Random Factors in Gaming

Die Siedler is something of a phenomenon, when it first came out it took the gaming world by storm. Everyone was playing it, it won all the awards and people just couldnít get enough of it. Lately, the game seems to have lost some of its appeal, however. Personally I think itís a case of a game simply being overplayed but many mention that theyíve lost interest because the game is "too random". Its pretty easy to see where this idea comes from, after all the game does use dice as its driving mechanism. The player that receives the lionís share of the rolls IS more likely to win but does that mean that the game is "too" random? Certainly thereís a random element and thereís been plenty of anecdotal evidence of a game that was won purely by a series of lucky die rolls. In spite of this Iím not sure that Iíd want to classify the game as luck based. Some have suggested that any skill in the game is in the initial placement of settlements, the game is one-third skill (the initial placements) and two-thirds luck (the rest of the game). Iím not sure that I agree totally with this although my opinion may have something to do with my record:

Iíve played the game 21 times at my weekly gaming session (from which the results are recorded) and Iíve managed to win a total of 16 times. These were all 4-player games. I suppose its partly ego that leads one to the conclusion that success in a game is attributable more to your skill and intelligence than anything as unseemly as luck.

Still, thereís something to this argument. You would expect, in a game of pure skill, that the better (i.e. more "skillful") player would win most, if not all, of the time. If this is so then it seems a natural conclusion that a games "skill" level could be gauged by the regularity with which certain players win. Unfortunately, this "test" has a couple of problems, primarily the fact that you have two unknown (non-quantifiable really) variables: the degree to which the game is "skill-based" and the actual skill of the players. Consider world championship Chess, usually played over a series of 20 or so games with the final result often in the neighbourhood of 11 to 9. Compare this with a "Roll the Dice" contest which will usually result in a similar final score. I think it safe to say that Chess is much more skill based than "Roll the Dice" so these results donít really tell us much in and of themselves. At the very least they donít confirm what we already suspect, which is that Chess is a more skillful game. Even with this misgiving I still think that itís a useful test, a rough indication of a games level of skill, even if it is a rather loose one. In any event why do certain games feel more random to some players than others? Maybe it would help if we had a look at some of the different random elements in games.

The most obvious element is the use of physically unpredictable devices such as dice. This would also include such things as spinners or exotic items such as the devil's pot from In Teufelís Kuche. (If you havenít seen it its a small pot belly type stove with a button on top. Players alternately press the button until the devil lurking inside pops out, very cute!) Basically this includes anything that has a physical mechanism thatís not predetermined.

Two related, and very commonly used randomizing elements, are cards and tiles. A little distinction is necessary here. What Iím thinking of is a closed, known set of items and these can take many forms. In Bridge you know exactly what cards are in the deck. In Acquire you know that there is a single tile for each space on the board. In Settlers you know that there are four sheep, wood and wheat hexes, three brick and ore hexes and one desert. The random factor in each of these is in how the cards are distributed, the tiles drawn or the hexes placed. I should also note that these items are not necessarily random influences. The commodity cards in Settlers arenít, theyíre simply an accounting tool. The tiles in 1830 arenít a random element as theyíre chosen rather than blindly drawn. (I should also note that cards can be considered as a "dice-type" randomizer in certain circumstances. If you are drawing and then replacing a card from a fixed, constant deck then its much closer in function to dice than if you are drawing and discarding or keeping a card. The specific example Iím thinking of is Hase und Igel where the Hare cards are constant in number; you draw one, follow its instructions and then replace it in the deck. In fact, the original English version uses dice to perform the same task, albeit slightly modified.)

Another random element is the seating/turn order. In a two-player game this is usually simply a case of who has the first move, normally itís an advantage to go first. In the case of games that have unequal sides (such as wargames like Hannibal: Rome vs. Carthage) its also a matter of who plays which side. In multi-player games its a little more complicated. The order in which you are sitting can have a great impact on your strategy in a game. In Illuminati its generally better to ally yourself with someone sitting next to you as you will have back to back turns. In Show Manager itís very important that you try to stage a different show than the person to your right otherwise theyíll be hiring the actors that you want. This is in addition to any advantage of going first. (Note also that its not always an advantage to go first, some insist that going last in Die Siedler is better as you get to place two settlements at once. Also the first two players in Durch die Wuste only get to place a single camel instead of two.)

