hawks in the population.  Neither Hawks nor Doves have an advantage when exactly 5/12 of the population is Doves and 7/12 of the population is Hawks.

Hawks, Doves and Poker

So what do Hawks and Doves have to do with you spewing your chips?

When poker pros talk about line balancing and optimum bluffing frequencies, they’re talking about a game in which the strategies at the table are in equilibrium.  Here’s the theory behind it:

Let’s say 10 strong, thinking no-limit hold’em players sit down at a table and each of them has a different default strategy.  Some of these strategies will be successful and others will be unsuccessful.

Now let’s say that these players have an infinite amount of money and can never leave the table.  Being strong, thinking players; the players using an unsuccessful strategy will alter their playing style to exploit weaknesses in the superior strategies at the table.  Soon some of the previously successful players will start losing money and will have to adjust.

In time, these 10 theoretical players will reach equilibrium.  No strategy will be superior to any of the others at the table.

Now if one of these players leaves and you sit down in his place, one of two things will happen. First, you could have a superior strategy to the equilibrium and start cleaning up.  In that case, the other players will adjust their strategy and a new equilibrium will develop.  Second, you could get your ass handed to you at first until you adjust your strategy to fit the current equilibrium.  In this kind of game, the strategy suggested by your favorite pro will work just fine.

Poker Games Aren’t in Equilibrium

Poker is a lot more complicated than a game like Hawks and Doves.  There are multiple streets and multiple moves you can make on each street.  There is no single “best” poker strategy – which brings us back to why you’re losing money when you play a balanced strategy the second you sit down at a table.

Don’t Balance Your Play.  Exploit Theirs’.

Poker favors the aggressor and balancing your line for the sake of making your play unexploitable is a defensive strategy.  You should look for weaknesses in your opponents’ strategies and attack them.  Here’s an example (don’t bash the stats. They’re round numbers to make things easy):

Let’s say you sit down at a table and notice that a player continuation bets 100% of the time but gives up on the turn if he doesn’t have at least top pair.  To simplify the example we’ll say that you can only call or fold and the game ends after the turn.  The game is $1/$2 heads up no-limit hold’em.  Your opponent will always raise to $8 pre-flop and always bet the pot when he bets. Given these restrictions, you adopt the following strategy to exploit your opponent…

Call anytime the player raises pre-flop.

Call 100% of his flop bets.

If he bets the turn and you can’t beat top pair, fold.

If he bets the turn and you can beat top pair, call.

If he checks the turn, bet.

Your opponent will make top pair or better 20% of the time by the turn.  Again, for simplicity’s sake, we’ll consider the times you win the turn and the times your opponent wins the turn are equal.  Here’s how it plays out (100 games):

You call pre-flop and call flop but fold turn (18 times) – Lose $432 [($8 preflop + $16 flop) x 18 times].

You call pre-flop, call flop and lose (1 time) – lose $56 [$8 preflop + $16 flop + $32 turn]

You call pre-flop, call flop and win (1 time) – win $56 [$8 preflop + $16 flop + $32 turn]

You call pre-flop, call flop and bet turn (80 times) – win $1920 [($8 preflop + $16 flop) x 80 times]

Total: Won $1976 – lose $488 = $1488 total profit

Obviously your strategy is highly profitable – even more profitable than if you folded your poor hands and called with a balanced range of big hands, suited connectors, etc.

“But a Balanced Strategy is Unexploitable.”

True.  If you bluff with optimal frequency and balance your lines, your opponents won’t be able to read you and will make mistakes.  The trouble is that you’re not going to develop a balanced strategy after reading one article or watching one video.  Hell, a TON of pros don’t even play a balanced strategy.  It’s difficult to do.  It takes study, discipline and a total lack of emotion and…oh yeah…the perfect, unexploitable poker strategy doesn’t even exist.  At least, no one has found it yet.   You’ll make a lot more money in the long run if you can put your opponents on accurate ranges and exploit leaks in their games.

Does Game Theory Help Your Game?

I’m not saying that game theory is worthless.  Far from it.  Game theory provides a reliable framework for analyzing your lines to make sure you’re taking the most profitable line possible.  Game theory will show you where you’re missing out on money and where you’re making –EV plays (plays that lose money in the long run).  Of course, you still need to practice and learn to put your opponents on a range.

I believe that poker is too complicated to ever have a single dominating strategy.  However, you can use game theory to exploit your opponents’ weaknesses and modify your game when you encounter a strategy that dominates yours but it’s going to take more than one article  or one video to teach you how to do it.

Reviewing your play is the most important thing you can do to improve your poker game.  You know it’s true and still you don’t do it.

You tell yourself all kinds of lies.

• I just need more experience at the tables.
• I don’t make money when I’m reviewing my hands.
• I already know what I did wrong.
• I don’t make mistakes. (If you say that, just kill yourself now.)

You are losing money if you don’t review your play.  Of course, there is one valid excuse for not reviewing your play – you don’t know how.

If that’s the case, I’m going to change that.

How to Review Sit ‘N Go Sessions

Sit ‘N Goes are the easiest games to review.  There’s no line balancing, no real post-flop play; just value raises and shoves.

