Players acquire tiles in a somewhat unusual fashion. One player will blindly draw up to three tiles out of a bag and then set a price. The other player may choose to buy the goods for that price if he wishes, with the money going to the bank. If he does not choose to buy the goods, the player who drew the goods must purchase them for that amount. Whoever purchases the goods gains control of the bag and pulls out the next set of tiles.
Each round ends when one player's boats have been filled. There are other rules involved in the loading of boats which make things interesting but aren't quite worth detailing here.
A couple of weeks ago I played my third game of MvS against my brother. I had won the first game, but he had clobbered me in the second. The lesson I learned in that second game, and which should have been obvious in retrospect, was that the monopolies are worth a bit more in the first round, as the monopoly meters persist from round to round. My brother was setting prices that I thought were too high in the first round, and the round ended with me having filled up very little of my cargo space. At the end of the second round, I was sixty or eighty florins behind him.
This last game was the opposite; this time, I was the one who was setting high prices in the first round and trying to get traction on the monopolies. I ended the round a few florins behind my brother, but I had a monopoly edge going into the next round. In the second round my brother was setting extremely high prices, and I think I ended up with only two goods loaded. Regardless, I still earned a lot of points, and at the end of the reckoning I was eighty points ahead.
We didn't play the third round—I noted our positions and we might pick the game up next weekend, but it will be hard for my brother to bounce back from that kind of deficit.
Overall, I think Medici vs. Strozzi is a neat game. It's engaging, it's beautiful to look at, and there is an amazing amount of depth to it considering how short the rules are. However, though the waters run deep, they are also a bit murky; there are so many nebulous factors which come into play that setting the "right" price can be a very difficult task. At first glance it might seem that everything is calculable, but it isn't so; this is only the case at the very end of the third round. Players must take into account the fact that monopolies persist from one round to the next and the fact that the buyer gets control of the bag. Payers must also be concerned with the end of the round and how many empty spots there are in their cargo holds (I did not go into the rules for allocation of commodities into the holds, but suffice it to say that there are times when a set of goods is more valuable to one player than to the other, and orchestrating and capitalizing on these situations is key to success). Beyond that, there is the matter of simple psychology; what misconceptions might my opponent have, and how can I exploit that?
There's also something which is a little unintuitive about the game; in particular I have read complaints that the game doesn't make sense because players can end the game having lost money. For those who have played and are mystified by this phenomenon or feel it anti-thematic, here is a explanation that I wrote elsewhere:
The reason that players end up in the hole is not because they're playing poorly but because the game is not modeling real-world business. There is no "bottom line"; players are only concerned with their profit/loss relative to each other. Here's a super-simplified analogy:
Imagine that two rival donkey salesmen have their stalls across the street from each other. These donkey salesman aren't ordinary donkey salesmen, however, because neither care about the profit margins on the donkeys. They're not even trying to make a living. All they care about, vindictive jerks that they are, is that their rival does not have a better profit/loss than they do. In short, they would rather lose five dollars than see their rival make six.
A donkey wholesaler comes through town and auctions a donkey to the two retail salesman. Well, both salesman know that the retail price for a donkey is fifty dollars, and because of their competitive mania, the wholesale auction price of the donkey is also going to be fifty dollars. One would not suffer the other to buy the donkey for even $49.99, because he'd be making an entire penny!
With that in mind, you can understand how if two players somehow played a "perfect game" of Medici vs. Strozzi they would both end the game breaking even.
Except that you can gain ground on your opponent in cases when a lot is worth more to you than it is to your opponent. For example, if you have the marker just before the +10 bonus on your side; a matching tile for you would move it to 10, whereas if your opponent wins the tile his situation remains the same. If the tile had no other effect on income, the correct price to set is five. If your opponent allows you to buy it, you make a five dollar profit. If your opponent buys it, he is spending five dollars and getting nothing in return. Either way, you there is now a five dollar difference between your fortunes and your opponent's.
Anyway, what this all means is that the game can be maddeningly opaque at times—not so much as to spoil the fun, but perhaps just enough to keep it from being ranked among my favorite two-player games. Of course, this might be my inexperience talking and I might gain a deeper appreciation with more plays, so take what I say with a grain of salt.