Reiner Knizia’s board game Modern Art presents a series of art auctions that players will bid on. From there, you will redeem the paintings you’ve purchased for money. How much money is dependent upon how well that painting’s artist ranks. At a high level, it’s like playing the stock market if companies were artists and shares were paintings. But understanding its strategy can take some time to figure out.

To win, you need to make the most money. And to make money, you need to be able to figure out how much a painting will rank so that you don’t overbid. It’s difficult to do when everyone is trying to do the same thing. 

Furthermore, this rundown of Modern Art’s strategy may not be apparent when the game is explained to you. Some players will look at Modern Art and will think that making a profit is sufficient. If you buy a painting for $19 from someone and it’s worth $20, you’re ahead of the game, right? Wrong. What ultimately matters is total profit, and the player to make the most profit will win.

There’s a lot to unpack there. To understand how to do well in Modern Art requires understanding the math behind Modern Art’s strategy. If you’d prefer to see it in video form, check out the video below. Otherwise, read on!

The Math Behind Modern Art Strategy

The foundation for Modern Art lies in understanding where the money comes from. From there, you’ll need to understand how to calculate profit. To start, money comes to you in one of two ways. The first way is from purchasing pretty paintings and redeeming them for profit. The second way is from selling paintings. The question then becomes how to maximize your take from each of those activities. To do that, we turn to basic accounting, using the concept of cost, revenue, and overall profit in our analysis.

Let’s illustrate this using a mock 3-player game. Here, you’ll be a buyer in a game where You, Alpha, and Beatrice each start out with $100.

A single painting purchase

Alpha puts up a painting by Sigrid Thaler that will go through an open auction. The bids fly fast and furious, but in the end, you’ve beaten out everyone else and buy the painting for $12. Now, let’s evaluate each player’s position.

For Alpha, that’s easy. She adds that $12 to her bankroll. Everything the seller makes from selling the painting is pure profit, so she makes a profit of $12, increasing her bank balance to $112.

A breakdown of your ending money depending on how well a painting ranks in Modern Art

For you, it’s murkier, depending on how the art markets pan out. If the painting goes for $30 at the end of the round, You’ll make a profit of $18. That’s $30-$12, to get $18. That means you’ll have $118, putting you in first place. That’s a pretty awesome result from the auction.

If the painting goes for $20, you’ll still make a profit. It won’t be as high as before, but it’s not too bad. You’ll make a profit of $8. That’s $20-$12 to get $8. That gives you a total of $108, leaving you in second place.

But if the painting goes for $10, you don’t make any profit. In fact, you’ve lost money on the deal. That’s $10-12, losing you $2. That leaves you with $98, leaving you in third place behind Beatrice who did nothing and still has $100. And as you might expect, it’s even worse if the painting winds up being worthless.

Understanding a painting’s profitability split

From the previous example, buyer and seller have to figure out what price to sell the painting by forecasting how much the painting will be worth at the end of the round. When you’re the seller, you want to keep a figure in your mind of how much to let a painting go for.  The price you’ll set it at will be different if you think a painting will be worth $30 versus if a painting will be worth $10. That is because the buyer and seller split the painting’s final value. 

An even split if the value of the painting is $20.

So what does an even split look like?  Easy: take the painting’s final valuation and divide by 2 and that value will be the even split between the two players. If you buy a painting from Alpha for $10 and its value at the end of the round is $20, both you and Alpha will wind up having $110. Any selling price beyond $10 benefits the seller, Alpha, say $112 vs your $108, and any selling price below $10 benefits you, the buyer, say Alpha’s $105 vs your $115.

But no price is a guarantee and that’s where Modern Art’s challenge comes in: figuring out what the probable value of that painting will be at the end of the round. A painting could be worth $10, but with some conspiring, could easily be worth $30. Or someone thinks a painting will be worth $20, only for it to wind up being worthless. 

Multiple art auctions can skew the mathematical incentives

And if that wasn’t hard enough, the concept of the even split tells an incomplete story because it only looks at a painting auction in isolation and not the entirety of the system where many paintings are sold. Sometimes, it behooves buyers to give sellers slightly better deals on a painting’s revenue split, say paying $12 for a $20 painting, but making up for the higher cost in volume. 

