The following is the first in a series of generic strategy articles that will appear sporadically over the next several issues. Each will focus on one small aspect of strategy that can be applied to games. I recognize that some of the articles will appear to be rather obvious in the "lesson" they contain, but I'm not necessarily trying to avoid this. Sometimes, things which are obvious to some are hidden to others. Hopefully, by stating "obvious" maxims, it will provide a framework for a more involved discussion of subtler aspects of strategy.
The Art of the Trade
Consider the following fictitious (and extremely simple) game:
Game: Gem Trader
Rules: Each player has a collection of gems in their own colour. On your turn, you can trade one of the gems in your colour for any number of another player's gems (with that player's consent of course). At the end of the game, you score 1 point for each "foreign" gem you possess. (Gems in your own colour are worthless to you.)
Most people will only trade when a deal is equitable. That is, they'll only agree to a trade if they profit as much as the other party. With such players, there will be many "1 for 1" trades. Why would anyone offer a better deal? Well, Clever Hans thinks about this and realizes that the important thing is to gain points not just on his turn, but on the other players' turns as well. Consider what happens in a game with players who insist upon getting a "fair trade":
It's Al's turn and he asks for offers from the other players. As expected, Bob, Carol, and Dan all quickly shout "I'll give you one of my gems for one of yours." Clever Hans, on the other hand says "I'll give you two of my gems for one of yours!" Al is overjoyed at the idea of receiving two gems while giving away only one so he happily accepts Hans' offer.
Now, it's Bob's turn and again Hans offers two of his gems for one of Bob's (the other players offer only one gem). As expected, Bob accepts Hans' offer. The same deal is struck on Carol's turn as well as Dan's.
At first glance it may appear that Hans' deals were anything but clever as he gave away more than he received. How could such a strategy pay off? Well, after the fourth round of trading (before Hans has even taken a turn himself), he's well ahead of the pack. Al, Bob, Carol, and Dan each have two of Hans' gems and thus two points apiece. However, Hans has one gem from each of the other players and four points in total! Hans hasn't even had a turn and he's got twice as many points as anybody else!
The lesson here is that you need not limit yourself to "even trades" in order to come out ahead. When most people contemplate a trade, they consider only the two involved parties and this is why they fail to appreciate the value of "unequal trading". There are really three parties involved: you, your trading partner, and the other players. Even though your trading partner has gained more victory points than you (on any single trade), you've gained on everyone else.
In Gem Trader (and most trading games), the critical rule is that only the current player is entitled to make a trade. Clever Hans realized that you make points in two ways:
- On your own turn.
- On another players' turn when they trade with you.
|The key is to entice the other players to trade with you on their turn. By offering a better deal than the other players, Hans profited on every turn and this was instrumental to his victory.|
In a real game, there are other concerns you must consider. First and foremost is the fact that you will not usually have an endless supply of "gems" that are worthless to you. More likely, you'll have limited resources and so you cannot simply give away "gems" at every opportunity. To illustrate this, consider Gem Trader with the added restriction that you start with only ten of your own gems. Clever Hans will run out of trade material after only five deals and it's unlikely that this will be enough to ensure victory.
The second complication is that you can't "give away the farm" in search of a deal. Offer too much and you may not be able to make up in volume what you "lose" on the individual trades. What happens if Hans offers five gems rather than two? The other players will each have five points while Hans will have only four. Instead of winning, he's in last place!
The final complication is that sometimes it matters not only what deal you make, but with whom. This is especially true as a game nears its conclusion — if a deal allows another player to win, then it's a poor one to have made. Imagine the final turn of Gem Trader with Al in second place, trailing Clever Hans by a single point. It's Hans' turn but Al is the only player willing to trade and he demands the same 2 for 1 deal that Hans has been offering. Clearly it's better for Hans to decline (and win outright) since accepting would result in a tie. Many games do not have open victory points, so it may not be obvious when you need to decline a deal, but it's something you must always consider.
A practical example is Modern Art (although it's an auction game, the same principle applies). Bob has offered a painting likely to be worth $100 at the end of the round. (One reason Modern Art is a great game is that you can rarely be sure of the exact worth of a painting. However, for the purposes of this example we'll assume that it really will be worth $100.) How much should you pay? Inexperienced players might suggest a limit of $50 — any more and Bob will realize a greater profit than the buyer. These people are destined to lose many, many games of Modern Art. However, you've learned from Clever Hans and realize that bidding $51 is good if it guarantees that you win the auction: Bob gains $51 and you gain $49 ($100 when you sell the painting at the end of the round minus the $51 you paid Bob). Overall, Bob has gained $2 more than you, but you've gained $49 more than everyone else. More importantly, consider what will happen if you don't raise a $50 bid that Carol has placed: Carol will gain $50 compared to you (rather than you gaining $49 on her), Bob will gain $50 on you (rather than gaining only $2), and you won't gain anything on anybody else (rather than gaining $49). This is a disastrous change of events!
This is illustrated with the following graphs which show the relative change in money for each of the players compared to you. Red bars are good as they represent a relative gain in money for you over the listed player. Blue bars are bad since they represent a relative loss in money as compared to the listed player.
Figure 1. The net result of you paying $51 for Bob's $100 painting.
Figure 2. The net result of Carol paying $50 for Bob's $100 painting.
In a real game, your opposing players are not likely to be as dense as Al, Bob, Carol, and Dan. They'll likely also realize the wisdom of bidding $51 on Bob's painting and this makes things much more complicated. Why? Because bidding $52 then becomes a reasonable proposition (since the relative gains will be: -$4 versus Bob, +$48 versus everyone else). Of course this continues as the bids escalate. Is a bid of $75 reasonable? (+$25 versus everyone else but -$50 versus Bob.) In a game such as Modern Art, this is not an easy question to answer, but knowing that you need not always get the better part of a trade will undoubtedly improve your game.
- Greg Aleknevicus