Modern Art - Any Strategy or Tactics Tips?
Nicholas Sauer
In article: <329ec6d5...@news.hol.gr> ba...@hol.gr (Alex) writes:
>
>I recently played Modern Art with my friends. I was impressed by the
>depth of the game and the difficulty of finding the right "moves".
The "right" moves are probably more of a function of what a particular
group's "group think" style of play for the game is. This is one of
the things I like a lot about the game because, it forces you to adapt
your tactics to the environment in order to win. As a result it would
be difficult for the game to become "old" unless you play with the same
players over and over again (and none of them change their play style).
>If anyone out there has come up with a good strategy I would be very
>glad to hear about it. Any ideas? Any tips.
Watch what the other players do with respect to how they purchase paintings.
There is much to this game's economics that I still don't understand yet.
>My experience is so far quite limited. My impression is that we tend
>to overestimate the value of the auctioned picture. As a result the
>auctoneer gets the largest share of the profits. Since everyone in my
>group did the same thing, the result was the same (I think).
>Why should one pay $25 to another player and in the end sell the
>picture for $30? His profit is $5 while the other guy gets $25. (Maybe
>game theory would help here).
I won my first two games by buying no paintings. After the other players saw
me do this they changed what they were willing to pay for paintings and, as
result I haven't been able to use this strategy ever since. At first I would
have guessed the way to break this strategy would be for everyone to buy their
paintings for less money. However, in practice it seems that the reverse is
true in that games where paintings go for close to their market value don't
favor non-buyers. I suspect that this has something to do with some kind
of economic building curve I am missing. In any case, if paintings are going
for cheap in the game, I would try the sell only strategy. In games where
paintings go for very close to their final value, I wouldn't. I have yet
to see a "balanced" game where games go for some consistent value between
half and just below their final value. The game also seems to favor risk
taking in that I have seen people who bought paintings that didn't finish
(i.e. they were worth nothing at the end of that round) actually win games.
I would normally have thought that buying a worthless painting would have
been a death sentence to victory. Again, I think the best advice is to
seriously watch what the other players are doing and try to adapt to it
in such a way that you make more money. The only problem is that it is
not always obvious exactly what form that adaptation should take.
>Any help will be greatly appreciated.
I hope the above is worth something to you. Modern Art really is a great
game.
Nick Sauer
Aaron D. Fuegi
Nicholas Sauer (n...@spin.att.com) wrote:
: In article: <329ec6d5...@news.hol.gr> ba...@hol.gr (Alex) writes:
: >
: >I recently played Modern Art with my friends. I was impressed by the
: >depth of the game and the difficulty of finding the right "moves".
: The "right" moves are probably more of a function of what a particular
: group's "group think" style of play for the game is. This is one of
: the things I like a lot about the game because, it forces you to adapt
: your tactics to the environment in order to win. As a result it would
: be difficult for the game to become "old" unless you play with the same
: players over and over again (and none of them change their play style).
Agreed. How the other players play makes a very big impact on what
the best things to do is (particularly in things like hidden bids).
: >My experience is so far quite limited. My impression is that we tend
: >to overestimate the value of the auctioned picture. As a result the
: >auctoneer gets the largest share of the profits. Since everyone in my
: >group did the same thing, the result was the same (I think).
: >Why should one pay $25 to another player and in the end sell the
: >picture for $30? His profit is $5 while the other guy gets $25. (Maybe
: >game theory would help here).
Well, listen, here's the deal. A person starts a once-around on
a painting which it seems very clear will in the end pay off $30. Basically,
here is what will happen. The last person to bid will (and should) basically
_always_ bid what the previous person bid+$1 assuming that number is still
under $30 (even if it were $29). Even in this worst case situation, he is
only giving $1 more to the bidder and is getting $1 profit for himself rather
than giving $2 profit to the person before him. Of course, usually numbers
aren't quite this high. Generally the price of a once-around will be
opening bidder's offer + (players-2) as each player ups the bid by 1 and the
player on the right buys it. Other bid types are similar. Of course, it
is usually not quite so clear what the painting will in the end pay off so
bids are more variable than this.
The single most obvious strategy tip is to play those paintings by
painters whose works you have already bought and thus you are both increasing
the value of your own paintings for sale at the end of the round and probably
making more money on the sale because you are playing an artist who has already
been played and will thus likely end up paying off. Given this, if possible
you usually (particularly at the beginning of a round) wish to buy the
painting offered by the player on your right (usually possible without paying
outrageous prices except for once-around auctions where you will almost never
get this painting) and then put up another painting by the same artist.