The final element (that I can come up with at least) is the players themselves. What Iím thinking of is the mechanism (if there is one) that causes a player to perform a certain action. It would be quite easy to argue that there is no randomness in this at all and I donít necessarily disagree with that line of thought. In any case such a debate is not likely to lead to any useful conclusions and is best left to another forum. I simply include its mention for completeness and that some of my opponentsí moves sure as hell SEEM random to me!

I suppose that each one of these elements is going to bother every player to a different degree. A lot of this is going to have to do with how a game "feels" to us. There are going to be people that have a problem with any game that includes dice. Equally, there will be players for which cards are too great a random factor. I believe that itís possible for any of these elements to be modified to an acceptable level. (I donít think you can actually modify my final element, the players themselves, but weíll ignore that.)

The unpredictability of dice or cards can be modified in many ways. In Die Siedler the dice are added together which gives a bell curve distribution. The game is less random because there is greater predictability in the commodity rolls than if it was a single die that was rolled. Any particular result is still random of course but you will expect more 6ís to be rolled than 10ís over the course of the game. This is another important concept: as you increase the number of die rolls you will get closer to the expected average. I often hear someone make the comment that they donít like a particular game because "Itís too random, thereís too many dice rolls." This might at first seem to be a logical argument but it ignores the law of probability that as you increase the instances of a random event you are more likely to get an expected average. To illustrate this, consider a dice contest between Danny & Roger: A single six-sided die is rolled. On a 1 or 2, Danny wins otherwise Roger wins. If the "game" is a single throw of the die Danny will expect to win 1 out of 3 times. However, if the game is the best out of three rolls Danny can only expect to win 7 out of 27 times which is slightly less than 1 out of 3. This is a result of Rogers advantage in the game. As we increased the number of rolls the random effect became less of a factor and the advantage became more significant. The point is that the more dice rolls in the game the less pronounced their individual effect. There are, as always, a couple of points to note about this specific example. First is that each roll had exactly the same effect on the outcome as all others. In a real game certain rolls are more important than others, for example, in Titan your movement roll is far more important than any attack roll. Also, the order of the rolls was not significant whereas in a real game the effects of earlier dice rolls often affect later ones. e.g. In Titan if you roll lots of hits at the start of a battle your opponent will have fewer attacks to make on subsequent turns and so, in general, it is better to roll well earlier. So, one way that you could decrease the luck in a game that uses dice, such as Die Siedler, would be to increase the number of individual rolls in the game. This is probably going to be somewhat difficult to actually implement in a game outside of the design process. Another, more easily added method would be to actually remove the dice from the game and there are a couple of ways this could be accomplished. One particular method Iíve heard proposed for Die Siedler involves a set of 36 cards with each card showing a number from 2 to 12. The total number of each card listing a particular result would match a standard distribution so that you would have one card showing a "2" and six cards showing a "7". These cards would then be used in place of a die roll to determine which commodities appear. There are even multiple methods by which you could employ them; one is to have a single common shuffled deck from which you drew a card. Another would be for each player to have their own decks and they would choose which card to play each turn. Iím not so sure that the final results would be all that much different in a game like this but it would eliminate the rare games in which a wild and unusual set of rolls determined the outcome.

In the case of cards, their unpredictability can be modified as well. First consider the case of a game where players draw from a face down deck. A common method of reducing this random effect is to have several face up cards beside the stack. A player now has the choice of choosing one of the face up cards or drawing blind from the deck. Alan Moon often employs this so-called "drafting" method in his games and it works very well. A particular bonus of this method is that itís very easy to tailor it to a particular level, if you want less predictability, have fewer face up cards, if you want more, increase the number of face-up cards. Simple. Another way of reducing the random effect of drawn cards (at the design level anyway) is to reduce the variety of cards. In Euphrat & Tigris there are only four types of tiles so while you can never be sure exactly what youíre going to get you have a pretty good idea.

What about the randomness in turn order involving games where itís advantageous to go first? In these cases a bidding mechanism can be introduced where players compete for this right. In the case of two player games you could play a pair of games with the cumulative score determining the winner. Unfortunately thereís not much that can be done for the "randomness" of other playersí strategies. As there are many that would argue that this isnít really a random factor anyway its probably best to take the practical approach and resist any attempt to "fix" it.

As a practical exercise letís have a look at some real games, specifically Reiner Kniziaís so called "tile laying trilogy", Euphrat & Tigris, Durch Die Wuste and Samurai. What random elements are there?

