In both Game of Thrones and A Song of Ice and Fire the cunning of the characters that fill out the ensemble cast is both monumental and extremely variable. Each noble house applies its own tactics at trying to win the Iron Throne, and there is a range of success across each one of them that stands as a testament to the virtues of different strategies.
Some tried brute force, some tried clever deception, some formed wise alliances and some used political maneuvering and marriages to keep themselves on top. Yet, perhaps the greatest strategy of anyone came from House Tyrell, and it boiled down to one simple principle: try every strategy and be the best at all of them.
Game of Thrones proved a fitting name for a series that primarily revolved around the political machinations of its medieval fantasy setting. Toward the end of winning the supreme political power in Westeros, the many noble houses that vied for the position each applied their own strategy. There were the Baratheons, who first wrested the throne through force in Robert's Rebellion and then attempted to do so again with Stannis and Renly's contention in the War of Five Kings. There were also the Lannisters, who used their wealth and alliances in a deceptive fashion that perpetually kept them in positions of influence. And, of course, there were the Starks, moral paragons who reluctantly accepted leadership thrust upon them through repeated demonstrations of their piousness and honor.
But in all those arenas, it was House Tyrell that incorporated the best of all possible worlds. In fact, looking across every metric it is hard to say that they did not have each of the other major houses beat. First introduced primarily as opportunists hitching their wagon to the success of Renly Baratheon, to whom Margaery Tyrell is wed as his star rises, it is eventually revealed that the matriarch Olenna is the real mastermind pulling the strings. By utilizing the full force of the family, Olenna manages to beat every other house at their own game, and it is ultimately fortune alone that robs them of their success.
In terms of sheer strength, the knights Loras and Garlan Tyrell are famed as some of the greatest in Westeros. Loras won tournament matches against both the Mountain and Jamie Lannister, and Garlan was said to be even better and frequently trained against three or four men at once. In terms of wealth, the Tyrells were actually richer than the eventually debt-ridden Lannisters, and they applied every bit the same amount of cunning in positioning Margaery by the Iron Throne and steadily ingratiating their family to all of the most powerful places in Westeros. To cap everything off, the Tyrells earned themselves a reputation every bit as sterling as the Starks, and by feeding the hungry and spending time with the smallfolk, created an image as heroes of the people with near unanimous support.
Even that does not give a full picture of the varied ways the Tyrell's cleverly expanded their influence, and even when it came to minor houses, they proved to be the better. Their breeding and proliferation offered greater opportunity for political marriages every bit the superior to House Frey. Their subtlety and mercilessness allowed them to conduct assassination plots against even more ambitious targets than those of Petyr Baelish. Across the board, they proved to be the most adept players of the game of thrones, and by the end of the HBO series, it's hard to chalk up their failure as anything more than raw misfortune.
There was no way that Olenna or any of the other Tyrells could have predicted the rise to power of the High Sparrow or the death of Margaery that resulted from its fallout. The folly of planning and the destructive role of sheer dumb luck were major themes in the TV series that frequently saw the mightiest and the cleverest robbed of victory they were owed. The Dothraki warrior Khal Drogo was not bested by a superior fighter but by a random infection from a wound, and the Tyrells lost the game of thrones not because of a failure in their strategy but because no strategist in the world could foresee Cersei Lannister killing all those people with a sept full of wildfire.
In its own way, the show did more credit to Olenna and Margaery's characters than they were done in the books. But the book series gives an even more complete look at the larger Tyrell family and Olenna's deeper strategies. Fans of the family from the TV show do well to read the novels to inform their appreciation of the Tyrells, as there's really no other family that goes through the chaos of the series and comes out the other end still smelling like roses.