I'd like to talk about something that, in my opinion, doesn’t get enough coverage in poker strategy articles: the often-misapplied concept of ‘implied odds’. In a game of incomplete information, we as poker players like talking in terms of principles that can, to a certain extent at least, be ‘proven’. We like our theories to be mathematically sound and to anchor our decisions around accurate probabilities. The problem with implied odds is that the factors that determine them are considerably more intangible.

I’m going to assume a certain amount of knowledge on the concept of ‘pot odds’. If this phrase is unfamiliar to you, have a read of Nik Persaud’s ‘Fundemental Theorum of Poker – Lecture Two’. ‘Implied’ odds are defined by the amount of money we expect to win when we hit our hand, not just from the current pot, but also from the stack our opponent has behind (again, a more detailed explanation of the basic concept can be found in Nik’s ‘Fundemental Theorum of Poker – Lecture Three’). It relies on us making up the pot odds we are missing when we make a call by extracting further chips from our opponent on later streets. The problem here, of course, is that it is extremely difficult to accurately predict just how likely it is our opponent will pay us that money we are relying on! As such, what I cannot give you in this article is implied odds as a ‘solved’ principle. What I can do, however, is help you with the way that you think about them. Misapplying implied odds was once a leak in my game, hopefully we can stop it becoming a leak in yours.

First of all, I want you to admit something: you love implied odds. You feel like someone on a covert mission with your cleverly disguised hand just waiting to pounce and take someone for their entire stack. All of their money is at risk and they don’t even know it. You shouldn’t feel guilty about this; feelings like this one are why we play poker. It only becomes an issue when we allow this feeling to cloud our perception of what our implied odds really are. Let me give you an example. You have been playing in a $0.50/1, 10-handed game with $100 in front of you for over an hour and nothing much has happened. UTG+1 has not played many hands and is nursing a $39 stack. He raises to $4. It’s folded to you in the small blind and you look down at pocket threes. Do you call?

Set Mining

This is exactly the kind of spot where most people are making blunders. First let’s look at some simple maths. The odds of flopping a set in Texas Hold’em are about 7.5:1. Therefore, to make calling with a low pocket pair preflop profitable - assuming you are going to fold when you miss - you need the effective stack size and money already in the pot to add up to over 7.5 times the amount of your call, right? Well, not quite. We know of course that when we hit our set, our opponent does not automatically just pass over his stack. Nor do we always hit our set and win. So we need our implied odds to make up for the fact that sometimes when we hit we won’t get paid off and sometimes we lose. So what do we need? 10:1? That would seem to be the popular consensus. Where this figure came from exactly is unclear, but it has been attributed to Reuben and Ciaffone’s Pot-Limit and No-Limit Poker 5/10 rule. Here they advocate calling raises only if the bet is less than 10 percent of effective stack sizes, but they are not simply talking about set mining. What they are referring to is calling with any hand preflop and they take into consideration many factors including positional advantage. More on that later. Let's go back to our example. It’s $3.50 to call and your opponent has $35 behind. Along with the money in the pot, you have over the 10:1 you need to set mine, right?  Let's take a closer look at those numbers. Most of the figures in this example must be attributed to a great piece of work by Eric Dickson.

We put our tight opponent on an early position raising range of Q-Q+ and A-K. For simplicity, however, let’s say for now that we know he has A-A. As we know for sure what our opponent holds, our chances of flopping a set stand at 12.23%. Let's say then, also for simplicity, that our opponent will stack off when we hit. Perfect, no?

87.77% of the time we miss and lose $3.50. 12.23% we hit but 2.01% of the time we will run into an over set or be outdrawn on the turn/river (ignoring flushes and straights for a minute) and lose $38.50. Therefore assuming a $3 max rake (offset by the $1 big blind) over 10,000 calls our profit looks like this:

1,022 times we win his stack = +$37,814
8,777 times we lose $3.50 = -$30,719.50
201 times we lose to a better hand= -$7,738.50
Total: A Loss of $644 over the 10,000 calls

That’s a loss of over six cents per hand in what would appear to be a perfect set mining situation. So here we need only a bit more than that 10/1, but as you can imagine, we do even worse against his entire range. Let’s say with K-K and Q-Q he continuation bets the pot, but then shuts down/folds to a raise if there is an overcard. Now of the 1,223 times when we hit, about 24% of the time we only win $12 ($1 rake) vs. K-K and 32% of the time we only win $12 vs. Q-Q. Factoring in the same redraws as before, that requires us to have implied odds of around 13:1 and 15:1 respectively. With A-K we’ll say he c-bet/folds the approximately 76% of the time that he fails to make exactly top pair, and stacks off the 23% of the time he does along with the 1.4% of the time he makes two pair or trips. Factoring in the redraws there and we need over 18:1.

When we give proper weighting to the six combinations of each pair and the 16 combinations of A-K, our required break-even implied odds versus the player in Eric’s example are around 15.5:1. We however do not want to just break even, we want to be profitable, so we might say we only want to set mine here if we are getting at least 17:1 implied odds, i.e. an effective stack size of about 60 big blinds.

Wiiiiiiiiiiiiiiii! Solved, right?? If only. Of course, the above example is a simplification. Our opponent has a defined range and we assume too much knowledge about exactly how he plays it. I just thought it was important to disprove the 10:1 rule first of all. Now we know that 10:1 is not enough, we need to go over some important considerations when deciding on necessary implied odds, which will be the focus of tomorrow’s article.

Read Part Two...