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TOURNAMENT KILLER POKER BY THE NUMBERS ** The Keys to No-Limit Hold'em Success **

**By Tony Guerrera**

**LYLE STUART BOOKS****Copyright © 2008**

**Tony Guerrera**

All right reserved.

All right reserved.

**ISBN: 978-0-8184-0723-9**

**Chapter One**

**CONVENTIONS**

** Introduction**

In tournament NLHE, we need to consider many variables when making our decisions:

Payout structure

Blind structure

Our cards

Our opponents' cards

How our opponents play

Depth of stacks

Analyses not accounting for all these variables are incomplete. This chapter describes conventions used throughout this book-conventions that make the precise description of situations concise and quick to read.

**Tournament Chips vs. Money**

Central to the theory of tournament poker is the idea that there's a difference between a quantity of tournament chips and the monetary value associated with a quantity of tournament chips. Suppose you're in the following tournament:

*Format:* Winner Take All (WTA)

*Entrants:* 50

*Starting chips:* 5,000

*Buy-in:* $10+$11

*Payout structure:* 1st = $500

If you win this tournament, the (50)(5,000) = 250,000 chips you'll have will be worth $500 instead of $250,000. Now take the following example:

*Format:* Single-Table Tournament (STT)

*Entrants:* 10

*Starting chips:* T100

*Buy-in:* $100+$9

*Payout Structure:* 1st = $500; 2nd = $300; 3rd = $200

If you win this tournament, the T1,000 chips you have will be worth $500 instead of $1,000.

In our coverage of tournament NLHE, we'll be flip-flopping back and forth between talking about chips and the monetary value that we can assign to those chips. To avoid confusion, a T will always precede a number of tournament chips, and an appropriate currency symbol will always precede a number referring to an amount of money.

**Position**

Your absolute position at the table will influence some of your decisions. Your position relative to certain players at your table will also influence your decisions. Because position is so important, we need a quick, convenient way to describe the position of players at the table. And because we can simply refer to players by their position, a quick, convenient way to describe position will also give us a quick, convenient way to refer to players.

The positions present in every hand are the *button* (B) and the *big blind* (BB). Most of the time, there will also be a *small blind* (SB). As long as at least 4 players are dealt into a hand, the player to the left of the BB (who acts first preflop) is *under-the-gun* (UTG). The player immediately to his left is called UTG+1, the player two to his left is called UTG+2, and so on, until you get to B (e.g., B at a 5-handed table, though 2 to the left of UTG, is always referred to as B instead of UTG+2).

Meanwhile, as long as 4 players are dealt into a hand, the player to the right of B is called the cutoff (CO). The person immediately to CO's right is called CO -1, the person two to his right is called CO -2, and so on, until you get to BB (BB is always referred to as BB). Figure 1.1 provides two examples of how this notation works.

With this naming convention, it's often possible to refer to a specific player in two ways. For example, UTG at a 4-handed table where the SB and BB have been posted normally also happens to be CO. One label isn't more correct than the other is-as long as the table size is indicated, they both uniquely identify the same player. At a 10-handed table, the player 5 to the left of the BB is UTG+4 and CO -2. Since 2 is smaller than 4, this player would usually be referred to as CO -2; however, UTG+4 is still acceptable.

**Hand Descriptions**

Some readers didn't like the modified Mike Caro University (MCU) notation I used in *Killer Poker by the Numbers (KPBTN)* to describe the action in a hand. I'll be truthful when I say that I also thought it was too bulky-it looked better on my 20 monitors than it looked in print. But when following the action in a hand, I don't like to read through a bunch of text. I'm the "By the Numbers" guy, but I hate constantly having to update stack sizes with mental arithmetic while reading through a bunch of text. I'm very visual with my poker-I like to see the present state of affairs in front of me. Textual hand descriptions seem to dominate pretty much every poker forum on the Internet, and maybe it's because I haven't spent much time on Internet poker forums, but I'm much quicker at parsing through a well-executed graphical or tabular presentation of some sort. After some thinking, I came up with a new tabular format; see table 1.1 (p. 7) for an example hand.

This format is designed to be read from left to right in a columnar fashion:

*Column #1 (Player):* This column refers to players by name or position or both.

*Column #2 (Stacks):* This column lists each player's stack before blinds for the hand in question are posted.

