Last year's Spiel de Jahrs award went to Camel Up, a racing game where you bet on camels as they make their way around a track. Every turn you pop out a dice from a tower to see how fast one particular camel moves or you bet on a color. Ultimately the game concept is very unique looking and the stacking of camels that are on the same space is an innovative way to demonstrate a tie, as well as how you break the ties by keeping camels above others in the same position as they race along. For my money, it feels like Camel Up is a literal "bet on a race" game, simply because you bet on them and either win or don't. There doesn't feel like much strategy to be had because it's all down to dice as to what camels end up winning. It's more an odds game and statistically you might be able to predict a winner eventually, but ultimately your decisions are more about what's happening beside the game than what's happening in the game. It's a flawed game, but won the game of the year award for design and play. Its' randomness is critical to the game working, but ultimately the game plays itself and you just bet and hope you win.
There's a certain degree of player involvement that is necessary to keep a game interesting. King of Tokyo manages to be a dice rolling game with decisions to be made on "what you keep" by rolling the dice 3 times and deciding what your turn will be about. You might not always get the rolls you need, but you'll get 80% of what you want, making for a feeling of importance as to what you're doing in the game versus what the dice are just randomly doing to you. If the game is simply random, then it loses replay-ability, as you know next time you play it'll be down to luck whether you win or not. So long as the game has inherent strategy that governs when things are random and when you get to make decisions, it'll benefit the longevity of whether or not you keep playing.
Deck builders tend to have a good handle on when to deal with randomness by having shuffling increase the odds of randomness, while the cards you add to the deck are up to you. Magic: The Gathering does this very well, given that you craft your entire deck and when cards come up is the only luck available to you. Although the game gives you options for statistical improvement with scry effects (looking ahead at the top of your deck), fetch effects (thinning out your deck by fetching a card and reshuffling the remainder, thereby improving the odds of finding anything else) as well as the ability to play from your discard pile (graveyard) or your opponents deck. The elements of randomness are handled as an inherent probability that is within your power to control. This makes most games of Magic varied and about decision making. The choices you make to interact with your deck determines how random you want your game to be, which is why it remains a popular game that has infinity replay-ability.
Finally, when it comes to randomness, there is the King of Random to consider: RPGs. You roll a dice, add your associated skill to improve the odds of success, and get a result. When I play RPGs at low levels I have very few skills, so how I interact with the world is erring on the side of more decisions versus hoping randomness works in my favor once. If I constantly roll dice to make decisions I should have no possible ability to succeed at then eventually I will succeed and build my character's arc. For instance, as a low level Wizard I snuck onto a boat with low level spells and simply because I knew people were of similar level to me, I became invisible and went below deck to set a trap on their powder kegs. I have no inherent ability to do this trap, but because I rolled well my experience and decision making was rewarded. Even if I had failed, my decision would feel like my own so the randomness of the dice would feel like more of a character flaw than a game system flaw.
The point of randomness is definitely one of making the game feel tense, but it doesn't have to mean the game is pitted against you either. I try to play all games with an RPG mindset so that so long as I can make decisions that allow me to give the game personality from my own decisions I can enjoy it. It isn't down to just the pages of text and dice in the game because ultimately a game is something we share as a group in our imagination and if it's all numbers and chance, there's no imagination or influence we grow the game as a valuable experience for players.
