Quite some time ago, I wrote an essay explaining, in basic terms, what I consider to be the four basic elements of games, and how any one of them alone, in my book, makes for an unenjoyable game. It's right here if you'd like to reread it. In this essay, I'm going to be taking a closer look at one of these elements, Randomness.

When I first listed my four elements of gameplay (Strategy, Randomness, Hidden Information and Social Factor), someone confronted me, asking if I was, perhaps, missing an element, citing Settlers of Catan as an example. Typically, we have 4 people playing, all of whom clearly have an impact on each other's progress, but not in a way that fits my elements at first glance. Hidden Information doesn't play much of a role at all in Catan. Victory Point cards are hidden from opponents, but at best, they marginally obscure how close someone is to winning. This could only have a real effect on things if Social Factor was an issue, but the only ways to really stick it to another player in Catan are to cut off their road with one of your own (which is an oppurtunistic action that you can't very well have everyone get together and do at once), or refuse to trade with them (which is irrelevant as players nearing a victory in Catan will no longer be reliant on trading as research producers are the primary source of victory points). This leaves Strategy, which clearly isn't our element, and Randomness, which, at first glance, would also not appear to be at play here, but let's take a closer look at what Randomness really is.

Traditionally, randomness is added into a game through a very limitted number of easily recognizable sources. There's dice, there's cards, and there's various things that emulate them (spinners, coins, and computerized random number generators, are all dice for all intents and purposes for instance). What though, do these really add in to the game? Two things really. Probability, and Chaos.

Probability can effect a number of things. In Catan for instance, the active player rolls 2d6. Any space on the board labelled with the number rolled produces resources for any town bordering it. Thus, the majority of the game's strategy is in getting your own cities along spaces whose numbers are closest to 7.

If you don't see how that works out (and you'd be surprised how many people don't), make yourself a little grid with columns numbered 1 through 6, and rows labelled likewise. Fill in each space with with the sum of its row and column label, then go and count up how many times each result appears in your grid. Make a bar graph out of THOSE and you get this:

Each # represents an equally likely possible roll, so a 7 is going to come up 6 times as often as a 2, and twice as often as a 4. A more interesting graph (but more of a pain to arrive at) happens when you work this out using 3 dice. Basically, the more dice involved, the closer the result curve comes to the shape of a bell. With 3d6 for instance, you'd get this:

Getting back on track, the other thing randomness adds to a game is Chaos. Sticking with Catan as an example, my best possible strategy is to go for the high likelihood spaces, but there's always the possibility that the dice will defy the odds and constantly roll 2s. It's rare, obviously, but it does happen now and then. So even if I dedicate my life to the mastery of a game where dice are rolled, and play as perfect a game as imaginable, it's always possible for someone with more or less no clue what they're doing to beat me if they get lucky enough.

Cards differ a bit from dice, in a way I find rather interesting. Let's say that rather than play Catan in the standard fashion, using dice, I instead take a deck of 36 cards, including a single 2 and 12, two 3s and 11s, etc. etc. The first time someone pulls a card off the deck, the odds of each possible result are exactly the same as if I were to roll the dice. For the next draw though, the odds have changed. If I just pulled out a 7, there are only five 7s left in the deck, a 6 7 or 8 now all have equal odds of coming up. If I pull the only 2, it's impossible for a 2 to come up again until the deck gets reshuffled. After 36 turns, what's come up will match the probability curve perfectly. Chaos is far less of an issue. There's still some, because we are only taking one card at a time, so the order in which these cards are pulled is a major factor. There's two ways you can add some of the chaos back in to a deck of cards. You can either increase the total number of cards (casinos do this by mixing multiple decks together), or you can throw in reshuffle cards.

The first time I ever saw reshuffle cards put into practice was in my own game, The Massive Vs. The Masses. I use them strategically (and to avoid some headaches). If you've used up all of your best cards already, you can use the reshuffle card to get them back into the deck. While writing this very essay, I just learned that there is an optional Event Deck for Catan, which contains the exact set of cards I was just discussing, and a similar reshuffle card, to leave at least some value to the 2 and 12 spaces, by introducing the ever-present possibility of putting them back in the deck.