*Column #3 (Preflop):* This column (split into subcolumns) displays preflop action. In table 1.1, sbT10 means that a small blind of 10 was posted and bbT20 means that a big blind of 20 was posted. In this column, and in general, dashes indicate folds, and numbers indicate the total number of chips a player is in for to that point in the betting round. For example, the T20s in the second subcolumn of preflop action in table 1.1 indicate that SB completed to T20 and BB checked his option. The cell in the bottom of this column displays the size of the pot at the conclusion of preflop action. In table 1.1, the pot contains T140 at the conclusion of preflop action.

*Column #4 (Stacks):* This column lists stacks for players still in the hand going into the flop.

*Column #5 (Flop):* This column shows the flop, and the subcolumns show the betting action. In table 1.1, the T0 entries indicate checks. The cell in the bottom of this column displays the size of the pot at the conclusion of flop action.

*Column #6 (Stacks):* This column lists stacks for players still in the hand going into the turn.

*Column #7 (Turn):* This column shows the turn, and the subcolumns show the betting action. The cell in the bottom of this column displays the size of the pot at the conclusion of flop action.

*Column #8 (Stacks):* This column lists stacks for players still in the hand going into the river.

*Column #9 (River):* This column shows the river, and the subcolumns show the betting action. The cell in the bottom of this column displays the size of the pot at the conclusion of the hand (uncalled river bets are included in this total).

*Column #10 (Stacks):* This column lists stacks of all players at the conclusion of the hand.

If action doesn't make it to the river, tables will exclude columns from the betting rounds not played, but the rightmost stacks column will always display what the players' stacks are at the conclusion of the hand.

**Hand Distributions**

When our opponents act, we can *put* them on ranges of hands based on their tendencies. For opponents yet to act, we can predict things such as the hands they'll call raises with. *Hand distributions* are an essential part of the game, and we'll be talking about them a lot.

Listing out hands individually can get cumbersome quickly, so we need some notation to help us express hand distributions concisely. *Killer Poker by the Numbers* and *Killer Poker Shorthanded* used something I referred to as *interval notation* to express hand distributions. But a more common way of referring to hand distributions is much more concise. I'll be using the following conventions:

1. Plus signs following unpaired hole cards signify that you should keep the first card constant while incrementing over the second card until the rank of the second card is one below the rank of the first card (e.g., J7+ = {J7, J8, J9, JT}).

2. Minus signs following unpaired hole cards signify that you should keep the first card constant while decrementing over the second card until the second card is a 2: (e.g., 85P = {85, 84, 83, 82}).

3. Plus signs following a pocket pair signify all pocket pairs equal to and higher than the indicated pocket pair: (e.g., JJ+ = {JJ, QQ, KK, AA}).

4. Minus signs following a pocket pair signify to include all pocket pairs equal to and lower than the indicated pocket pair: (e.g., 88P = {88, 77, 66, 55, 44, 33, 22}).

5. A short dash between two sets of hole cards where the first card is the same in both signifies to include all hands where the first card is the same and the second card goes from the second card in the first set of hole cards to the second card in the second set of hole cards: (e.g., K9-K6 = {K9, K8, K7, K6}).

6. A short dash between two sets of hole cards where the first card is different in both signifies to include all hands where the first and second cards increment or decrement simultaneously: (e.g., JT-54 = {JT, T9, 98, 87, 76, 65, 54}).

7. The letter *o* means that a hand is offsuit and the letter *s* means that a hand is suited. No letter designation after a hand indicates that the hole cards can be either suited or unsuited: (e.g., AKs = {A[??]K[??], A[??]K[??], A[??]K[??], A[??]K[??]}; AKo = {A[??]K[??], A[??]K[??], A[??]K[??], A[??]K[??], A[??]K[??], A[??]K[??], A[??]K[??], A[??]K[??], A[??]K[??], A[??]K[??], A[??]K[??], A[??]K[??]}; AK = {AKs, AKo}).

8. *{Rand}*, for random, refers to the distribution of all possible hole cards.

**Chapter Summary**

As we progress through our exploration of tournament NLHE, I'll be introducing additional conventions as needed. But at least we're now on the same page regarding much of what's needed to ensure that we're speaking the same language.

