The Golden Formula: Your Key to Mastering Poker Math Calculations!

It's quite well-known that numerous poker enthusiasts dislike dealing with mathematics. Furthermore, it often seems like there's an overwhelming amount of information to retain—

• Pot odds
• Implied odds
• Breakeven thresholds
• Bluff-to-value ratios

It’s quite common to feel daunted and disregard anything that has to do with mathematics.

What if we were to tell you that by mastering just one straightforward concept, we could address all these concerns? poker formula?

Indeed, the importance of this formula is such that it's often referred to by poker players as the golden formula.

In this instructional piece, we will present the golden formula and discuss how it can assist you in:

• Perform pot odds calculations
• Calculate breakeven thresholds
• Determining the ratios of bluffing to value in GTO.
• Perform implied odds calculations

Introducing the Golden Formula

Let's define the golden formula from the outset: poker games :

Winning percentage >= % of total pot invested

Put simply, our likelihood of winning must meet or exceed the proportion of the pot we've wagered.

For instance, if we decide to invest 25% of what’s in the pot, we should aim to win at least 25% of the time.

This concept is remarkably straightforward, and a significant portion of poker mathematics is based around this simple principle.

Golden Formula – Utilization in Pot Odds

Let’s examine a scenario where we can use the golden formula to determine pot odds.

Example:

Imagine there’s $100 in the pot on the final round of betting, and our opponent places a bet of $50. Our equity in the pot is 35%.

Should we make the call?

Now, let's picture ourselves calling that bet. poker board After our call, the pot would total $200, and we would be contributing $50 towards it.

This investment represents 25% of the entire pot.

According to the golden formula, we need to have a winning percentage of over 25% for our call to be considered advantageous. If we win exactly 25% of the time, we would simply recoup our investment.

Given our pot equity suggests we will win 35% of the time, this means we have a clearly favorable situation for calling based on the golden formula.

Golden Formula – Determining Breakeven Ratios

Understanding how frequently a bluff must succeed to be lucrative is invaluable. Once more, we can utilize the golden formula for this calculation.

Example:

In a situation where there’s $100 in the pot, we make a $50 bet, hoping our bluff to work 40% of the time. Is this a sound bluff?

Although the figures may seem similar to the prior example, there’s a vital distinction to be made regarding the size of the pot. In this case, since we are the ones betting, the total pot would only be $150 after our bet is placed.

Here, we are putting in $50 of the total pot, which equals 33%.

According to the golden formula, our bluff must succeed more than 33% of the time in order to be worth it.

If it only succeeds 33% of the time, we wouldn't gain or lose any money on the bluff.

This critical threshold is known as the breakeven threshold .

This golden formula can also assist in grasping more intricate game theory ideas, such as calculating bluff-to-value ratios.

Consider there's $100 in the pot, and we decide to place a $50 bet. How frequently should we attempt a bluff to maintain balance?

Example:

In this scenario, we need to ascertain how often our opponent must win to break even, which corresponds to their pot odds. Our previous calculations show that they face pot odds of 25% when considering the call.

Golden Formula – Analyzing Bluff-to-Value Ratios

Our optimal bluffing frequency under GTO does not directly align with our opponent's pot odds, even though it’s often depicted this way.

Another variant of pot odds is referred to as implied odds. The key distinction is that instead of relying on the current pot amount, we base calculations on a projected or implied pot size.

When we make a strong hand, the implied pot takes into account our potential winnings on future betting rounds.

The effective stacks on the turn are $300, with $50 in the pot, and we hold a nut flush draw with an estimated 18% equity. Our opponent bets $50 (the pot size).

Example:

From a fundamental pot odds calculation standpoint, we don't have an adequate price to continue. We’d be putting 33% of the pot at risk ($50 out of a $150 pot), while our estimated equity is only 18%.

Do we have a profitable call?

However, relying solely on pot odds doesn’t provide the complete picture, as we could potentially win our opponent’s remaining $250.

Let’s apply the golden formula, assuming our $50 investment represents exactly 18% of the pot to make a break-even call. bad beat jackpot !) if we hit our nut flush.

At this stage, the total pot size would ideally need to be $277 (more details on calculating this will follow).

To clarify, we would want the pot, after turn action, to be $277, while in reality, it’s only $150, creating a deficit of $127. This is the amount we need to break even on the river on average after successfully hitting our flush.

We should evaluate whether it's realistic to achieve this average amount on the river, acknowledging that at times we may not get compensated when we hit.

As a prudent guideline, it’s reasonable for our opponent’s remaining stack to be at least double what we need to ensure we adequately make up for the cases we won't be paid when hitting our draw.

The golden formula greatly simplifies our thought process surrounding poker math, but familiarizing ourselves with specific values can enhance our efficiency.

Using Pre-Memorised Values

For instance, when facing a half-pot bet in the river, it's beneficial to simply remember that we require 25% equity to justify a call without needing to perform calculations every time.

While determining implied odds, we calculate the total implied pot needed to offset the shortfall anticipated from later streets.

If $50 represents 18% of the total pot, the overall pot must amount to $277.

Let’s take a look at that again:

The only way to derive this figure is by dividing 100 by our equity (18%) to yield a multiplier:

However, we encounter a couple of critical issues—

100 / 18 = 5.55555

We can then multiply our call amount ($50) by the multiplier (5.555) to generate the total implied pot of $277.

Calculating anything involving a multiplier of 5.555 in practical gameplay is not feasible.

1. Dividing 100 by 18 is not practical in-game.
2. Instead, we can commit to memory approximate multipliers based on the type of draw we possess. It’s akin to having a

When encountered with a $50 bet while holding a flush draw, we can instantly multiply $50 by our recalled multiplier of 6, resulting in a total implied pot of $300. poker cheat sheet !

We only need to assess the shortfall and determine if it's practical or favorable.

Although pot odds are a precise calculation when our equity is known, implied odds rely on estimation.

Simplifying Approach to Poker Maths

This tutorial is designed to unveil the key formula in poker that can assist you in tackling all your mathematical challenges related to the game.

The Key Formula: Your Answer for Handling Poker Math Calculations!

The Essential Formula – Consolidating Your Poker Mathematics into a Single Equation.

It's well-known that a lot of poker enthusiasts aren't fond of mathematics. Additionally, it can seem like there's an overwhelming amount of information to retain.