Emotional impact

Obviously different people play for different reasons - you have problem solving, beating others, playing with others, etc. For me, I think what's important is tension.

If you can create those few moments in each game where there's a razor's edge between victory and defeat - that's what players crave, I think. Randomness does not necessarily have to factor in there either. Diametrically opposite of chess might be poker - and there's tremendous tension there. What they both have in common is the fact that there are "make or break" moments.

So I think you want to find ways to create tension - for the person in the front to lose and be beat by the person behind them. And vice versa. That's the essence of competition.

I think a differentiation should be made between randomness and predictability.

Randomness is a way to reduce predictability.

Predictability is what makes games boring, sooner or later.

When your brain is making new connections as it learns a game, it can be almost like a drug. But the more it learns, the more it needs to keep that high going. Once you have mastered a game, one of the major motivations for playing that game is gone.

That is why a simple game like chess is so enduring. The possibilities are so huge, that it can be hard for your brain to predict everything that will happen. Those little surprises when the enemy does something your brain didn't predict is practically what humans thrive on. It goes back to evolution and the need to adapt and survive.

Back to randomness. It simulates deeper mechanisms that would otherwise reduce predictability, while reducing learning curves and making a game more accessible. If you are a chess master and you play a novice, how fun is it? On a competitive level, not very much. How about Yahtzee? Suddenly anyone can win, and now you have the necessary tension.

I also believe that randomness is a tool that can be used to increase those "OMG!" events. Lets face it, +95% of people are not strategic geniuses, and without controlled randomness, "OMG!" events are going to be hard to come by.

The key is to understand your audience. Chess Masters? Preschoolers? Something in-between? Design your systems based on the people that will be playing your game and the level of randomness that would be best for them.

"that knowing when and how to use randomness is the most important part of game design"

I agree with that. I try to use randomness in all my games, it's now a matter of knowing were it must be appropriately used.

For example: Rolling to move is not interesting because it gives the player no choice on where they want to go, but rolling for battle resolution is better accepted because it abstract tons of variables and combat steps which are summarized in a roll.

Games with no randomness or which are completely predictable tend to create brain burning effects. This is the case of "Dominant Species" where you know the status of all the pieces, and all the actions that are going to be done by all players.

I look at 5 ingredients when I consider designing a game and 2 emotional factors.
Here is a list of the 5 ingredients and the sport / game that are the best at showcasing them:
1- Player selection “The Triple Crown of Horse Racing.” Based on your game’s complexity or simplicity determines the odds of each player winning but these odds mean nothing once the game starts.
2- Strategy “Chess.” Simple rules but must be well read in how the game is played and even then you are not going to be a master.
3- Bidding “Bridge.” Specific conventions are used to keep the champions on top. But if you follow their rules a good card player with a flair for poker has a shot at winning.
4- Bluffing “Poker.” Major factor if you’re concealing an element of the game.
5- Randomness “Roulette.” You walk by the table you look at the wheel then you look at the numbers and then you see it! Now your decision! Bet the number (37-1) bet the colour (1-1) or stop and watch. They call this intuition, divination, fate or a hunch. But it’s been statistically proven that this method of playing roulette is the best.
Emotional factors:
1- Am I enjoying the designing part of the game and when I test it, is it better than I thought it would be?
2- Then I do the most tedious part of designing which is to determine whether my game is an original or a knock off. And the answer to this question determines that a change in venue is in order.

Czman, all who responded to your question are giving excellent advice. But we are all prejudice to how and what we do to design a game. And as far as users I don’t think that should be an issue.

Designing is like roulette, there is a whole bunch of different approaches but following your instincts could be the best way to go.