Poker Lesson #11: Poker Odds for Beginners, Part I
by Oliver Butterick

Most of my articles assume a lot of prior poker knowledge, and might be a little too advanced for some readers.  This lesson, we've gone back to basics, with a look at how to make mathematically sound decisions.

Review of Odds

Odds, probability, and percentages are three expressions to describe uncertain events, and are easily confused.  For example, when predicting which number will come up when rolling a six-sided die, we can express this uncertain event by using probability, odds, or percentages.

The probability of rolling a “4” is 1 out of 6.  There are 6 total possibilities, and 1 of these possibilities is the number 4.

The odds of rolling a “4” are 5 to 1.  Out of the 6 possible results, 5 of them are “unsuccessful” (1, 2, 3, 5, and 6), and one of them is “successful” (4).  So, odds is a ratio of unsuccessful outcomes vs. successful ones, and can be expressed as 5 to 1 or 5:1.

The percentage of the time that a "4" will be rolled is determined by dividing the number of successful possibilities (1) by the total number of possibilities (6).  The result is .167, and can be converted to percentage by moving the decimal two placed to the right.  So, you will roll a "4" 16.7% of the time.

How Odds Apply to Texas Holdem

There are two main ways that odds come into play in Texas Holdem, and it is important to be able to calculate two different sets of odds and compare them so that you can make mathematically sound decisions.  There are other types of odds that more advanced players should consider, like "implied odds," but since this lesson is geared for beginners, I've left out a discussion of implied odds.

1. Odds of “Making Your Hand”

This is the expression of the chances that your hand will improve and become the winning hand. For example, if your opponent has pocket 9’s, and you have AK suited, and you are all-in before the flop, your odds of winning the hand are approximately 1:1, meaning that you have approximately a 50% chance of winning the hand.

2. Pot Odds

This is the expression of the amount of money that you can win vs. the amount that you have to wager.  For example, if there is already $100 in the pot, and your opponent bets $50, you are getting 3:1 pot odds.  This is because you can win $150 (the $100 in the pot plus your opponent’s $50 bet), or you can lose $50.  This makes the pot odds $150:$50, which can be reduced to 3:1.

3. Comparing Odds

Generally, mathematically sound poker decisions are made when the odds of making your hand are more favorable than the pot odds.  For example, let’s say that you have a hand that has a 16.7% chance of winning, which translates as 5:1 odds to make your hand (which is the same odds of rolling a “4” used in the above example).  Let's also suppose that there is $60 dollars in the pot, and you are required to call $10, which is 6:1 pot odds.  5:1 is more favorable than 6:1, so mathematically, it is correct to call.

4. Counting the pot to determine Pot Odds

***Money that you have already put in the pot is no longer your money, but is now money that you can possibly win.***  The reasoning that “I’ve already invested X amount of dollars in this pot” is faulty reasoning, and is no excuse for mathematically bad decisions.  This is sometimes known as "throwing good money after bad," which is something you want to avoid.  Even if you made a bad decision on a previous street, you should use all of your tools to make a correct decision as often as possible.

Example #1: You have invested $5 in the big blind, and there has been a raise to $15, with two callers before the action returns to you.  So, there is $15 x 3 = $45 PLUS your $5 big blind, for a total of $50 in the pot, and you are required to call $10 more to stay in the hand.  Thus, you are getting 5:1 pot odds on your call.  Since you cannot decide NOT to bet your blind, it is considered to be in the pot already, and it is money that you can win.  It doesn’t matter that it used to be your money.

Example #2: There is $50 in the pot, and you make a pot-sized bet of $50.  Your opponent raises to $200.  Now, you are required to call $150 more to stay in the hand.  The pot size is $300 ($50 in the pot plus your bet of $50, plus your opponent‘s raise to $200)—it is the total amount that you can win.  You are getting 2:1 pot odds on the call, because you can win $300 or lose $150.

“Outs” and “The Nuts”

An “out” is any card that you believe will make your hand into a winner.  For example, if you have QJ of Hearts, and the flop is: 10-9-4, with two hearts, you may have as many as 21 outs (9 Hearts to make a flush, 3 each of the non-Heart Kings and Eights to make a straight, and 3 each of the non-Heart Queens and Jacks to make top pair).  That is assuming that your opponent has something like A10—top pair, top kicker.  Here’s how many outs this hand with this flop has against opponents with different holdings:

Vs. J-10

Now, you have 18 outs, since the Jacks will have two pair for your opponent and only one pair for you.

Vs. QQ

Now, you have 15 outs, since neither the Jacks nor the Queens are outs for you.  You only have the straight and flush outs.

Vs. AK of Hearts

Now, you have 12 outs: the Non-Heart Kings and Eights to make a straight, and the non-Heart Queens and Jacks to make a pair.  Also, if the 10 and 9 are both hearts, then the Eight of Hearts is also an out for you, since it will give you a straight flush, giving you 13 total outs.  With two cards to come, holding two overcards and an open-ended straight flush draw, you are actually a favorite against all possible holdings of your opponent except a bigger flush draw, and in the worst-case scenario, you have 12 outs, which translates to you being a 1.75:1 underdog.

Looking at the examples above, you can see that the number of outs you have depends largely on what your opponent is holding, and the above example assumes that you only have one opponent.  Against multiple opponents, you may have fewer outs (or even no outs at all).

For example, playing that hand against the following three opponents:

A-8 of Hearts, 10-10, and Kh-Q

Collectively, they have taken up a lot of your outs:

In this case, you have 6 outs: the non-Heart Kings, and the non-heart Eights.

However, if one of those cards come on the turn, each of your opponents will still have “live” draws to beat you on the river:

“The nuts” refers to the best possible hand, with a given set of board cards.  Another way to put it is that "the nuts" is a hand that cannot be beat (though sometimes it can be tied).  Some people confuse this phrase to mean the “winning hand.”  It is important to understand that the nuts refers to the best of all possible hands with a given board.

In the example above, when you had QJ of Hearts and the 10 and 9 of hearts were on the board, you could only make the nuts by making a straight or straight flush.  This is because any other flush that you could make could possibly be beaten by a bigger flush.

Another example is if the board comes: A-K-Q-J-10, with no flush possibility.  In this case, the nuts are on the board.  That means that everyone who stays in the hand will get a share of the pot.

I strongly believe that a lot of money can be saved by avoiding starting hands that do not have a lot of possibilities to make the nuts.  Of course, any two cards can make the nuts: 7-2 can make the nuts if three 7’s or three 2’s come on the board, but this doesn’t happen nearly as often as AK suited or pocket Aces makes the nuts.

In the second part of this article, I will bring all of these concepts together and illustrate how to make mathematically sound decisions when you have a drawing hand, and how to give your opponent bad pot odds when they are on a draw.

Oliver can be reached at oliver@babblog.com.

|

 

© Copyright Babblog and the Respective Authors, 2004-06
Web Design and Graphics by Jeff Lewis.