Now, finally getting back to the issue of how other players impact Catan, I again say, it adds in Randomness. In any game where players have any sort of choice in what they do, one choice is always better than another (unless the game is poorly designed), either in raw strategic terms, or in terms of probability. "Better" of course meaning that making this choice will put you closer to winning by either bettering your own position, or hurting your opponent's. This is the basis of Strategy. There's always a "correct" move, it's just a question of how well you can spot it. In two player games which are heavy on strategy, you are constantly thinking ahead, considering what the best move for your opponent will be based on what you're doing, what you'll do next, and so forth, making sure your move is truly the best in the long term. There is always the possibility that your opponent won't make the move you think he will (either because he either misses the move you're expecting, or spots an even better one). So long as you're actually taking into account all the best possible moves though, this can't hurt you. Either they act as you planned, or they slip up and open a new, even better road to your eventual victory.

Adding more players in however changes the game. Each extra person playing means another chance between now and your next turn from things to deviate from your expectations. With a single opponent, you can see all their possible moves (unless Hidden Information is a part of the game) before you make your own. It's easy to work out every possible configuration of the board when your next turn rolls around and plan accordingly. Let's say though that on any given turn, any player will always have 10 possible moves they can make. With two people, you know there are 10 variations of the board that could appear at the start of your next turn if you make a particular move. Some work to your advantage, some to your opponent's. You can work with that. Now though, let's throw in a third player, 100 possibilities. A fourth? 1000. The odds that the board will look how you expect it to are constantly dropping. Working out everyone's most likely move is also getting harder, as there are more people's positions to factor into the equasions for everyone. Your loss is my gain and vice versa if there's just two of us, but if there's more, their losses and gains don't necessarily have anything at all to do with either of us (especially if the game has little to no Social Factor). The more people, the less certainly we can possibly have in our plans. Just like mixing together multiple decks of cards reduce the certainty of drawing the card you need.

So there you have it. All those extra players in Catan make Randomness that much more of a factor. In fact, between the players, the dice rolls, the starting setup, and the development cards, I'd say Catan relies perhaps a little too heavily on luck. I'd seriously recommend the aforementioned Event Deck to tone the chaos down a tad accordingly.

Adding more players in however changes the game. Each extra person playing means another chance between now and your next turn from things to deviate from your expectations. With a single opponent, you can see all their possible moves (unless Hidden Information is a part of the game) before you make your own. It's easy to work out every possible configuration of the board when your next turn rolls around and plan accordingly. Let's say though that on any given turn, any player will always have 10 possible moves they can make. With two people, you know there are 10 variations of the board that could appear at the start of your next turn if you make a particular move. Some work to your advantage, some to your opponent's. You can work with that. Now though, let's throw in a third player, 100 possibilities. A fourth? 1000. The odds that the board will look how you expect it to are constantly dropping. Working out everyone's most likely move is also getting harder, as there are more people's positions to factor into the equasions for everyone. Your loss is my gain and vice versa if there's just two of us, but if there's more, their losses and gains don't necessarily have anything at all to do with either of us (especially if the game has little to no Social Factor). The more people, the less certainly we can possibly have in our plans. Just like mixing together multiple decks of cards reduce the certainty of drawing the card you need.

Of course, this only applies in games where your opponents have some effect on you. In bingo for instance, having more players doesn't add new random factors into the game, it simply increases the chance that one will win before you.

Now then, to round out this discussion of Randomness, here's what does and doesn't work. Randomness and Strategy mix together quite well in a couple of ways. Any time you can make decisions based on probability, that's a marriage of these two elements. Randomness and Hidden Information is found in drawing a hand of cards, again, an easy combination to incorporate into a game. Social Factor and Randomness is simply a matter of having a random mix of Benefit Me options and Screw (or Benefit for that matter) You options, which is more or less the entire basis of games like Kill Dr. Lucky and Munchkin.

And finally, having a strategy game where each round, one of my units is randomly chosen to be struck by lightning can add a lot to a game. Having a game where each round I gain a new unit somewhere on the board meanwhile is lame. The key difference is that I can plan around the former in some fashion (making sure nobody's left alone guarding an important space for instance) while the latter is just a matter of total luck whether it helps me or is simply pointless.