For example, let’s say you bought a painting that you’re absolutely certain will be worth $20 for $12 from Alpha. Quick math puts it at $112 for Alpha and $108 for you. Good, but not first place material.

But now, it’s Beatrice’s turn and she puts up a painting that you know for sure will be worth $30. And let’s say you wanted to buy it and decide to give Beatrice a good deal. Instead of doing a 50/50 split by paying $15 for it, you decide to give her $18.

That means you’ll earn net $12 from the profit, pulling you from $108 to $120. Beatrice now has a total of $118 and Alpha still has her $112. Despite giving the sellers a greater share of the profit for each painting, you’re still ahead in overall profit, putting you in the lead.

You can still win by buying more paintings.

So yes, there is a lot to Modern Art. There are a ton of wrenches you can throw into the system and a lot of manipulating you can do. Do those well and you’ll be in a very good spot to win. The logical next question is what levers you have at your disposal to clear up the uncertainty and tilt the field in your favor? Here are three tips that I think are worth using.

Understand your market positioning and market power.

Discerning pricing can be difficult because of all of the unknown information out there. Thankfully, you have one source of information you can rely on: your hand. Look at your hand and use that as a guidepost for how hard you can bid on a painting during any given auction. And also use that to see when others might be undervaluing a painting.

Let’s say someone just put out a painting by Ramon Martins for auction. Look at your hand. Do you have 3 other Ramon Martins paintings in your hand? If so, maybe you can push the value of Ramon Martin’s paintings to $20 by the end of the round by auctioning off some of your own. But if you don’t have any, maybe hold back a bit until you can make a better guess as to whether any given artist’s paintings will rank and score before you bid. And if the response to an auction is tepid, but you can push the value of that painting up through your hand, you might want to feign uninterest when bidding to get that painting on the cheap.

What it comes down to is that the more certain you are of a painting’s value, the more you’ll be able to devise an optimal bid according to the Modern Art Mathematical Mastery technique I highlighted earlier.

See what paintings other people are bidding on and buying

I just talked to you about using your hand as information to help guide you on how hard to bid. If your opponents are smart, they’ll do the exact same thing. In light of that, pay attention to what paintings other players are bidding on and how much. You can use that information to figure out what paintings your opponents might have in their hands and how they might be valuing a given artist.

So how would you take advantage of this information? It helps you decide which paintings you should be putting up for auction. If a painting from an earlier auction provoked a furious bidding war, that’s an opportunity for you to capture value from a painting in your hand. If two artists are neck and neck in ranking for value, maybe now’s the time you support the one that can get you the most value based on others’ bidding behavior.

This is even more relevant if you put in those double-painting auctions. Timed well, you can bring about chaos and capture more value from an auction than you otherwise would.

Develop (informal) alliances

Two heads are better than one and that adage holds true in Modern Art where two heads can better manipulate the market than one. The idea behind forming an alliance is simple: with all the market manipulation that goes on in a game of Modern Art, you want someone on your team who has an interest in manipulating the value of the paintings from the same painter you want to manipulate.

A potent Manuel Carvalho alliance.

So let’s say you own a Manuel Carvalho and Alpha owns a Manuel Carvalho. Both of you now have an incentive to make sure that Manuel Carvalho ranks and ranks reasonably high to maximize your profits. In this arrangement, it’d be best if you allied with Alpha to auction off more Manuel Carvalhos and ensure its high ranking.

To make an alliance work, you may want to auction off a painting for very cheap. Maybe you auction off a painting you think can be worth $20 for $8 so that someone else is more willing to buy it. Once that other player does, they now have a vested interest in making sure that painter ranks, giving you an ally you can somewhat rely upon to help you get rich. 

Nothing is worse than being the only person owning a certain painter’s paintings because no one else will really want to help you out. It’s really hard to rank an artist without help.  But get someone else to put skin in the game and you can steer the art markets in your favor.

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