Finally, in terms of the bidding types: 1) Fixed-price sucks and are
usually best saved for ending a round - if actually offered for sale at a
reasonable price they will usually be bought by the player on your left - also
they are the most likely bidding type where you can get stuck buying your own
painting (which almost always is terrible based on the economics of the
game). 2) Once-arounds get you a reasonable amount of money and are almost
always bought by the player on your right - good lead particularly if the
player on your left is winning - once-arounds screw that person. 3) Hidden-bid
(closed-auction?) - Generally these get you less money than once-arounds. I,
however, find them to be very good paintings to lead to open a round. Often
there is one (or more) person who for some reason really wants to get this
painting as it will help there later strategy (perhaps they have a double by
the same artist) and who will thus pay quite a bit for the painting, even as
the first painting played to make certain they get it. 4) Open auction - How
much money you get for these really depends on group dynamics and who is in the
lead. If you are in the lead and the other players collude, you will usually
get very little (less than any other type probably). On the other hand, if you
are behind and two other players really want this item you can get very large
amounts - a good type to play with a Double generally. 5) Doubles - by far the
most important type and must be used very carefully as you only get a limited
number of them. Never play one to end a round unless you absolutely must.
Late in the game, very seriously consider playing a double without a match - if
nothing else this will basically skip the turn of the player on your left.
Generally don't use your doubles in the first round where there is less money
at stake. A good use of a double I would say should get you a minimum of $40
(and hopefully $60) and can sometimes get $100+. Doubles are of such
importance that if I get none in my opening hand I would say it cuts my chances
of winning by at least half and probably more.
: I won my first two games by buying no paintings. After the other players saw
I have never seen anyone win without buying anything. Late in the game, if
one is way in the lead, it is in fact a very reasonable strategy to buy
basically _everything_ to avoid anyone catching you.
: Nick Sauer
Aaron
aar...@bu.edu
http://www.bu.edu/~aarondf/ (the Last Homely House)
afor...@aol.com
In article <594gvb$2...@nntpa.cb.lucent.com>, n...@spin.att.com (Nicholas
Sauer) writes:
>>If anyone out there has come up with a good strategy I would be very
>>glad to hear about it. Any ideas? Any tips.
don't spend much money and see what happens.
Milton Soong
In article <596ja3$p...@news.bu.edu>, aar...@bu.edu (Aaron D. Fuegi) wrote:
> Nicholas Sauer (n...@spin.att.com) wrote:
>
[snip]
> Agreed. How the other players play makes a very big impact on what
> the best things to do is (particularly in things like hidden bids).
>
> : >My experience is so far quite limited. My impression is that we tend
> : >to overestimate the value of the auctioned picture. As a result the
> : >auctoneer gets the largest share of the profits. Since everyone in my
> : >group did the same thing, the result was the same (I think).
> : >Why should one pay $25 to another player and in the end sell the
> : >picture for $30? His profit is $5 while the other guy gets $25. (Maybe
> : >game theory would help here).
>
> Well, listen, here's the deal. A person starts a once-around on
> a painting which it seems very clear will in the end pay off $30. Basically,
> here is what will happen. The last person to bid will (and should) basically
> _always_ bid what the previous person bid+$1 assuming that number is still
> under $30 (even if it were $29). Even in this worst case situation, he is
> only giving $1 more to the bidder and is getting $1 profit for himself rather
> than giving $2 profit to the person before him. Of course, usually numbers
> aren't quite this high. Generally the price of a once-around will be
> opening bidder's offer + (players-2) as each player ups the bid by 1 and the
> player on the right buys it. Other bid types are similar. Of course, it
> is usually not quite so clear what the painting will in the end pay off so
> bids are more variable than this.
I see some flaw here. In Modern Art, one has to keep close attention who
has the most $$$. This requires very good memory (which I do not have),
but it's essential to playing the game at the highest level.
The reason I think there's a flaw in your resoning is that you think it's
better to "giving $1 more to the bidder" as oppose to "giving $2 profit to
the person before him". Now my thesis is that it's ok to give more to
another person if he is not currently LEADING, then it is to increase the
lead of another.
Another aspect of bidding is that whatever you bid, it gets paid to
ANOTHER player. One should NEVER pay $29 to another player a painting that
worth $30 for the simple reason that:
1) Nothing is quaranteed. I have seen an artist with 4 paintings showing,
No other artist on board, finishing 3rd.
