A secret of game-fu
<p>Last night I utterly trounced three opponents at the slick new Fantasy Flight reissue of a classic interstellar trade and exploration game, <cite>Merchants of Venus</cite>.  My end score was nearly three times that of the runner-up, and I had acquired so many fame points (which each become 10 victory points at game end) that we ran out of fame tokens.</p>
<p>One of the other players half-humorously protested that I had gotten incredibly lucky.  &#8220;Nonsense&#8221;, I said, &#8220;it was planning&#8221;.  He sputtered that I had frequently had the victory conditions for lucrative missions apparently drop in my lap.  Which was true, and he was right to view those individual occurrences as luck.  But it was also true that I planned my way to victory. </p>
<p>I made chance work for me.  Pay attention, because I am about to reveal why there is a large class of games (notably pick-up-and-carry games like <cite>Empire Builder</cite>, network-building games like <cite>Power Grid</cite>, and more generally games with a large variety of paths to the win condition) at which I am extremely difficult to beat.  The technique is replicable.</p>
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<p>I have a rule: when in doubt, play to maximize the breadth of your option tree.  Actually, you should often choose option-maximizing moves over moves with a slightly higher immediate payoff, especially early in the game and most especially if the effect of investing in options is cumulative.</p>
<p>This rule has many consequences.  In pick-up-and-carry games, it means that given any choice in the matter you want to start by deploying or moving your train or spaceship or whatever to the center of the board.  You minimize your expected distance over the set of all possible randomly-chosen destinations that way.  You give yourself the best possible chance  to &#8220;get lucky&#8221; by finding a fattest possible contract or trade opportunity that you can deliver in minimum time.</p>
<p>More generally, in games with multiple paths to victory, open as many of those paths as you can.  And heavily favor moves that help you explore the possibilities faster than your opponents.  In <cite>Empire Builder</cite>, buy the faster train as soon as possible.  In <cite>Merchants of Venus</cite>, the first ship upgrade I bought was better engines.</p>
<p>In games with an exploration mechanic, like <cite>Merchants of Venus</cite> or <cite>Eclipse</cite>, push it hard in the early game.  Again, the payoff here is that you&#8217;re generating options for yourself.  This effect is particularly strong in <cite>Merchants of Venus</cite> because on a first-contact planetfall you get to do <em>two</em> buys and sells with the natives rather than the normal one &#8211; you have that much better a chance of a trade good you previously bought on spec being highly valuable, or of picking up a spec load that will pay off large at your next first contact.  (Of course, when this happens, it looks like luck.)</p>
<p>Look for other ways to broaden your option tree. In the <cite>Merchants of Venus</cite> game one of my other early purchases was a second mission-card slot.  From early in the game to shortly before the end, this meant I had a choice of two missions to work on rather than just the one other players were pursuing.  So of course I fulfilled them more often!  It looked like I was getting lucky; what I was actually doing was maximizing the number of possible <em>ways</em> I could get lucky.</p>
<p>In network-building games like <cite>Power Grid</cite> and <cite>Empire Builder</cite>, bias towards moves that make your network closer to a minimal spanning tree for all destinations of interest &#8211; that is, accept somewat lower immediate payoffs and/or higher costs for building such links. This maximizes your chances of being able to reach anywhere quickly in the later game.</p>
<p><cite>Power Grid</cite> is an instructive example of a game with positional, network-building strategy in which maximizing your option tree can also be done in some ways that aren&#8217;t at all positional.  One relatively obvious one is to buy hybrid plants, which increase your options for both price-taking in the fuel market and (less obviously) manipulating it.  </p>
<p>Another one is to be willing to pay what you have to to get a game-ender plant (a 5 or 6) within the first few rounds, even if it means you don&#8217;t get to build cities in that turn and your revenue doesn&#8217;t go up.  The real payoff here is being able to sit out several auction rounds while other players are scrambling for plant capacity to match their city-building. Their options are narrow in each round; yours aren&#8217;t &#8211; you can pile up money or opportunistically grab only the most efficient plant buys as they go by.   </p>
<p>I rely particularly heavily on the latter tactic.  I made the national <cite>Power Grid</cite> finals with it this year.</p>
<p>If you are in a game where other opponents can directly mess with you, maximizing your option tree also makes it more difficult for them to correctly predict which countermoves will damage you the most.  And even if they close off one tactical path, you&#8217;ll have others.  More generally, you may overwhelm their capacity to model your behavior, so the game looks to them like constant surprises with you coming at them from very direction at once.  Weak players often fail a morale check in this situation and become even weaker. </p>
<p>(This happened last night &#8211; one total morale collapse and one partial out of three opponents.  Unsurprisingly to me, the third guy, the one with the most sitzfleisch, came in second.)</p>
<p>Afterwards, they think you &#8220;got lucky&#8221;.  This is an illusion they foist on themselves through picking a <em>single</em> path to victory and working it as hard as possible.  Because this makes their range of usable lucky breaks smaller and less likely to occur, they overestimate the element of chance in your victory &#8211; they judge it by how lucky <em>they</em> would have had to be to win by a similar margin.</p>
<p>And why am I OK with telling you this secret? Because ha ha, Grasshopper, I have <em>other</em> secrets.  Perhaps I will share some of them in future posts.</p>