There are tons of articles across the net that will tell you what hands you should play during the different stages of a SNG.  Despite what I may have said in an earlier article, the right way to play the early stages of a SNG is super tight.

You’re basically waiting for premium hands and that’s it.  It’s the late stages of a Sit ‘N Go that get interesting.

In the late stages of a SNG, you’ll shove AJo, K7o, T8o and worse.  Whether or not your shove is correct will depend on your position, the action, the stack sizes, the size of the blinds, how loose or tight your opponent is and how many players are left.  It’s a lot of information to digest, fortunately there’s a mathematical model that takes all these factors into account: the Independent Chip Model.

The Independent Chip Model is too complicated to figure out using a pen and paper.  Fortunately, Sit ‘N Go grinders can just import their tournaments to SitNGo Wizard and easily find their mistakes (there’s a 30-day free trial too. This software is REQUIRED for all serious SNG players).  Once you import your tournaments, SNGwiz will tell you which shove/fold situations you got right and which ones you botched.  There’s even a simulator for you to get a feel for when to shove.

Of course, there are situations that SNGwiz can’t figure out.  For example, if you want to know if you made the right move raising with the intention of folding to a shove, you’ll have to do a little more work. 

Let’s say you have a $3000 stack with 5 players left and the blinds are 60/120.  It folds around to you in the small blind.  Your opponent is a very tight-aggressive regular with 1800 chips.  You think he’ll shove over your raise with 20% of his hands.  Should you raise to steal?

If you raise to $360, you’re risking 300 chips to win 180.  In 100 trials, you’ll win 180 chips 80 times (180*80=14400) and you’ll lose 300 chips 20 times (300*20=6000) which means that your steal has a positive expected value of 84 chips.  (14400-6000=8400/100=84).

Next you can use an ICM calculator to see how that chip gain will affect your equity.

Now you have no excuse not to review your Sit ‘N Go sessions.  Not only did I tell you how to do it, I gave you a link to a free 30-day trial of the best Sit ‘N Go software on the market.

In the next part of this series, I’ll talk about reviewing your cash games.

The ability to put your opponent on a range of hands is one of the most important skills in poker.  Hand reading has nothing to do with reading your opponent’s “soul” and everything to do with pattern recognition and combinatorial analysis.

Pattern recognition is identifying which hands make sense given the villain’s line.  Most experienced players have this aspect of hand reading nailed down, but the statistical part of hand reading eludes them.  If you’re one of these players, learning combinatorial analysis will definitely improve your game.

What Is It?

Combinatorial analysis is the act of determining how likely your opponent is to hold a certain hand given the number of possible ways the hand can be made.  Here’s an example:

You’re in position in a 3-bet pot with AJ and the flop comes J57.  Your opponent open shoves for 50 big blinds more.  You know he’ll only take this line with JJ, AA or AK.  Should you call?

Some players would reason that there are two hands that beat them and one hand that doesn’t therefore their odds of winning are 1-in-3 and they should fold.  That reasoning is flawed.

Combinatorial analysis will give us a better understanding of the situation.  Since there is a Jack on the board and we’re holding a Jack, there is only one way for our villain to hold JJ.  Since we also hold an Ace, there are 3 ways to hold AA and 12 ways to hold AK.  All in all, there are only 4 ways for our opponent to hold a hand that beats us and 12 ways for our opponent to hold a hand we beat so we’re almost a 3-to-1 favorite.  Even when you consider the fact that AK will out draw us about 12% of the time, it’s a clear call.

Combinations to Remember

There are certain situations that pop up over and over again and it’s worth taking the time to remember the combinations for those situations.  Here are some combinations to remember:

Basic Combinations

There are two basic hands a person can hold: two unpaired cards and a pocket pair.  Here are the possible combinations.

Any two unpaired cards: 16

Any pair: 6

Combinations to Pair a Card on the Board

Combinatorial analysis becomes more complicated when you use it to consider how likely your opponent is to hit the flop.  The first thing you have to do is put your opponent on a range of hands.

Let’s say, for example, that your opponent raises in middle position in a 6-max game and you call on the button with pocket 8s.  You know your opponent’s range in mid position is KJs+, KQ+, A2s+, AT+.  We’ll ignore pocket pairs to make things easier.  The flop comes Ah3s6c.  How likely is your opponent to hit that flop?

We know that when a card is on the board, your opponent has 12 ways to hold any unpaired hand.  Your opponent’s range has 72 combinations (12 ways for each AT+, 3 ways for each A2s – A9s) that have an ace and 16 combinations (12 for KQ and 4 for KJs) that miss.  Your opponent is 4 ½ times more likely to have hit this flop than miss.  You should fold when he c-bets.

It’s usually a bad idea to play back at an opponent on the flop when an Ace is showing since Aces make up a large portion of almost every player’s range.

Combinations That Make Trips

There are only three ways to make trips for each card on the board.  Assuming all pocket pairs are in a villain’s range, there are 9 ways to make trips using any card on the flop.