2) If you pay $29 for a $30 painting, you make $1, the seller of the
painting makes $29. It's not a good trade (under most circumstances).
In Modern Art, there's always a danger of overpaying for something and let
someone else make more profit than yourself. One other consideration to
complicate the game is that it's OK to overpay someone else as long as the
RIGHT person is getting overpaid. It's OK to overpay someone that's behind
you in $$$ than it is to overpay someone that's winning. It's OK if you
make $10, and another makes $20, if YOU are getting closer to the ultimate
leader (or pulling your lead ahead). Once again this requires an awesome
memory, but since all transactions are open, it's not hard if you get the
grey stuff.
> The single most obvious strategy tip is to play those paintings by
> painters whose works you have already bought and thus you are both increasing
> the value of your own paintings for sale at the end of the round and probably
> making more money on the sale because you are playing an artist who has
already
> been played and will thus likely end up paying off. Given this, if possible
> you usually (particularly at the beginning of a round) wish to buy the
> painting offered by the player on your right (usually possible without paying
> outrageous prices except for once-around auctions where you will almost never
> get this painting) and then put up another painting by the same artist.
> Finally, in terms of the bidding types: 1) Fixed-price sucks and are
> usually best saved for ending a round - if actually offered for sale at a
> reasonable price they will usually be bought by the player on your left - also
> they are the most likely bidding type where you can get stuck buying your own
> painting (which almost always is terrible based on the economics of the
> game).
I disagree again. Buying your own painting could be the MOST beneficial
way to buy given the economics of the game, since you are paying into a
bank, not to another player. You can usually afford to pay more and
maintain the same adjusted profit margin (since you are not enriching
another) then it is to buy from someone else. For that reason, fix price
bid is a good thing. (the argument provided that the painting is from a
VERY desirable painter, otherwise I agree that it's not so hot to buy your
own painting).
One other use for selling fix price is right after an over-valued open bid
has just happened for the same artist, you can usually sell (at fix price)
the same artist for slightly less, and get away with it.
[snip]
--
-------------------------------------------------------------
Milton Soong
so...@apple.com
Nicholas Hills
A few tips for Modern Art:
1. Don't buy your own art.
As auctioneer, you should normally try to avoid buying your own
paintings, but instead collect money from another purchaser.
Exception: Be prepared to bid 1/2 as much as an auctioneer for a
painting as you would as an ordinary bidder. This keeps other players
honest and stops them making easy profits.
2. Be prepared to bid high.
As a bidder, I'm prepared to bid up to 75% of what I think a painting is
likely to be worth. Sure, that means the Auctioner gets a certain large
profit, and I get a risk smaller profit. But particularly in a five
player game, I'm less concerned about what the auctioneer gets. I want
to make a large number of small profits, and prevent other players doing
the same.
Example: I pay $60 for a painting that ends up being worth $80. Sure,
the auctioneer makes $60 and I only net $20. Put that's better than the
auctioneer only getting $59 and another of my rivals making $21.
3. The player to the left of the auctioneer has a good idea of likely
values.
The player to the left of the auctioneer is the next to be auctioneer.
You know what art will be played next. If you have a double auction
card + one other by the same artist you know the current card is likely
to be quite valuable. If you are void in that artist and intend playing
something else, the current card is worth much less to you.
Great game! I've still got a lot to learn. Any more tips out there?
Nich
Graham Wills
Aaron D. Fuegi wrote:
[A good starting point for a discussion - I agree with a lot of it, but
there are some differences I have noticed. So anything I snip, I agreed
with]
> Agreed. How the other players play makes a very big impact on what
> the best things to do is (particularly in things like hidden bids).
Certainly. And I wonder if people's tactics and understanding of the
game are very dependent on their usual players. It certainly seems so
since ...
> Well, listen, here's the deal. A person starts a once-around on
> a painting which it seems very clear will in the end pay off $30. Basically,
> here is what will happen. The last person to bid will (and should) basically
> _always_ bid what the previous person bid+$1 assuming that number is still
> under $30 (even if it were $29).
This has never happened with my players. If the auctioneer is not in the
lead, the first bid will quite often be $29. If the auctioneer is in the
lead, we might keep it lower - say $20.
> Even in this worst case situation, he is
> only giving $1 more to the bidder and is getting $1 profit for himself rather
> than giving $2 profit to the person before him. Of course, usually numbers
> aren't quite this high. Generally the price of a once-around will be
> opening bidder's offer + (players-2) as each player ups the bid by 1 and the
> player on the right buys it.
