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Subject: Selling and Bidding Strategy rss

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Mike Taylor
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All of the money earned by players in Modern Art comes from selling (auctioning) paintings and the profit (or loss) from the portfolio of paintings purchased during each round (season). Players generally make much more money from selling paintings than from their portfolio of purchased paintings.

There are only two types of decisions to be made during the game: which painting to sell (hand management) and how much to bid in each auction. The choice of which painting to sell not only determines how much money the player receives from sales but also heavily influences the value of each player’s portfolio, so hand management is, somewhat surprisingly, significantly more important than bidding decisions in this auction game.


WHICH PAINTING TO SELL

Besides the obvious goal of selling paintings that will immediately get you a lot of cash, each selling decision should be based on increasing the value of your own portfolio and/or decreasing the values of your opponents’ portfolios. The following selling tactics are listed in approximate order of decreasing importance:

Prepare for Later Rounds
Paintings are worth $30 at most in the first round, but some paintings could sell for $60 or more in later rounds. If you have several paintings by one artist in your hand during the first or second round, reserve some of them, including double auction paintings, for later rounds when they will be more valuable but sell a few as necessary in the early rounds to help that artist rank in the top three places.

Reserve Double Auctions for Later Rounds
Use double auction paintings in later rounds when you can sell a pair of paintings for $80 or more.

Sell Artists That Are in Your Portfolio
By selling a painting by an artist that you already have in your portfolio you help maintain or increase the value of your own portfolio.

Don’t Sell Artists Owned by Your Opponents
If you don’t have an artist in your portfolio but one or more of your opponents do have that artist in their portfolios, avoid selling a painting by that artist. Selling that artist would increase your opponents’ profit from their portfolios.

Sell Fixed Price Paintings Early
As explained below, sellers earn less money from fixed price auctions. So use those paintings as early in the game as possible when paintings are selling for lower amounts.

What to Do with Single Cards
If you have only one painting by a particular artist in your hand you are better off waiting until you have purchased a painting by that same artist before you sell that single painting. Then the sale will likely bring you more money and support your own portfolio’s value. If you have a double auction painting in your hand with no other paintings by the same artist, watch for an opportunity to close a round by playing the double auction painting as the fifth painting by that artist.


HOW MUCH TO BID

Sometimes you may need to refrain from bidding on a painting if you already have one or more paintings by that artist in your portfolio but none of your opponents have that artist in their portfolios. That way one of your opponents will have the incentive to drive up the value of that artist, thus increasing the value of your portfolio. There may also be times when you don’t want to bid on a painting in order to preserve your cash for more important anticipated purchases. However, with a couple of other exceptions explained below, it is usually in your interests to bid as close to the expected value of the painting as possible without bidding higher.

Bid Just Below Expected Value
Expected value means your best guess of what the painting will be worth at the end of the round based on all available information, including all of the paintings in everyone’s portfolios and the paintings in your hand that you expect to sell that round if you are successful in purchasing the painting being auctioned. For example, you may believe that the artists’ paintings will be worth either $10 or $20 at the end of the round and that the likelihood of $20 is about 40%. In this example the expected value is $14 and you should normally bid $13.

The reason you should bid close to the expected value is if you do not purchase the painting your opponents (the seller and the buyer) will collectively gain the expected value of the painting and you gain nothing. However, if you are the buyer you will gain a (small) portion of the expected value with the seller gaining the rest. It is normal and expected that the seller will gain nearly all of the expected value in every transaction.

Sellers Should Bid About 60% of Expected Value
Sellers should not bid close to expected value because when sellers win their own auctions they only gain the difference between the expected value and the selling price instead of gaining close to the expected value. The optimal bid for a seller varies depending on the number of players and is 60% (3/5) of expected value in a three player game, 57% (4/7) in a four player game, and 56% (5/9) in a five player game.

Bids in Fixed Price Auctions
The seller sets the price in fixed price auctions. The seller’s opponents have an incentive to bid less than expected value in fixed price auctions because they can force the seller to pay the fixed price by refusing to buy. For fixed price auctions the optimal bid from the standpoint of the seller’s opponents is based on the number of players and is 75% (3/4) in a three player game, 80% (4/5) in a four player game, and 83% (5/6) in a five player game. So, using a four player game as an example, the seller should set the price somewhere between 57% of the seller’s expected value and 80% of what the seller thinks the buyers’ expected value is.
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Mark Evans
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Your principles are fine. I think what I notice is that not everybody plays rationally and that leaves me thinking this game may have more to do with psychology than strategy, though I follow the basic principles you outlined.
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Steve Norton
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I don't agree with your "bid just below expected value" principle. If the expected value of a painting is $14 (as in your example) and you successfully win the bid for $13 then you expect to make $1 profit and the seller makes $13. Is this sound strategy?