E&T: The only random elements are the tile draw and the seating order. Implementing an above-described "drafting" tile draw would reduce much of the luck in the present system.

DdW: The only random elements are the seating order and the initial setup. (Iím assuming a four-player game where each player has all five caravans in play. In a five player game, where each player only has four of the five caravans, it depends on how you remove each players "extra" caravan. Obviously if you determine it randomly thatís another random element.) As a particular layout does not necessarily favor one player over another Iíd suggest that thereís very little luck involved at all. Thereís recently been some discussion on the Internet about how to conduct this setup and a couple of people have suggested that the board be setup as follows: Each player, in order, chooses an oasis or waterhole token and places it on the board. Placement proceeds clockwise around the table until the board is complete. I really doubt that all this extra effort is worth it in the end but each to his own. If the turn order was seen as a problem this could probably be solved by implementing a bidding system for who goes first. There are a couple of ways that you could increase the luck in the game: Instead of choosing which camels to place you secretly draw from one of five concealed bags. The game ends when one bag is empty. Instead you could have 6 hidden camels behind a screen, you may play any of them and you replenish your "hand" to 6 from a common stock. Game ends when 12 oasis tokens have been awarded.

Samurai: Random elements are the initial setup, random draw of tiles and seating order. As with DdW you could solve the initial setup "problem" with a similar placement mechanism. I donít think thereís a bidding system that would work for determining the first player though. The only thing I can come up with would be something along the lines of bidding how few of your initial 5 tiles you get to choose. I doubt that this would work all that well in practice. The random draw is interesting to me especially when compared to E&T. On the one hand Samurai seems less random due to the fact that everyone will get the same distribution of tiles. On the other hand there are more varieties of tiles, which makes it less likely that youíll draw the one you want at the right time. Which is more random? The biggest complaint Iíve heard about E&T was the random draw of tiles and I can understand this somewhat, itís very frustrating if you never draw those damn green tiles! There are a couple of tactics that can be used to overcome this however and I personally feel that this is what separates the good players from the bad. Iím not sure if Knizia designed the tile draw in Samurai as a direct response to this but it does seem that people have fewer problems with it.

All three of these games exhibit some degree of luck. I think its safe to say that DdW has the least of the three but Iím not sure how Iíd rank the other two. In Samurai I often have to speculate whether or not Al has his 4 Buddha available. In E&T the equivalent is speculating if he has 3 red tiles. For this situation Samurai "feels" more random to me but perhaps Iím in the minority?

There are also many games where a certain degree of randomness is "built in". The best, fictitious example I can think of is Chess-Dice. (Which I first read of in a post to rec.games.board by David desJardins. Iím not sure if its his original idea or not.) The game is played in two parts. First a regular game of Chess is conducted and then each player rolls a single die. If there was a winner in the Chess game, that is, the game was not a draw, then that player adds 1 to his roll. Highest roll wins. I think everyone would agree that the game is pretty random even though it also rewards skillful play. In fact, there is just as much depth and skill inherent in Chess-Dice as there is in regular Chess. The big difference though is that the rewards for skillful play are not as pronounced in Chess-Dice as they are in Chess. This is fairly obvious in this case but Iím only using it to make a point. The point being that some games have the appearance of requiring great skill but the game does not actually reward that skill as much as others. There have been a couple of situations where random events have totally ruined a game for me. The most obvious ones have been games that have a "switch positions" rule. Twice Iíve been the victim of this, the first in a PBEM game of Cosmic Encounter, the second in Flying Carpet. Iíd argue that these rules make the games as ridiculous as that of Chess-Dice, a single random event overwhelming any skill that the game requires.

So, back to the original question (was it the original question?), why do some games feel more random to some players than to others? It could be a simple case of closely matched opponents. Most people play with the same group of people and its quite likely that they are of approximately the same level of skill. This is going to have the effect of emphasizing any luck inherent in the game. It could also be the small number of times a game has actually been played by an individuals. Even the 21 games that Iíve played of Die Siedler are probably not statistically significant to make any claims about my ability in the game. Also, if youíve only played a game two or three times any aberrant events are more likely to cloud your opinion. So, once again Iíve rambled on about a subject but have I actually stated anything useful? I suppose thatís for others to decide but I think the most important point Iíve made is that itís usually possible to fine-tune a game to your particular luck/skill ratio. As always Iíd be interested in hearing any thoughts on this subject.

This article originally appeared in Counter #4.