But the first player knows that other players willover-bid him and
therefore it's a lousy strategy. Once-around bids in our games are
*quite* different. If you're in the lead (or close to it) you should
*always* bid close to 30 to stop others profiting.
Let's look at a simple situation. I'm in the lead, the rest are equally
far behind and we're doing nothing but $30K paintings (unrealistic, but
it models the probabilities more understandably than using them). If I
offer a painting for any auction, the *worst* I can make is half the
eventual value. So I will have $15 from that. If I bid $(30-X) for each
other painting and buy them all, then I will make 4X (5 player game) for
a total profit of 15 + 4X. Everyone else makes 30-X. So, to stay as far
ahead as I am, 15 + 4X = 30 - X, leaving X=3. I should bid $27 for a $30
painting at least.
If they are completely conspiring against me, then it makes no
difference what I bid. They will always bid $30 (or in fact a *higher*
number value - it makes no difference). In the long run, each auctioneer
makes $30 and each buyer makes nothing. It's better for them than
letting me bid $29, since then each auctioneer makes only $29 and I make
$1, giving me a $2 better deal.
Moral: make sure someone else is obviously doing well, even if you're
actually winning.
> Other bid types are similar. Of course, it
> is usually not quite so clear what the painting will in the end pay off so
> bids are more variable than this.
Ay, there's the rub.
> The single most obvious strategy tip is to play those paintings by
> painters whose works you have already bought and thus you are both increasing
> the value of your own paintings for sale at the end of the round and probably
> making more money on the sale because you are playing an artist who has already
> been played and will thus likely end up paying off. Given this, if possible
> you usually (particularly at the beginning of a round) wish to buy the
> painting offered by the player on your right (usually possible without paying
> outrageous prices except for once-around auctions where you will almost never
> get this painting) and then put up another painting by the same artist.
A common way to make a huge killing is if you have a double of an artist
who has one painting already sold and and the player to your right
auctions that artist. Bid high for this card and then auction your
doubled card. Voila, the card you bought is valuable and the cards you
are auctioneing ill make money. If it's Lite Metal, it guarantees he'll
come in at number one!
This brings up a sub-strategy. If you have a double, keep it as late as
possible and keep it with another card by that artist. If it's a high
ranked artist such as good old LM, you will have a late game bonanza. As
an example, a player did exactly that with a LM in the penultimate
round, with Lite already valued at $60 (thereby guaranteeing he'd be
$90). The auctioneer brought ina coll $170!
> Finally, in terms of the bidding types: 1) Fixed-price sucks and are
> usually best saved for ending a round - if actually offered for sale at a
> reasonable price they will usually be bought by the player on your left - also
> they are the most likely bidding type where you can get stuck buying your own
> painting (which almost always is terrible based on the economics of the
> game).
But there is an advantage to this auction type; it is the ONLY auction
where you can stop someone (except the right-hand player) from getting
the card. Great if they're in the lead. Also, when the price of a card
is known, all auction types will bring in the same optimal bid, so the
type of auction is pretty irrelevant.
> 3) Hidden-bid
> (closed-auction?) - Generally these get you less money than once-arounds. I,
> however, find them to be very good paintings to lead to open a round. Often
> there is one (or more) person who for some reason really wants to get this
> painting as it will help there later strategy (perhaps they have a double by
> the same artist) and who will thus pay quite a bit for the painting, even as
> the first painting played to make certain they get it.
Novices qute often wildly overbid on closed auctions. Definitely agree
with them for an early auction type, for the same reasons.
> 4) Open auction - How
> much money you get for these really depends on group dynamics and who is in the
> lead. If you are in the lead and the other players collude, you will usually
> get very little (less than any other type probably). On the other hand, if you
> are behind and two other players really want this item you can get very large
> amounts - a good type to play with a Double generally.
Yes.
> 5) Doubles - by far the
> most important type and must be used very carefully as you only get a limited
> number of them. Never play one to end a round unless you absolutely must.
> Late in the game, very seriously consider playing a double without a match - if
> nothing else this will basically skip the turn of the player on your left.
> Generally don't use your doubles in the first round where there is less money
> at stake. A good use of a double I would say should get you a minimum of $40
> (and hopefully $60) and can sometimes get $100+. Doubles are of such
> importance that if I get none in my opening hand I would say it cuts my chances
> of winning by at least half and probably more.
I think doubles are the most important factor in winning a game. In
general auctioneers make more money than buyers, and it basically
doubles the number of auctions you can do. Keep it till the optimal
moment.
