Yet, only three clubs in Scotland – Rangers, Celtic and Aberdeen – have won the trophy more than the Gorgie club’s four times. But those victories arrived between 1954 and 1962.
Since then, Aberdeen have won it five times, Hibs three times, Dundee United twice, while Ross County, Raith Rovers, St Mirren, Livingston, St Johnstone, Kilmarnock, Dundee and Partick Thistle have all had success.
The country’s secondary cup competition seems to startle the men from Tynecastle
Over the years, Hearts have unearthed new ways to get knocked out of the tournament. You’d forgive fans of thinking ‘how are we going to exit this season?’ rather than any thoughts of winning it.
On Saturday afternoon, they begin their campaign with a trip to Peterhead in the newly-named Premier Sports Cup – the 12th name change in the League Cup’s history. Matches with Cove Rangers, Stirling Albion and Inverness CT will follow before the start of the league season at the end of the month.
It will force some to revisit a painful memory from four years ago when the team lost 2-1 to the Blue Toon, then in the fourth tier, at Balmoor.
Of the team which lost to a 90th minute Rory McAllister penalty, only Jamie Walker and Michael Smith remain at the club.
Goal scorer Kyle Laffery has moved to Cyprus, while others who played that night include Jack Hamilton, Rafa Grzelak, Jordan McGhee and Esmael Goncalves.
It was, unsurprisingly considering the result, an insipid performance and was a key defeat in the end of Ian Cathro’s spell in charge.
The campaign began with forgettable 1-0 and 3-0 wins over Elgin City and East Fife respectively. However, the way the group stage ended for Hearts will be hard to forget.
The end of Cathro
At a Tynecastle which resembled a cake which had been relieved of one of its sides – owing to the rebuild of the Main Stand – Hearts welcomed Dunfermline Athletic knowing they had to win to progress to the knockout stages.
What followed was a bonkers and captivating encounter in front of nearly 8,500 fans.
Things were going swimmingly for the home side after 20 minutes when Don Cowie arrowed in a shot after link play between Goncalves and Lafferty. Well, for eight minutes they were.
Jo Cardle turned John Souttar and curled a fine shot past Hamilton. The camera panned to Cathro sipping water on the bench. Sixty minutes or so later he would likely have been hoping for something a lot stronger.
Seven minutes after half-time, all three of Hearts centre-backs were on the ground in the space of five seconds as Kallum Higginbotham teed up Declan McManus after a Souttar slip.
The afternoon, having started in the summer sun, was now subject to a downpour.
Cathro needed his side to score two goals. One arrived via Goncalves late on and the second should have been scored by Cole Stockton, only for the lumbering striker to shoot over.
That was it for the Hearts manager. As the rain teemed down and disgruntlement and anger poured his way from the stands, he was left with the ignominy of having to watch the most pointless penalty shootout of all time. A bonus point still needed to be allocated after the draw with the Pars having won the group and Hearts out.
Just when you thought it couldn’t get any worse, it did.
Hearts missed three of four penalties. Cowie, McGhee and Malaury Martin all firing wide or over.
The list of headaches
Where does that sit in League Cup exits? Since 2000, it is certainly up there.
There was the heartbreaking semi-final loss to Motherwell in 2005 at Easter Road. Late goals from Mark Burchill and Hjalmar Thorarinsson took it to extra-time only for Marc Fitzpatrick to score right before the game was set to go to penalties.
Two years later, Hearts put in one of the most listless derby performances in the club’s history when they got battered 1-0 at Easter Road. Ibrahim Tall was right-back with Robbie Neilson playing on the right of a midfield five.
Another eye-gouging, hair-tearing performance was to follow in the semi-final in 2010, Billy Mehmet scoring the only goal of the game for St Mirren at Fir Park.
The year before Airdrie United won a penalty shoot-out at Tynecastle after 120 soporific minutes with David Obua putting his case forward for the worst penalty of all time.
Who can forget Suso Santana’s individual genius against Falkirk in 2010. He pulled Hearts to within ten minutes of winning with ten men, only for the Bairns to score twice late on.
Then, only last season, there was the team's first ever defeat to Alloa Athletic – if you don’t count the loss in the 1946 Victory Cup – in the second round.
The nine men of ICT
But, for a League Cup exit, it is hard to look past February 2, 2014. Easter Road again. But this time the opponents were from the Highlands. John Hughes’ Inverness CT.
A double from Jamie Hamill had given Hearts a 2-1 lead against ten men going into the final 20 minutes. ICT went down to nine men in stoppage time, Josh Meekings following fellow centre-back Gary Warren down the tunnel.
Yet, inconceivably, Nick Ross netted a 95th minute equaliser.
Thirty disbelieving minutes followed. Gary Locke’s men could not come up with a winner and the game went to penalties.
If you were to look up ‘recipe for disaster’ on the internet, there is every chance it would take you to a penalty shoot-out involving Hearts in the League Cup.
Hamill missed, as did Paul McCallum. Inverness progressed.
More than seven years on, Hearts are back ready to give the League Cup another go.
Can they end a near 60-year wait to lift the trophy or will it be a new entry into the folder of farcical failures?