Poker is one of the most popular games, among the classic card games that can be found in every real money casino. It is a game of not only luck but also great skill. However, it is no secret that most poker players hate math. There are even successful players who claim that they play “intuitively” and do not use math to win at poker. But if it’s possible to win without using math, isn’t it better not to bring it up at all? Then we can all have a happy day without math.
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The Best Players Use Math
It’s true that there are strong players with good intuition who don’t need math to win. However, the fact is that the best players use math to make decisions all the time. It’s not necessarily about complex mathematical calculations. The math of poker is often quite simple. It can help us tweak the decisions we already make with our gut.
Even players with good intuition may be surprised to learn that some of their decisions can cost them money. The only way to know for sure if a decision is the right one is to check it with mathematical calculations.
Although math is optional in amateur games, understanding the basics of poker will make us better poker players. But if you want to take part in the highest level online competitions, you can’t do without math.
What Exactly Is Math Useful For?
Math comes in handy in all aspects of the game. Let’s see how using math helps us answer two specific questions.
1. Bank Odds
Question – When playing heads-up on the river, the pot size is $10. The opponent bets $5. How often do we need to win to afford a call?
In this situation, our intuition can let us down. We might think we need to have at least a 50% chance of winning in order to call such a bet. But the truth is, we don’t even have to be a favorite to respond.
Think of it this way:
Suppose we have $1,000,000 in the pot. Our hand has only a 20% chance. Our opponent bets $1. Call or fold?
Naturally, in this case, our intuition tells us to call. We don’t care that we’ll come up short most of the time. We risk only $1 and win a million 20% of the time. This is a very easy decision, even though we will lose $1 most of the time.
Although our situation is initially much less extreme and somewhat more realistic, the principles of decision-making remain the same. There is no need for us to have a 50% chance of winning what’s in the pot since there is already a bet on the table. So what are the odds of winning that we need?
In order to calculate this, we can use a simple formula:
- Percentage of the total pot we put in = The required odds of winning
Sometimes people who know a little more make poker math complicated, but it’s actually pretty simple. So what percentage of the total pot can we put in our call?
If we call, we put in $5 of the $20 total pot (remember, the total pot includes our opponent’s bet as well as our potential call). That makes 25% of the pot (5/20). That means we only need 25% or more to make a really profitable call.
- Ratio or Percentage
More traditional players prefer to estimate the odds of the pot as a ratio. In this form, we estimate our odds as if we were betting on a sport at a bookmaker’s office. Our odds in the example above can also be described as 3:1 (three to one).
We invest $5 to win $15, which is already on the table. Our odds are 15:5, which can be simplified to 3:1 (dividing both numbers by 5). Most old-school poker players calculate pot odds this way, but it’s much easier to look at pot odds as a percentage.*A good poker player should understand both formats if only to understand players who use different counting systems.
(*N.B. There is not much difference between whether you use odds or percentages. The reason it’s more convenient to calculate pot odds as a percentage is that in most cases we’ll be comparing pot odds and pot equity to see if it’s profitable to call. The equity pot is almost always expressed as a percentage. Comparing two percentages is easier than percentages and odds).
2. Successful Bluffing
Question 2 – On the river, the bets on the table are $100. We want to bluff by betting $50. What should be the odds of our bluff so that we can break the pot?
Again our intuition may tell us that we should have a 50% chance. If that’s not the case, then our bluff will be a loser in most cases, which means we can’t win. Again, our intuition fails us again.
Imagine a similar example. There are one million dollars on the table, and if we bluff by betting $50, we will win only 40% of the time. Is it worth bluffing? Absolutely! Perhaps our bluff will not always work, but we risk $50 and when the bluff is successful, we’ll win a million. Guess what formula you should use to calculate the necessary odds of bluffing!
Percentage of the total pot we put in = Necessary odds of bluffing
Look familiar? Well, it’s exactly the same formula as before, with just a slight correction.
But let’s go back to our original situation. We put in $50 to win the pot, which after our bet is $150.
50/150 = 33.33%
Assuming our bluff on the river will work in more than one out of three cases, we are in an incredibly good position, even though most of the time the bluff will fail.
But That’s Just the Beginning!
Let’s not lie to you – there are more complicated situations. There are many other aspects of poker in which math can be used, such as betting for a good bet, calculating optimal ranges, and calculating stack sizes for late streets. The math of poker can get infinitely more complicated, and even the best players don’t understand all aspects of it.
Nevertheless, we don’t need such subtleties at this stage. Even an understanding of some of the basics of poker math can make our decisions much better.
So even though few of us can boast a love of math, if we take poker seriously, it is possible to love the way math can help us crush our opponents at the table.