> : I won my first two games by buying no paintings. After the other players saw
>
> I have never seen anyone win without buying anything. Late in the game, if
> one is way in the lead, it is in fact a very reasonable strategy to buy
> basically _everything_ to avoid anyone catching you.
I have seen people come very close. Our group tends to buy very close to
the actual value, so that bidding is a marginal profit-making device. In
our group, auctioning strategy is by far the most importnant.
-Graham
--
Graham Wills Data Visualization group, Lucent
Technologies
gwi...@research.bell-labs.com Bell Laboratories, Indian Hill,
Naperville IL
Jay at MG
Graham wrote:
>>Bid high for this card and then auction your doubled card. >>Voila, the
card you bought is valuable and the cards you
>>are auctioneing ill make money. If it's Lite Metal, it >>guarantees
he'll come in at number one!
It is a minor, but important point that you cannot guarantee a LM first by
doing this is only four paintings and it takes five offered for auction to
win; it will, of course, guarantee no worse than second, but another
artist may still get first with five offered for auction.
Jay
Aaron D. Fuegi
Milton Soong (milton...@quickmail.apple.com) wrote:
: In article <596ja3$p...@news.bu.edu>, aar...@bu.edu (Aaron D. Fuegi) wrote:
: > Well, listen, here's the deal. A person starts a once-around on
: > a painting which it seems very clear will in the end pay off $30. Basically,
: > here is what will happen. The last person to bid will (and should) basically
: > _always_ bid what the previous person bid+$1 assuming that number is still
: > under $30 (even if it were $29). Even in this worst case situation, he is
: > only giving $1 more to the bidder and is getting $1 profit for himself rather
: > than giving $2 profit to the person before him. Of course, usually numbers
: I see some flaw here. In Modern Art, one has to keep close attention who
: has the most $$$. This requires very good memory (which I do not have),
: but it's essential to playing the game at the highest level.
: The reason I think there's a flaw in your resoning is that you think it's
: better to "giving $1 more to the bidder" as oppose to "giving $2 profit to
: the person before him". Now my thesis is that it's ok to give more to
: another person if he is not currently LEADING, then it is to increase the
: lead of another.
: Another aspect of bidding is that whatever you bid, it gets paid to
: ANOTHER player. One should NEVER pay $29 to another player a painting that
: worth $30 for the simple reason that:
: 1) Nothing is quaranteed. I have seen an artist with 4 paintings showing,
: No other artist on board, finishing 3rd.
: 2) If you pay $29 for a $30 painting, you make $1, the seller of the
: painting makes $29. It's not a good trade (under most circumstances).
: In Modern Art, there's always a danger of overpaying for something and let
: someone else make more profit than yourself. One other consideration to
: complicate the game is that it's OK to overpay someone else as long as the
: RIGHT person is getting overpaid. It's OK to overpay someone that's behind
: you in $$$ than it is to overpay someone that's winning. It's OK if you
: make $10, and another makes $20, if YOU are getting closer to the ultimate
: leader (or pulling your lead ahead). Once again this requires an awesome
: memory, but since all transactions are open, it's not hard if you get the
: grey stuff.
Well, read the next followup post where Graham indicates that in
his group they almost always go directly to $29 on the first bid of a once-
around. I think this a bit extreme but it makes more sense to me than how
your group apparently plays. Basically, with Graham's method the auctionneer
has the big advantage and with yours there is a reasonable split between the
auctionneer and buyer. Imho, your method should naturally turn into his
method or close to it as each person wishes to get the buyer's percentage
of the profit (no matter how small).
: I disagree again. Buying your own painting could be the MOST beneficial
: way to buy given the economics of the game, since you are paying into a
: bank, not to another player. You can usually afford to pay more and
: maintain the same adjusted profit margin (since you are not enriching
: another) then it is to buy from someone else. For that reason, fix price
I don't think this makes any economic sense unless your bids in your
group are absurdly low. Let us say I am selling a painting that will
eventually sell for $30 in an open auction (auction type here really isn't that
important to the economics). Players will always bid at least $15 as otherwise
I could bid $15 and get a $15 profit. Since I, as seller, can always get the
$15 profit the other players clearly wish to bid $15 so that both that player
and I get a $15 profit. However, the bid should never stay this low as the
other players will be saying to themselves: "I can bid $16, give $1extra to the
auctionneer and get $14 profit for myself." I could never see a painting go
for less than $16 and that only if the auctionneer was way in the lead and the
other players were colluding against him. Even with this totally minimal bid
of $16, though, I as auctionneer should take it ($16 profit vs (30-(16+1)=13)
$13 profit) unless the current buyer is in the lead (and this should never be
the case because if it were the other players should go way above $16 to like
$25 or even $29 before letting the leader buy it if they ever do). The
auctioneer should almost always remove himself from the auction the moment the
bid is at EXPECTED_VALUE/2.