Combinations That Make Two Pair

Figuring out the number of combinations that make two pair can get complicated.  First you have to put your opponent on a range and figure out how likely the flop helped them.

Let’s say your opponent’s range is AT+ and the flop is AJ3.  There are 9 ways your opponent could hold two pair.  If the flop is AJT, your opponent now has 18 ways to make two pair.

Things become even more complicated when you add more cards to your opponent’s range.  If KQ and JT are added to your opponent’s range on the AJT flop, they now have 16 ways to make a straight and another 9 ways for a JT two pair.

Combinations That Make Flush Draw/Flush Possibilities

It’s much less common to hold a suited hand than an unsuited hand and the number of combinations possible is highly dependent on the villain’s range and whether or not there’s a card from their range on the flop.  That’s one reason a suited ace on the flop reduces the odds of a flush draw.

Programs to Help You

Don’t worry if this all seems a little overwhelming.  There are free programs available that will do all of this work for you.  Two take come to mind are FlopZilla and Pokerazor.  Take some time and play with these programs to get a feel for how likely different ranges hit different flops.  This information will help you judge when to defend against c-bets as well as make other advanced moves.

In Finding Poker Leaks Part 1 I talked about how to use Hold’em Manager to find leaks in your c-betting strategy.  In the second part of this series of an undetermined size, I’m going to talk about analyzing your line to find out if your line has a good risk-to-reward ratio.  Like the C-betting article, this one was also inspired by Jason Ho over at Stoxpoker.  I highly recommend you sign up and watch his videos.  It’ll be well worth the money.  Enough ass kissing.  On with the show.

Here’s what you’ll need to analyze your line:

A program like Hold’em Manager or PokerTracker3 that’ll give you stats on your villain

A program like FlopZilla or Pokerazor to show you how often your villain’s range hits

This .xlsx file that I made from watching Jason Ho’s video

The hand history you want to analyze

Step 1

Grab the hand history you want to analyze.  And look up the villains VPIP stats and C-bet percentage in Hold’em Manager or PokerTracker3.

Step 2

Select your villains range (VPIP) in FlopZilla or Pokerazor as well as the flop cards and run an analysis to see what percentage of the time he makes certain hands with that range.

Step 3

Insert the percentages from Step 2 on the Excel spreadsheet as well as the villain’s C-bet percentage.

Step 4

Fill in the pre-flop, flop, turn, and river bets on the Excel spreadsheet.

Step 5

Enter the possible lines you could take (check/call, check/call, check/fold; check/call, check/raise, bet; etc.) in the designated are on the spreadsheet.  Then enter the minimum and maximum loss/gain that each line could give you.

Step 6

Using the percentages you got from Flopzilla/Pokerazor and your opponents actions, decide which line gives you the best return on investment.

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I realize these steps are a little vague if you’ve never done this before, but I promise that once you get the hang of it you’ll be able to find the most profitable line in any given situation and spot a ton of post-flop leaks in your game.  If you want to see a video version of this, you can sign up at Stoxpoker and watch Jason Ho’s videos.  When you do, you’ll understand why I have such a bro-ner for the guy.  He’s a genius.

This is the first part of a series of articles on poker leaks that I really don’t know when I’m going to end.  Hold’em Manager has features that I only dreamt of when I was using PokerTracker3.  To begin, I’m going to go over how to use Hold’em Manager to find poker leaks in a C-betting strategy.

Your Poker Game

Most people C-bet too often.  If you c-bet more than 80% of the time, I’d say you probably fall into this category.  But when should you c-bet and when should you check fold.  Before we go any further I have to say that if you ever check/fold after you raise pre-flop, you must check/raise occasionally to balance your line.  If you don’t balance your line, you’ll be too readable to a thinking opponent. That said; here’s how to analyze your c-bet strategy.

Step 1

Open Hold’em Manager and go to the Cash or Tourney tab (whichever one you want to analyze) then click the “Filter” button on the top right.

Step 2

Click the “More Filters” tab and add the following filters:

PFR=True

Called Preflop 3-bet=False

Faced Preflop 3-bet=False

Allin Preflop=False

Flop Continuation Bet Made=True

Then click “Save and Close.”

Step 3

Run your reports.

A good report to look at is the Plugged Leaks 03 – Flopped hand strength report.  You can see how much you’re profiting/losing when you flop certain hands.

If you’re a member of Stoxpoker, you can download several other kickass reports from Jason Ho’s videos.  One report that’s incredibly useful is the Stoxpoker Bucket by Hole Cards report.  This will show you your profit/loss based on your holdings.  It kicks the crap out of the Plugged Leaks report.  It’s worth subscribing just for the reports and filters that Jason Ho gives you.  I highly recommend them.  The videos are also excellent.

Step 4

Play with it a little.  Look at the hands where you saw a turn (saw turn=true) and where you didn’t see a turn (saw turn=false).  You can also check how profitable your double-barreling strategy is by adding (turn continuation bet made=true).  There’s a lot you can learn.

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Just another word of caution, if you’re analyzing a tournament you should filter your results by the number of players left so your results aren’t skewed by heads-up matches.  Other than that, enjoy and let me know if this helps you!