** Chapter Two ** **PROBABILITY **

** **

** Introduction**

Decision making in NLHE tournaments (and pretty much all poker tournaments) is a four-step process:

1. Calculate the distribution of stacks resulting from a particular line of play.

2. Calculate the monetary value associated with this distribution of stacks.

3. Iterate steps 1 and 2 for all possible lines of play.

4. Pick the line of play resulting in the most valuable distribution of stacks.

This process relies heavily on the branch of mathematics known as *probability*, so our first step is a crash course on probability.

As you go through this primer, you'll probably be thinking something like, "How the hell does Tony expect me to use this stuff when I'm at the tables?" The answer: the really in-depth analysis we'll be doing is stuff that can only be done reasonably away from the tables. When I'm playing, the extent of what I do in my head is on the order of estimating probabilities and assessing my expected gains/losses with respect to chips.

But the purpose of this chapter isn't just academic. We want the ability to perform sophisticated analyses away from the tables so that we can come to the tables armed with a bunch of useful information that we can draw on when we need it. Therefore, when we encounter unique situations that we can't deal with on the spot, we can go home, analyze them to death, and know what to do in the future when any similar situations arise. In the end, poker isn't just about what happens at the tables. It's really an ongoing process involving learning and relearning over and over again. And by the end of this book, we'll develop a synergy between in-depth analysis away from the table and general concepts that should motivate our play when we're at the table. With that being said, it's time for Probability 101.

**Probability Defined**

The definition of probability applicable to poker refers to relative frequencies involving sets of outcomes. The probability of a specific outcome is the number of ways that the specific outcome can happen divided by the total number of ways that an event can resolve itself. This idea is expressed by equation 2.1, which will be our working definition of probability:

*P*(Outcome of Interest) = Number of Ways an Outcome of Interest Can Occur/ Total Number of Ways Outcomes Can Occur (2.1)

*Example 2.1:* You have a bag of 10 marbles. 3 of the marbles are red, and 7 of the marbles are blue. What's the probability of drawing a red marble from the bag?

*Answer:* The bag only contains 2 types of marbles, but there are really 10 total possible outcomes for drawing a marble since the bag contains 10 marbles. Of those 10 marbles, 3 are red. Therefore, the probability of drawing a red marble, written as *P*(Red) or [*P*.sub.Red], is:

*P*(Red) = *P*.sub.Red = Red Marbles/Total Marbles = 3/10 = .3 (2.2)

*Example 2.2:* You have 8[??]3[??], and the board is T[??]5[??]2[??]7[??]. What's the probability that you'll hit a flush on the river?

*Answer:* Between your hole cards and the board cards, 4 hearts are in play, meaning that 9 hearts remain in the deck. Since we know 6 cards (your 2 hole cards and the 4 board cards), 52 P 6 = 46 cards remain in the deck. The probability of making a flush on the river is therefore 9/46 [approximately equal] .19576.

*Example 2.3:* You have two standard six-sided dice. What's the probability of rolling an 11?

*Answer:*

*P*(11) = Number of Ways to Roll an 11/Total Number of Possible Rolls (2.3)

What numbers should we place in the numerator (the top) and the denominator (the bottom) of equation 2.3? One possible answer is that *P*(11) = 1/11 [approximately equal] .0909 since it appears that 11 rolls are possible: {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12}, and only one of them is 11. However, this is wrong because each possible roll isn't equally likely. More ways exist for some numbers to be rolled compared to other numbers. To see why this is so, let's express each possible roll as (*a,b*), where *a* is the number on the first die and *b* is the number on the second die. The *outcome space* (the set of all possible outcomes) for rolling two dice is {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}. 36 equally likely rolls are possible. 2 of them, (5,6) and (6,5), result in an 11. Therefore, the probability of rolling an 11 is really:

*P*(11) = Number of Ways to Get 11/Total Number of Possible Rolls = 2/36 = 1/18 (2.4)

In example 2.3, notice that we completely define the outcome space by writing every possible way to roll two dice such that each possible way is equally likely. Then, we take the number of ways to get 11 as a subset of the outcome space. If you do all your probability problems like this, you'll never go wrong. Unfortunately, individually listing every outcome in an outcome space is usually way too time-consuming in most situations. 36 outcomes are possible when rolling two six-sided dice. Imagine how many possible outcomes exist when dealing with situations arising from a deck of 52 cards!

*(Continues...)*

Excerpted fromTOURNAMENT KILLER POKER BY THE NUMBERSbyTony GuerreraCopyright © 2008 by Tony Guerrera. Excerpted by permission.

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