The equitable bid would be $7 so that both seller and buyer make $7 each. For every extra dollar that gets bid, the more the seller stands to be the winner. This gets complicated when more than one buyer wants the $7 profit for themself (and the price inevitably goes higher) but buyers should, collectively, be aware that they are playing into the hands of the seller.

In the late game when someone puts up a double-auction with an expected value of $200 you are going to give the seller an easy win if you bid $199 just to make a $1 profit.

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Mark Evans
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Good call. I usually try to split the difference myself and then find myself getting outbid by people with bidding fever.
 
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Mike Taylor
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Steve, look what happens under your theory of an “equitable bid” in your $200 double auction example. If A auctions two paintings worth $200 and B makes an equitable bid of $100, then if C refrains from bidding any higher A and B each gain $100 while C gains nothing, causing C to fall $100 behind A and $100 behind B. Such a decision might seem equitable but it is strategically unsound because by bidding $101 C would dramatically improve her position against both A and B, falling behind A by just $2 (an improvement of $98) and advancing compared to B by $99 (which is a $199 swing from losing $100 to gaining $99).

The same holds true if B bids $180 for the paintings. The gains to A, B, and C would be $180, $20, and $0, respectively. By C bidding $181 the gains would be $181, $0, and $19, respectively, and C’s position with respect to B improves by $39 (from a loss of $20 to a gain of $19). This same analysis is valid all the way up to $199.

It is certainly true that the seller will make $199 and the buyer only $1. This game overwhelmingly rewards the seller for good hand management. Players should recognize the extreme importance of being able to sell expensive paintings.
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Steve Norton
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Yep. I said it gets complicated with more than one potential buyer. B and C have to play smart or they just hand the win to A.
 
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Brian S.
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There are a couple of guys I play with who spend the entire round buying as many paintings as they can and try to close the round as quickly as possible. They will even sacrifice a double auction painting and an accompanying painting to achieve this. I would never do that, because in my mind a double auction painting is big $$, but I've seen that strategy work. So many angles to the game, it really pays to have a very seat-of-the-pants approach to strategy rather than a pat strategy.
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Yannick Carriere
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I once played a game (4 or 5 players, I can't remember) in which two players tied in money at the end of the game. One purchased like crazy and ended the round quickly to make his profits, and the other player only sold paintings. Never bought one. Two different strategies, same result.

Granted, this doesn't prove much since I agree with a comment above: that this game is in large part psychology. This is a game where the behaviour of the players around the table will effect very much the end results. Insert in a game a player who doesn't calculate and get the financial implications of different strategies and just plays with his/her gut feeling, and the game is unpredictable. Still a blast. I really like this game.
 
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Adrian Brooks
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mdt325 wrote:

Bid Just Below Expected Value

Here's my problem. You tell me bid $1 less than the expected value, or even 56% of the expected value. It implies you can work out the EV of the bid to an accuracy of less than $1. I don't know how do that.

Show me a worked example, ideally from a real recorded game, for, say, the Player 1's third auction in a four player game from the perspective of Player 3.

And if you can't, well, you're just guessing. I know how to do that already.
 
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Mark Evans
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I think Expected Value is based on best guess.
 
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Steve Norton
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Slow Dog wrote:
And if you can't, well, you're just guessing. I know how to do that already.

You bid by guessing? I assume you don't win much..?
 
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Chris Linneman
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I may be stating the obvious, but this game is heavily subject to groupthink. Optimal strategy will always vary based on the tendencies of your opponents. If they are bidding $1 below expected value, you are not going to make any money from buying paintings. In this case, I would focus 100% of my energy on trying to set the paintings up in my hand to be worth a lot in later rounds and not worry at all about winning auctions. I would say this is the most common type of group I have encountered, people who bid too high in auctions.

You need some ability to evaluate the relative positions of your opponents when bidding. You should be willing to bid more for the paintings of opponents who are doing poorly and less for those from opponents who are doing well. There is no sense in gaining $1 on three players who you are already beating if it gives $199 to the one who is ahead of you.

