Ridere, ludere, hoc est vivere.

Thursday, March 21, 2013

Numerical analysis of "East India Company"

At UnPub 3, during the three-player playtest of "East India Company," Ben Rosset expressed concern that in the game, the dividend track wasn't rewarding enough to justify the cost.  He felt that in general, money can be better spent on ships and goods that will yield a better return on investment than declaring dividends.  It was an observation that I took very seriously; I hadn't had a playtest in which anybody completely ignored the dividend track before.  I wondered if it was a weakness that would emerge with extensive play and end up being a superfluous element of the game.

In a subsequent playtest at PrezCon, I tried a strategy of ignoring the dividend track until the very end of the game (when there was nothing else to do with the cash).  I won that game, but only by about two points, which makes me think that the "ignoring dividends" approach has merit but is not necessarily an obvious decision.  I needed to look more closely at how the numbers would really work out.

So I decided to take an analytic approach.  I just ran a couple of test cases in a spreadsheet in which I simulated the transactions of a player in a game.  I made a few simplifying assumptions and laid out how the cash flow would look under a certain strategy with minimal dividends, and then the same strategy with a more aggressive dividend declaration approach.  I used this side-by-side comparison for two strategies - the "Spicy Craig" (going into debt to invest in a big ship and sending it to China to load up on spices) and the "Reinvesting Rosset" (turning over profits into an expanding fleet of small and medium ships to trade in a variety of commodities every turn).  In each case, the difference between ignoring dividends and aggressively declaring dividends was very small.  For the "Spicy Crag," aggressive dividends won 54-50 over ignoring dividends.  For the "Reinvesting Rosset," ignoring dividends won 80-79 over the aggressive dividends.

These results are so tight that I've concluded that I should not adjust the dividend track at all, at least for the time being.  I'll continue to pay attention to the opportunity cost of investing in ships or paying off debts vs. declaring dividends, but I have a feeling that the dividend track is pretty tight the way it is, and that I've put players in a challenging decision space - which is exactly where I want them to be.


  1. I am intrigued by your results but I must ask a few questions about your methods. In your comparison when you compared aggressive dividends with Spicy Craig and Reinvesting Rosset were you only playing a game where they faced off each other one on one or were multiple strategies being played at once?

    The reason I ask is I want to know if multiple players are playing Reinvesting Rosset and Spicy Craig if they drive out the resources needed to succeed as a dividend player? The challenge is since the game is in the end a zero sum game you not only care about maximizing your point total at a given moment, but you also care about minimizing your opponent’s scores as well. The more you buy/sell resources before your opponents in EIC the less return your opponents can earn. Does the absolute difference in point separation from flooding the markets before your opponent can respond outweighs the extra points from the dividends? Do dividends only matter when both players are engaged in the same trade strategy (in terms of their commodity pickup plan)?

    That said, your post highlighted a key point which is not that you are looking to create a world where one strategy is favored over another the entire time but that the players are faced with a marginal decision to switch strategy throughout the game. That leads me to a third test I would like you to conduct, assume one initially commits to a non-dividend strategy, is there a point in which they should switch or is your best interests to commit to a single strategy and not diverge from it? (aka, the returns from dividends merit a change in strategy).

  2. Fair question, Aaron, and thanks for such a detailed, thoughtful comment.

    I used the phrase "simplifying assumptions" quite liberally, as it happens. I didn't so much simulate a full game as I did run through theoretical turn-by-turn transactions in a perfect, noncompetitive environment. I wanted to find out whether there was an obvious advantage in return-on-investment between ignoring and aggressively pursuing dividends, so I treated the competitive impacts on commodity prices as equally impacting.

    As I think about it, though, that's not really true. Ignoring dividends implies making up lost bonus points with profits on more sales. But if competition is strong, then the ROI on sales is less, whereas the ROI on dividends remains constant. So, if anything, the way I set up the comparison should show best-case for ignoring dividends, rather than average (or "representative") case. So that means that my simplified methodology may have skewed my results.

    But on the other hand, running a truly exhaustive analysis is just so much work. :-)

    You are right to point out that a big part of "EIC" is "beating your opponent to market." Dumping spices on the market in Europe - just when your opponent arrives with a shipload of the same thing - takes a big bite out of his profit. So the actual performance of a strategy does depend considerably on whether your opponents are doing the same thing. (Ryan Sturm on his podcast "Ludology" has often mentioned his general rule-of-thumb for multi-player games, "do whatever your opponents are not doing.")

    I like your last question about whether there is a kind of "inflection point" where the ROI on one strategy declines relative to the other and represents a point at which a player should switch strategies. I think I'll look more closely at the spreadsheet on a row-by-row basis and see if I can tease anything out of it.

    All caveats notwithstanding, I don't feel worried that I need to make any drastic adjustments to the dividend track. More playtesting may reveal some need for tweaks, but I'm gratified not to find any glaring faults (so far).

  3. Here is an idea that may help simplify your simulations. (If you have not already done them).

    First, identify the ROI for dividends that equals the ROI for plowing your money back into your business (in terms of VP).

    Second, identify what the conditions would have to be on the board for the that ROI between the two options to equate each other.

    Now, you can access from your previous game testing:
    A. How likely are those outcomes?
    B. And were people making the wrong investment choices?

    So for example, calculate how much the price of spice must fall to justify putting your money into dividends. The simplest way to do that is to get the skewed results where you assume that there is no other player shipping spice. Or better yet, calculate how much all prices must go down to equate the same rate of return for VP.

    This gives you a picture of the map where as a player you know when you should put your cash into dividends. And you can now ask yourself what is the likelihood of prices depressing to these levels.

    To assess the relative differences in VP’s between players you should construct estimates on how much money/VP’s your opponents would be making if their trade habits were pushing prices that low. (Or, if it was even possible for all the players in the game to push prices that low, such that, one would consider the switch to dividends).

    Now here is the twist that helps you assess the competitive affects. Does the VP return in dividends (assuming that by the time you return the cargo to port and you face the depressed prices) beat the separation from your opponents by you then depressing the price of the good?

    In other words, even though you may have the same ROI in dividends you may benefit more from dumping spice in the spice market to depress prices so your opponent can not get more VP’s than you. For example, if you ear 6 VP from dividends and your opponent ears 10 VP form flooding the spice market, you may find it in your long term interest to keep investing in the spice market because if you too depress prices you each may only be earning 3 VP from spice which means your opponent is not expanding their lead on you in the game.

  4. I like the way you think, Aaron. I'll give this further thought and see what I want to do next with it.