: bid is a good thing. (the argument provided that the painting is from a
: VERY desirable painter, otherwise I agree that it's not so hot to buy your
: own painting).
: One other use for selling fix price is right after an over-valued open bid
: has just happened for the same artist, you can usually sell (at fix price)
: the same artist for slightly less, and get away with it.
: Milton Soong
: so...@apple.com
Milton Soong
In article <59mkgu$4...@news.bu.edu>, aar...@bu.edu (Aaron D. Fuegi) wrote:
> Milton Soong (milton...@quickmail.apple.com) wrote:
[snip]
I can see how the difference in group dynamics can cause different optimal
strategy. In our group(s), if a player wins the game by pursuing a sell
stragety, because everybody is paying him $29 for a $30 painting (to use
your example here), believe me, bids will be lower all around the next
game.
In most of our games, our philosophy is that "if A gets a big win by
selling high, we'll make sure we don't pay high next time". I guess in
another game group, the thinking would be "if A wins with a sell high
strategy, I want to sell high also".
I guess if everyone in the game is selling high, a player is not going to
win by buying low. I see that now. It's amazing that Modern Art's optimal
strategy is play-group dependent!
One thing I do disagree with you though is your last statement. I don't
see my scheme turn into his method unless there are some fundamental shift
in playgroup dynamics.
[snip]
>
> I don't think this makes any economic sense unless your bids in your
> group are absurdly low. Let us say I am selling a painting that will
> eventually sell for $30 in an open auction (auction type here really
isn't that
> important to the economics). Players will always bid at least $15 as
otherwise
> I could bid $15 and get a $15 profit. Since I, as seller, can always get the
> $15 profit the other players clearly wish to bid $15 so that both that player
> and I get a $15 profit. However, the bid should never stay this low as the
> other players will be saying to themselves: "I can bid $16, give $1extra
to the
> auctionneer and get $14 profit for myself." I could never see a painting go
> for less than $16 and that only if the auctionneer was way in the lead and the
> other players were colluding against him. Even with this totally minimal bid
> of $16, though, I as auctionneer should take it ($16 profit vs (30-(16+1)=13)
> $13 profit) unless the current buyer is in the lead (and this should never be
> the case because if it were the other players should go way above $16 to like
> $25 or even $29 before letting the leader buy it if they ever do). The
> auctioneer should almost always remove himself from the auction the moment the
> bid is at EXPECTED_VALUE/2.
>
I still disagree with your analysis. When a bidder pays $15 for a $30
painting, the seller makes $15, and the buyer gets $15. If the seller is
currently in the lead, the buyer did NOT pull closer to the game leader
(we are ignoring the distribution of winning paintings, and other more
intangible factors here). If the buyer pays $16 to buy a $30 painting from
the current game leader, the seller just pulled himself $2 further AWAY
from the lead. Whenever a buys pays over EXPECTED_VALUE/2 to buy a
painting, one has to be extremely careful not to pay to the current winner
(or others in front of you), as this will increase their lead over you.
To get back to the buying your own painting discussion, with the above
point in mind, I contend that it's ok if the seller pays over
EXPECTED_VALUE/2 for his own painting as long as the seller is ensuring
that his lead in the game increases (or gets closer to the current
leader). Thus if I am leading, it's OK for me to sell at EXPECTED_VALUE/2
to the 5th place player, because if both 1st place (me) and 5th place
player moves ahead, it just put me that much further ahead of the 2nd
place player. But I don't want to sell the same way to the current 2nd
place guy, I don't want the $$ difference between myself and 2nd place to
be unchanged, or worse, decreased. In this case it's better for me to buy
my own painting, even at a profit of < EXPECTED_VALUE/2, since that'll
increase my lead over the 2nd place guy.
I still contend that the MOST important facet of the game is the ability
to keep track EXACTLY how much $$$ each person have. If you can do that,
then no matter how you play (sell high or buy low), as long as you make
sure that every buy/sell you make will put you ahead RELATIVELY to all
other players, you'll do OK. Now all I have to do is get a brain that can
actually remember details to that degree... :-)