In the early game, I'm usually willing to give 2/3 or 3/4 of the profit to the seller. It is their turn, and you should expect players who spend their turn selling a painting to make some profit. However, if you give them 99% or even 90% of the profit, there is too big a chance they will get too far ahead in the game and too small of a chance that the peanuts you made will make any difference to you catching them.

If other players are doing this (giving 99% of the profit to the seller), your best strategy is to try to exploit their tendencies by reaping the same rewards with your sales. Got a lot of Kryptos in your hand, including a double? Try to get Krypto to place each round, regardless of whether you have any or not (and you shouldn't have any paintings if your opponents are bidding too high). I frequently win games barely buying a painting all game because my opponents are bidding too high. Instead, I try to make a killing in later rounds with selling my paintings. One advantage to this tactic is that you never have to waste your turn ending the round and not selling a painting.

Another thing you have to consider is there is almost always some risk when buying, but once you sell a painting, it's money in the bank. You could be almost positive your Lite Metal will come first, but especially in this game opponents are unpredictable. Some double Christin Ps could suddenly come out and ruin your day. Unless you will end the round on your next turn, you can only estimate the value of the paintings you are buying. For this reason, you should err on the side of underbidding. If you give 90% profit to the seller, but the painting only sells for 20 instead of 30, suddenly you have overbid by 35%! This is very bad. Losing money when buying is doubly horrible since you have hurt yourself and given another player more money than they rightly deserved.
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Brian S.
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ReggieMcFly wrote:
Slow Dog wrote:
And if you can't, well, you're just guessing. I know how to do that already.

You bid by guessing? I assume you don't win much..?

Well, it's all guessing until the round ends. It's not that rare for a "sure thing" to be skunked at the end of a round.
 
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Daniel Kearns
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mdt325 wrote:

Prepare for Later Rounds
Paintings are worth $30 at most in the first round, but some paintings could sell for $60 or more in later rounds. If you have several paintings by one artist in your hand during the first or second round, reserve some of them, including double auction paintings, for later rounds when they will be more valuable but sell a few as necessary in the early rounds to help that artist rank in the top three places.


Artists seldom have more than two good rounds in them. If you are trying to get an artist to place a third time, other players can become suspicious and doubt that there are enough of those cards left to finish out on top. Clearly this is situational but if you wait too long to cash in, you can get burned as well.

mdt325 wrote:

Sell Artists That Are in Your Portfolio
By selling a painting by an artist that you already have in your portfolio you help maintain or increase the value of your own portfolio.

Sell Fixed Price Paintings Early
As explained below, sellers earn less money from fixed price auctions. So use those paintings as early in the game as possible when paintings are selling for lower amounts.


IMO the fixed price auctions are the most powerful in the game combined with the other rule above. Say you own a Yoko and it is behind in the race for that round. Offer a fixed price Yoko at a bargain (price they can't refuse) to the player on your left. The fixed price auction automatically increases the value of your Yoko (like any other auction). But since they just got a deal on the Yoko they will be highly motivated to auction a Yoko from their hand on their turn, thereby further increasing the value of the Yoko you hold. Often your painting can go from trailing to leading. I call this a slingshot.
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Doug Marley
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I do estimate the value of everything auctioned but I think the thing that is often overlooked is you want your opponents to prop up your strongest artist. Winning or losing an auction, I believe, is meaningless in the first two rounds because the values of an artist accumulates. It is far better to increase the value of your hand than to win an auction. Letting an opponent win an auction that lines up with your hand makes them vested in propping up that artist. If you have 3 or 4 Gitters, guess what, no one is going to close the round out for you because they don't have a vested interest in you making money on Gitters. So, letting stuff go below the expected value is often in your interest. When I play, 80-90% of my profits usually come in the last two rounds. I have had games were I scored around 350 in the last round. I don't think anyone should even be looking at their money ever during the game because it removes the focus from the goal of making your hand valuable. If your hand is valuable, the money will come when you sell. I only care about money if too much stuff is going cheap and I am running out of money because I am buying everything. That rarely happens.

The only other thing I think you should pay attention is to how many paintings of an artist has been played. If artist has had two 30 point rounds, it will be hard to score in one or two more rounds since there are not that many cards left of that artist. So, a hot artist will burn themselves out. It doesn't matter what an artist has done in the previous rounds if there aren't enough cards to get them in the top three.
 
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