Pot Odds 101 - an introduction

For some poker players the term ‘pot odds’ may appear intimidating, and for the uninitiated it can sound like you need a degree in mathematics to understand the basic principles. Anyone who regularly watches poker on TV may have heard the commentators talking about, ‘implied odds’, ‘game theory’, ‘being priced out’, or heard players like Roland de Wolfe declaring that they are an ‘88.1% favourite’ post flop… but does this mean that pot odds are difficult and only for the advanced player?

Thankfully, the answer is no and once you grasp the basic principles you may be surprised how your game opens up: you may well find yourself playing hands that you previously mucked on a regular basis. Conversely, you will be able to identify more situations where the stakes are too high and it is not worth committing any more chips to the pot.
Before we start, there are two pieces of good news:
The mathematics involved is not complicated. If you can mentally multiply and divide with small numbers then you should be well set. As with any discipline, the more you practice the more likely you are to improve and, over time, your calculation speed (and poker instincts) will get better.

## It's easier than you think!

Being vaguely right with your maths is often all you need – you don’t need to be a human calculator! For example, let’s say you were mid-hand and reckoned that you had a 40% chance of improving post flop when the exact maths said that your chances were actually 37%. Is the small 3% difference really likely to affect your next decision? Rough maths is fine as long as you can get to within a few percent of the correct figure.
This first article is going to concentrate on the basic principles and mathematical notations we need to use by looking at simple, non-poker related examples. Later on we will look at how to work out your pot odds in different poker situations and how to apply this information to your game.
So, what are pot odds and what do we hope to achieve with them? Well, pot odds are a guide we can use to work out how likely our hand is to improve at any stage of play (pre and post flop, turn and river), and then identify if we are getting good value to play those hands. They can even be used sometimes after the river to help you decide whether or not to make marginal calls.

The main principle involved is one of comparison. Most of the time we are looking to work out the odds of our hand improving to the point where we think we will have the best hand over our opponent(s), and then compare that against how many more chips we are going to have to spend to continue with play and how much we can win from the pot if we do so. In short, we are always looking to be spending chips when we can identify good value bets.
Sound complicated? Well, let’s look at a couple of simple, non-poker examples to illustrate the point:

1) Tossing a coin – heads or tails.

The chances of calling heads or tails and winning (or losing) is equal, or 50 – 50. If I offer to pay you \$5.10 for every time you win, and you pay me \$4.90 every time I win, then you would be daft not to take me up every time because you have identified a good value bet: your chances of winning or losing are equal, but you will make more cash by winning than you will have to spend by losing.

Now, you could quite easily play and lose three or four times in a row and be out of pocket, but the important point here is that in the long run you will always expect to profit, even if you happen to lose in the short term. Whatever the stakes, big or small, once you identify a good value bet then you should almost always take it because if you continue to make similar decisions in similar situations then, over time, the law of averages will play out and you will profit. Remember, luck is only a short term phenomenon!

2) Rolling a die and getting a 6.

Let’s say that I’ll give you \$10 if you roll a 6, and you give me \$1 if you don’t. Is this a good value bet?

So what are the odds telling us here? Well, let’s introduce some maths. What are the chances of you winning? There are obviously six numbers on a die and only one of them is a six, so your chances of winning are 1 in 6. If we like we can convert this into a percentage: 1 divided by 6, multiplied by 100 = 17% (to the nearest percent).

But, there is one more useful way of expressing these odds, as 5 to 1 (or 5:1). What this means is there are 5 numbers on the die that will cause you to lose, compared to the 1 number on the die whereby you will win. So, 1 in 6, 5:1 and 17% are three different ways of expressing the same probability.

Okay, we know you are 5:1 to win. The last stage is to compare the ‘cash odds’ (in poker we would be saying ‘pot odds’) and see what they are telling us. We know that if you win you will get \$10 and if you lose you will pay \$1, so the ‘cash odds’ are simply 10 to 1, or 10:1.

Now we have two sets of odds that we can compare. We know you are 5:1 to actually win, so if the ‘cash odds’ are any better than 5:1 then you are getting a good value bet… and the ‘cash odds’ are much better at 10:1 so you should always take that bet even though you only have a 17% chance of winning. I.e. you are very likely to lose in the short term, but if you play this situation repeatedly you will make money in the long term.

To prove this, let’s just look at six rolls of the die and assume that the law of averages is being fair, so you will expect to lose 5 times and win just the once: You will lose five times and have to pay \$1 each time, meaning a loss of \$5. You will win once and receive \$10. So by playing the game just six times you have won \$10 and spent \$5 so overall you have a profit of \$5, and that’s by playing a game with only a 17% chance to win!

Even without looking at a poker hand, that is an introduction to the principles and mathematics that we will be applying to our poker situations.

In the next lesson we will be getting used to working out and converting between the three mathematical notations introduced here, e.g. the ability to calculate probabilities as, say: 1 in 5, 4:1, or 20%. The good news is that if you can master the next lesson then you will have a grasp of most of the mathematics you will ever need…

…and if you recognize that 1 in 5, 4:1 and 20% are actually different ways of expressing the same probability then you are already ahead of the game!

JW – July 2011