The Probability of Achieving a Straight in Poker

The likelihood of flopping a Straight with a strong connector is estimated at 1.29%, or about 1 in 77.5.

Definition of Straight –

A Straight consists of five cards that are all in sequence.

Example – JT987

In the context of a Straight, Aces can act as both the highest and lowest card, but they must be positioned at either end of the sequence. For instance, QKA23 is invalid as a Straight since the Ace is placed in the middle of the series.

Odds of Making a Straight on the Flop

Achieving a Straight while flopping in Hold’em isn't particularly common. This often depends on the nature of the starting hand we possess.

The chances of flopping a Straight with any given starting hand is approximately 0.39%.

When using connectors from 54 to JT, the odds of flopping a Straight rise to 1.29%.

With any connector, the chances of hitting a Straight is about 1.04%.

For one-gappers ranging from 53 to QT, the odds of making a Straight drop to 0.96%.

The likelihood of flopping a Straight with any one-gapper stands at around 0.85%.

Using two-gappers between 52 and KT gives a probability of 0.64% for completing a Straight.

For any two-gapper, the odds are slightly lower at 0.61%.

If the cards are unconnected, the chances of flopping a Straight are essentially 0%.

When holding a pocket pair, your odds of flopping a Straight are also 0%.

Why do we make a distinction between connectors like 54-JT and others? It's simple: connectors from 54 to JT generate the highest number of possible Straights . A hand like AK can only create the AKQJT Straight, making it less likely to yield a Straight.

Odds of flopping a Straight with T9s = 1.29%

Odds of flopping a Straight with AKs = 0.32%

Chances of Flopping a Straight Draw

Though completing a Straight may seem rare, Straight draws are highly playable hands that often allow us to progress beyond the flop. Understanding the odds of different Straight draws can be invaluable.

The odds of flopping any Straight draw with connectors from 54 to JT sits at 26.2%.

If you have a 54 to JT connector, the likelihood of landing an OESD stands at 9.6%.

On the other hand, the chance of hitting a gutshot with connectors from 54 to JT is about 16.6%.

For one-gappers between 53 and QT, the odds of getting any Straight draw is around 21.9%.

The probability of securing an OESD with 53 to QT one-gappers is 7.26%.

For a gutshot with 53 to QT one-gappers, the likelihood is 14.6%.

If we consider two-gappers ranging from 63 to KT, the odds of flopping any Straight draw are about 17.9%.

The likelihood of flopping any OESD with two-gappers between 63 to KT is 4.47%.

When aiming for a gutshot with the same two-gappers, the odds are roughly 13.5%.

For pocket pairs, the chances of getting any Straight draw amount to 4.12%.

If you're holding AK, the odds of flopping any Straight draw is 11.2%.

With an off-suit T5, the likelihood is about 9.66%.

It's beneficial to realize that when you hold a premium suited connector, you’ll likely hit a Straight draw roughly 26.2% of the time. As your card connections weaken, these chances tend to diminish.

The chances for unconnected hands to make a Straight draw can fluctuate. T5o might give you a Straight draw 9.66% of the time, while A9 only manages this 6.53% of the time. Mid-range cards are generally more effective for flopping Straight draws than high or low cards.

Chances of Achieving a Straight on Later Streets

The possibility of completing a Straight on later streets relies on the type of draw that was flopped. Open-ended Straight draws (OESD) provide 8 outs, whereas gutshots offer only 4 outs.

Odds of hitting from flop to turn

The odds of hitting an open-ended Straight draw from flop to turn is calculated as 8/47, which comes out to approximately 17% .

For a gutshot from flop to turn, the odds sit at 4/47, translating to around 8.5% .

Odds of hitting from turn to river

From turn to river, the chance of completing an open-ended Straight draw is 8/46, or about 17.4% .

For a gutshot from turn to river, the odds rise to 4/46, or approximately 8.7% .

Odds of hitting from flop to river

To simplify our calculations, we can use the handy method of figuring out the probability of not hitting and then subtracting it from 100%.

The chance of not landing an OESD on the turn is 39/47.

The chance of not hitting an OESD on the river drops to 38/46.

The total probability of not making a gutshot on either the turn or the river equals 39/47 multiplied by 38/46, equaling around 0.6855 or 68.5%.

The likelihood of not achieving a gutshot on the turn is 43/47.

The probability of not hitting a gutshot on the river is 42/46.

The combined chance of not obtaining a gutshot on both the turn and river is 43/47 multiplied by 42/46, leading to a total of approximately 0.8353 or 83.5%.

Therefore -

Consequently, the probability of hitting a gutshot on the turn or river works out to be (100 – 83.5), giving us an approximate chance of 26.5% .

The probability of securing an OESD on the turn or river is (100 – 68.5), leading to around 31.5% .

Implied Odds Analysis of a Straight

Straights are powerful holdings in Hold’em and usually warrant a significant investment of our 100bb stack when they are completed. Therefore, they offer excellent implied odds.

Nonetheless, one must keep in mind that not all Straights possess equal implied odds. Several key considerations must be taken into account.

Nutted-ness – A nut Straight inherently carries more value than a non-nut Straight. For instance, on a board showing 789, the perceived value of a Straight would rank as follows, from highest to lowest.

Texture 789

Hand 1 - JT -- Offers the best implied odds, as it will outclass all other Straights present on this texture.

Hand 2 - T6 – In the middle.

Hand 3 - 65 – The least favorable implied odds, as this hand could easily be bested by superior Straights.

Two-card or one-card – The strength of a Straight can significantly fluctuate based on whether it utilizes one or both of our hole cards. Straights emerging from just one hole card suggest that the board must contain a 'four to Straight' structure such as 5678x or TJKAx.

In such scenarios, our Straight becomes more apparent, or 'transparent,' since it only requires one specific card. This transparency may lead opponents to grant us more credit for completing the Straight, which can make receiving payouts more challenging.

However, to make a Straight on a board like QT8xx hinges on holding two specific cards, making it less likely that opponents will credit us (leading to greater chances of securing a payout).

Basic Strategy Advice

Generally speaking, Straights in Hold’em are formidable hands, and we should refrain from folding them when dealing with 100bb effective stacks.

However, some weaker Straights may not justify risking our stack - particularly non-nut one-card Straights.

Example: Board 789T42

Our Hand: 63

Indeed, we may have a Straight here, but our opponents may only need one Jack to construct a higher Straight.

In these scenarios, we might not feel economically compelled to commit to our Straight, especially with 100bb effective stacks (though it does depend on the overall action).