It’s no secret that many poker players hate maths. Besides, there seems like a lot to remember –

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

It’s easy to become overwhelmed and ignore anything maths-related.

What if we told you we could cover all the above areas by learning a single simple poker formula?

In fact, this formula is so critical, poker players sometimes refer to it as the golden formula.

In this guide, we will introduce the golden formula and consider how you can use it to:

• Perform pot odds calculations
• Calculate breakeven thresholds
• Calculate GTO bluff-to-value ratios
• Perform implied odds calculations

## Introducing the Golden Formula

Let’s immediately define the golden formula in poker games:

### % chance of winning >= % of total pot invested

Translated into words – our percentage chance of winning must be equal to or greater than the percentage of the total pot we have invested.

For example, if we are investing 25% of the total pot when making a decision, we need to win 25% of the time or more.

It's extremely simple, and so much of poker maths revolves around this simple idea.

## Golden Formula – Application to Pot Odds

Let's see an example using the golden formula to calculate pot odds.

### Should we make the call?

Let’s imagine for a moment that we make the call on any poker board. The pot (after our call) would be \$200, and we would be investing \$50 of that total pot.

This amount equates to 25% of the total pot.

According to the golden formula, we need to win above 25% of the time for calling to be profitable. If we were to win exactly 25% of the time, we would break even on our call.

In this case, according to our pot equity, we will win 35% of the time, which means we have a clearly profitable call according to the golden formula.

### Did You Know?

Traditionally, poker players use ratios instead of percentages to calculate pot odds. Facing a half-pot bet on the river gives us pot odds of 3:1 (three to one).

While there is nothing wrong with this approach, we ultimately convert that 3:1 ratio to its percentage value (25%) so that we can compare it to our pot equity.

Using the golden formula eliminates this unnecessary conversion step and focuses entirely on using percentages. It's much simpler—at least after getting used to it. As the saying goes, old habits die hard.

## Golden Formula – Calculating Breakeven Thresholds

It is useful to know how often a bluff needs to work to be profitable. Once again, we can use the golden formula to calculate this.

### Example:There is \$100 in the pot on the river, and we make a bet of \$50. We expect our bluff to succeed around 40% of the time. Is this a profitable bluff?

While the numbers may appear the same as in the previous example, there is a crucial difference here – the pot size. Since we are now making the bet, the total pot size will only be \$150, including our bet.

In this case, we are investing \$50 of the total pot, which equates to 33%.

Based on the golden formula, our bluff needs to succeed above 33% of the time to be profitable.

If it were to succeed precisely 33% of the time, we would break even on our bluff.

Unsurprisingly, this threshold is referred to as the breakeven threshold.

### Did You Know?

While the golden formula is useful for simple bluffs, things change when we are dealing with semi-bluffs on the earlier streets.

We would need a full EV calculation to determine the breakeven threshold.
for these more advanced types of bluffs involving specific poker combos

## Golden Formula – Calculating Bluff-to-Value Ratios

The golden formula can even help with more advanced game theory concepts, such as calculating bluff-to-value ratios.

### Example:There is \$100 in the pot on the river, and we make a bet of \$50. How often should we be bluffing here if we want to be balanced?

In this case, we look at how often our opponent needs to win to break even, i.e. their pot odds. We’ve already calculated using the golden formula that Villain is being offered 25% pot odds on the call.

According to GTO, we should bluff 25% of the time and value bet 75% of the time when we make this half-pot bet on the river.

### Did You Know?

Our GTO correct bluffing frequency does not precisely map to our opponent’s pot odds, even though it’s often portrayed as such.

The goal is for our opponent to face a bluff from their perspective 25% of the time. From our perspective, we might need to bluff more or less than 25% of the time to reach our goal. It depends on card removal effects.

Using the golden formula gets us very close, however.

## Golden Formula – Application to Implied Odds

Another type of pot odds calculation is implied odds. The essential difference is that instead of using the current pot size, we calculate based on a projected or implied pot size.

If we make a big hand, the implied pot will be based on how much we think we stand to win on later streets.

### Do we have a profitable call?

In terms of a basic pot odds calculation, we don’t get the price to continue. We would be investing 33% of the pot (\$50/\$150), and we estimate we only have 18% pot equity.

However, pot odds don’t reveal the full picture here because we might win Villain’s remaining \$250 (or a bad beat jackpot!) if we hit our nut flush.

Let’s use the golden formula and imagine that our \$50 investment equals exactly 18% of the pot for a break-even call.

In this case, the total pot would be \$277 (more on how to calculate this shortly).

In other words, we ideally need the pot after the turn action to be \$277, but in reality, it will only be \$150. There is a shortfall of \$127. This amount is what we need to break even on the river on average after hitting our flush.

We should ask ourselves if we think it’s possible to make this amount on average on the river, keeping in mind that sometimes we won’t get paid off when we hit.

As a conservative guide, Villain should have at least twice the amount we need in his remaining stack to compensate for the times we don’t get paid after hitting.

## Using Pre-Memorised Values

The golden formula greatly simplifies how we think about poker maths, but memorising particular values can make things even easier.

For example, if we are facing a half-pot bet on the river, it’s useful to just know that we need 25% equity to continue rather than having to run a calculation every time.

When calculating implied odds, we calculate a total implied pot needed to generate the shortfall earned on later streets.

Let’s take a look at that again:

If \$50 represents 18% of the total pot, then the total pot must be \$277.

The only way to calculate this number is first to divide 100 by our equity (18%) to generate a multiplier:

### 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.

We have a couple of key problems, however –

1. Dividing 100 by 18 is not practical in-game.
2. Multiplying anything by 5.555 is also not practical in-game.

Instead, we can pre-memorise rough multipliers depending on the type of draw we have. It’s like having a poker cheat sheet!

 Draw Type Multiplier Gutshot 12 Flush Draw / OESD 6 Combo Draw 4

When we face a \$50 bet with a flush draw, we can immediately multiply \$50 by the pre-memorised multiplier of 6, generating the total implied pot of \$300.

We need to simply calculate the shortfall and decide whether it is realistic/profitable.

### Did You Know?

While pot odds are a precise science when our equity is known, implied odds are an estimate.

The amount we get paid on a later street will depend on variables such as opponent type, remaining effective stacks, and our exact poker hand.

Implied odds are essentially a ‘best guess’, but it should help us to get into the right ballpark.

## Simplifying Approach to Poker Maths

The main idea is that the golden formula appears everywhere in poker. Being thoroughly familiar with its application will help make our game mathematically sound.

We can also take things further by removing unnecessary maths from our game.

Generally, we want to keep our heads in the game rather than occupy our brains with mental arithmetic.

By pre-memorising common values, we can keep our game as maths-free as possible.

With over 10 million registered members worldwide, 888poker is the fastest growing online poker room, with a new player signing up every 12 seconds. 888 has been a forerunner in the online gaming industry and a pioneer of safe and responsible gaming since 1997. We are one of the biggest and most trusted brands in the world, providing one of the largest selections of games, high value tournaments and exciting live events for poker players around the globe.