"Snake Eyes!"

In most games, you would not want to be rolling this with your pair of dice. In many popular board games, this means your progress is at an absolute crawl. If this (or similar low rolls) is the majority of your results, it can be a very long and frustrating session. From personal experience, these are the sessions that you want to end now, even if you lose by a large margin, just to end the misery. Its possibly enough reason for you to swear off board games forever.

For games like Chutes and Ladders (or its snake-y variant), Monopoly and even Risk, winning the game often has less to do with a player's wit and more with where you fall with 'Lady Luck'. While this may be interesting to some players, this reliance on the random can quickly become stale, and feel repetitive (read: boring).

But what if rolling the dice wasn't the only way to win the game? That would certainly change how chance affects one plays the game, and even the outcome. While classic games like Monopoly are still dependent on dice rolling results to win, modern games offer various alternatives to progress and even victory - lessening the impact of randomness on the game.

This then allows the game to be engaging for all the players involved, since each player has an active interest in the game no matter what results from their dice roll. Player's aren't simply counting spaces along the board and waiting for their next turn, but they actively observe what the effect of each person's turn has on their own possible plays - increasing the emphasis on planning and strategy.

A few games where chance plays a part in the game, but isn't central to it:

Settlers of Catan - the classic precursor to modern boardgames, Catan relies on the dice for resources to be produced (though not necessarily for the player rolling the dice)... However, if a player is short on resources, they have opportunities to barter with other players for what they need, or, being more mischievous, they can try to acquire the resource using the robber. As well, with various options in the game, the lack of a resource may just mean a shift in strategy on the way to victory (points).

King of Tokyo - players take the role of a giant monster (based on popular monster tropes: giant primate, destructive lizard, invading alien, etc) out to conquer Tokyo. Dice rolls determine if a player is attacking other monsters, gaining powers or accumulating (victory) points. A majority of results still allow a player to 'do something', especially since there are opportunities to re-roll the dice during the turn. Another game similar in mechanics would be Dice Town - this one is set in the American West.

Alien Frontiers - a colony building game set in outer space. Players race against each other to gather resources and build colonies on the newly discovered planet. Dice rolls determine which actions a player can perform during their turn, provided a previous player hasn't already performed that action. Though there are ways to work around that obstacle, or even just raid resources from other players outright. Considered to be a casual or moderate game, expert gamers may find Troyes a more complex and challenging game.