Friday, August 17, 2018

Blast from the past! Applying "basic strategy" to Riders of the Pony Express

For YEARS I've been searching for an article I once read about basic strategy, why it's not always bad to make a trade that's not obviously in your own favor. Nobody seemed to recognize it when I described the article, or the hypothetical gem trading game used in it as an example. Google searches had left me high and dry. At times I started to wonder if the article never really did exist...

The other day I was exchanging emails with my friend Rick, who's come on board to help me with my Worker Learning game, and he referenced (and linked to) an old article about "bombs" in games by Jonathan Degann. I clicked the link, and recognized the article. I'd read it some years ago. On top of that, I kind of recognized the look of the page. I wondered what else I had seen on it. I didn't see any navigation buttons, so I deleted the last part of the URL (showing the title of the article), and what I got was a text list of links to different article by name. I recognized that too...

Clicking through some of those links, I saw more and more articles that I remember having seen or read years ago. One of them, oddly enough, I have a printed copy of sitting right next to me at my desk!

And then it happened. One of the links I clicked on made my eyes light up. FINALLY, after all this time, I had found it. I had found that article about trading gems! It's by Greg Aleknevicus from 2004 in The Games Journal: Basic Strategy 1.0

I wholeheartedly recommend reading this short article, which talks about why it's not always bad to make a trade that's not obviously in your own favor. It's insight that applies to games, of course, but also to real life. Here's a highlight, maybe my favorite single line from the article:

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.

By the way, I also recommend the next article in that series, Basic Strategy 2.0 -- it gives a great and very simple description of how to start considering all the factors in your strategic decision making.

I am SO HAPPY to have found this! Now, to show how it is relevant to a game designer, let's consider one of my own designs: Riders of the Pony Express.

In Riders of the Pony Express, there's sort of a low-bid auction where you receive $10 and a parcel to auction off ("Anyone want to do this delivery for me? I'll give you $3. $4? How about $5?"). If someone claims the parcel for $4, then you keep the remaining $6. Each player will do that twice per round. There's a dynamic that has come up in which players can simply bid the absolute minimum ($3) for parcels, claiming every one right away. Since you only get $3 for doing that, I had hoped that it would not be worthwhile (except perhaps in rare circumstances). But in fact, especially in a 5 player game, claiming every parcel for the $3 minimum bid can be a dominant strategy for exactly the reason outlined in that strategy article linked above!
This is true for 2 reasons:
  1. In a 5 player game, you can get away with significantly more money than each opponent if you take every parcel for $3 (you get $3 x 4 opponents x 2 parcels/opponent = $24, and they each get $7 x 2 parcels = $14). This is less true in a 4 player game (you only get $18 to their $14, which is much closer), and in a 3 player game you don't actually make out ahead. So the issue is most pronounced when there's a full complement of 5 players.
  2. The costs of making a delivery that's out of your way do not appear to be high enough. As one playtester put it, you have to traverse the entire board anyway, so nothing really seemed out of the way. Now, I'm not 100% sure he's right, but it's possible the costs need to be a bit higher to go "off course," in order to make the route planning and parcel claiming properly interesting.
Again, it may be that this is only a problem in a 5 player game, which might just mean the game should only be for 2-4 players. If simply reducing the player count solves the problem, then it seems a reasonable solution. Besides, I've had complaints about game length and stuff in 5 player anyway. However, I'd hate for that to be the solution, I'd rather understand the problem and fix it! And re-reading Basic Strategy 1.0 might remind me how to do just that!


Glenn said...

I found it quite amusing to clearly see the application of the teaching method to the article itself.

Seth Jaffee said...

Thinking about this some more, here are a couple of ways I could address the problem of minimum bid dominance and maintain a 5 player game:

1. Increase the total amount from $10 to $15 (at least for 5 players). This changes the math a bit, bidding the minimum $3 would still get you $24, but your opponents would now get $12 x 2 = $24 as well.


2. Decrease the minimum bid to $2. This similarly changes the math such that bidding the minimum on everything nets you and the other players $16 each.

The reason for the $3 minimum bid is partly because I didn't expect a smaller bid to EVER be worthwhile, but MOSTLY because in the count-up auction version I started with, I didn't want to have to wait for players to say "1... 2..." To start every auction when they're not really relevant bids.

With the blind bid version, it would make more sense to just provide bid cards for $2 (and maybe $1), though that's extra components, and also might just shift the dominant strategy to "bid X every time".