Using Maths To Beat the Poker Tables

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It's no big secret that the majority of poker players hate maths. There are even some winning players who claim that they are “feel” players, and don't use maths to beat the poker games. So, if it's already possible to beat the games without using maths, shouldn't we just avoid the topic entirely? We can all then continue with our perfectly happy maths-free day.

The Best Players Use Maths

It's true that we find some strong players who have very good intuition and don't need maths to beat the games. However, the reality is that the very best players use maths on a regular basis to make their decisions. We are not even necessarily talking about difficult maths. The maths surrounding poker is often very simple. They can help us to refine the decisions we already make based on instinct.

Even very good “feel” players may be surprised to learn that certain decisions could be costing them money. The only way for them truly to establish whether certain plays are correct is by checking to see if the maths adds up.

So, while maths is not a strict requirement in soft games, understanding the poker basics will make us stronger players. And, in order to compete at the very highest level of online gaming, maths is an absolute necessity.

How Exactly Does Maths Help Us?

Maths helps us in all areas of the game. Let's see how we can use maths to help us answer two specific questions.

1. Pot-Odds

Question – There is $10 in a heads-up pot on the river. We face a bet of $5 from our opponent. How often do we need to win to make the call?

This is an area where our intuition may mislead us. We might intuitively feel that we need to be good 50% of the time in order to call. But in reality, we don't even need to be a favourite in order for calling to be correct.

Think about it this way:
There is a cool $1,000,000 in the pot. We have a hand that is likely to only be good 20% of the time. Our opponent bets $1. Call or fold?

Hopefully, our instinct tells us to call this time. We don't care in the slightest that we will lose the majority of the time. We are only risking $1 and 20% of the time we will win the million. It's a really easy call, despite the fact that we will usually lose $1.

Our original question is clearly a less extreme scenario and a little more realistic, but the same principles apply. We clearly don't need to win this pot 50% of the time because there is already money in the middle. So, how often do we need to win?

We can use the following simple formula to help us calculate this:

Percentage of the total pot we invest = How often we need to be good to call

Sometimes poker maths gets complicated by people who know a little too much, but it really is this simple. So, how much of the total pot would we be investing with our call?

If we called, we'd be investing $5 out of the total pot of $20 (remember that the total pot includes both our opponent's bet and our potential call). That equates to 25% of the total pot (5/20). This means that we only need to have the best hand 25% or more to make a clearly profitable call.

Ratio vs Percentage

More traditional gamblers prefer to describe pot-odds in the form of a ratio. This format is how we are usually told our odds, assuming we went to a bookie to place a sports bet. In the above example, our odds can also be referred to as 3:1 (three-to-one).

We are investing $5 to win the $15 that is already in the middle. Our odds are 15:5, which can be simplified to 3:1 (divide both numbers by 5). Most old-school poker players will describe pot-odds this way, although it's actually simpler to consider our pot-odds in percentage format.* A good poker player should understand how to use both, even if just for purposes of communicating with other players who may use one system or the other.

(*N.B. There is no inherent advantage to using ratios or percentages. The reason we describe pot-odds as easier to calculate in percentage format is that in most cases, we will be comparing our pot-odds to our pot-equity to establish whether we have a profitable call. Pot-equity is nearly always referred to as a percentage. It's simpler to compare two percentages, rather than to compare a percentage to a ratio.)

2. Bluffing Success

Question 2 – There is $100 in the middle on the river. We decide to bluff for $50. How often does our bluff need to work to make money?

Again our intuition may tell us that it needs to work over 50% of the time. If it doesn't, it would mean that our bluff is failing most of the time and, therefore, can't make us money. However, our intuition would once again be wrong.

Imagine a similar example to before. A million dollars in the middle and we are told that if we bluff for $50 it will work 40% of the time. Should we bluff? Absolutely – our bluff might not work every time but we only risk $50, and when it works, we make a million. Can you guess which formula we should use to calculate exactly how often our bluff needs to work?

Percentage of the total pot we invest = How often our bluff needs to work

Looks familiar? It's exactly the same formula as before with a slight adjustment.

Back to the original question. We are investing $50 to win the total pot that will be $150 after our bet.

50/150 = 33.33%

So assuming our river bluff works over a third of the time we are printing money in this spot - even though our bluff fails the majority of the time.

This is Just the Beginning!

We don't want to lie to you and tell you that it doesn't get more complicated in certain situations. There are many other areas where maths can be applied to the game of poker, such as value-betting, constructing optimal ranges, and setting up stack-sizes for the later streets. The maths surrounding poker can get infinitely complex, and even the best players don't understand it on every level.

However, the advanced stuff is not necessary at this stage. Just a little understanding of some of the more basic maths surrounding the game can go a long way towards helping us refine our decisions.

So, while very few of us can say we love maths, if we're serious about poker we can begin to love the various ways maths can help us destroy our opponents at the tables.

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