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Subject: Groupthink, auction values, and the taxation track rss

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George Heintzelman
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Disclaimer first: I've only actually played this game twice at this point, though I expect and hope to play more. I'm an over-analyzing sort, though, so I've been thinking a lot about the auction dynamics, spurred on by the articles by alexfrog and jimc. Okay, on with the show.

My first assertion is simply that Goa auctions are highly susceptible to groupthink, and that that groupthink tends to drive prices down. This is mainly because of two things: 1) the link back between a ducat in hand and victory points is very tenuous, other than through the auction iself, and 2) you can't go into debt. To demonstrate this, consider the following game: Everyone starts with 10 dollars. We then bid on N lots of 1 victory point, with the auctioneer getting the money (or paying the bank) as in Goa. But, there's no source of money. Suppose in this game everyone has decided that they are not going to spend more than 5 on a VP (the exact number affects the details but not the broad picture of the example). Now, one player who is willing to bid 6 will wind up winning early auctions, but running out of money and unable to bid more, since he still is paid only 5 for each of his VPs, and eventually will wind up winning fewer VPs than everyone else (as long as there are enough auctions, of course). This is groupthink making an overbidder pay, and it doesn't matter for this analysis what value the group has set for a VP. On the other hand, a single underbidder will accumulate cash but no victory points, until he drives prices down, since the others can no longer pay their desired prices. This takes longer, however, and for small N may not be noticeable except that the underbidder will lose... (Incidentally, in this game it should be possible to calculate a fair price for a victory point assuming everyone is rational and knowing N. What my example shows is simply that an irrational equilibrium can still be stable in these Goa-style auctions.)

The conclusion here is that, based on the auctions alone, groupthink is extremely important in Goa. Someone who overbids the group will run out of money, with his expenses exceeding his income, and will be unable to buy everything. If the game is long enough, someone who underbids the group slightly can end up winning more auctions cheaper eventually, and/or win the 3 VPs at the end of the game, without paying a large price in missed tiles. So, from the auction dynamics there is pressure to underbid.

As others have pointed out, however, there is also pressure to overbid in Goa. This comes from the inflationary tendencies in the game (correctly pointed out by Alex), and from the growth model of the game, where your actions will be more efficient earlier if you have tiles now. (Although the fact that the B tiles are better than the A tiles mitigates this to some extent). But, I think that after things have gotten started for a player, this effect is minimal. You need some spice capacity early to get yourself going, but after you have that, using your tiles to improve your actions isn't a big effect. (Winning the same number of tiles *eventually* is still important, of course, and is the major effect, since most tiles are worth somewhere between 1 and 2 actions. But most tiles don't improve the quality of a current action very much.)

How the balance between these two effects 'should' work in a game of experts isn't clear to me. However, I'm pretty sure that both of these effects are relatively small compared to the competitive disadvantage a player puts himself at by ignoring the groupthink, and overbidding consistently... if one considers only the auctions. So, we get to the only major tie between victory points, by way of their fairly strong proxy, actions, and money -- the taxation track. If a player is overbidding the others consistently, he will be short of money, and will need to use the taxation track, spending some actions so that he can replenish his net outflow of ducats and buy more than his share of tiles. Of course, this contributes to inflation, making his early overbidding more profitable (as others' stores of ducats lose value). But the real point is that the scale for how much 1 action is worth and thus how much tiles are worth, in ducats, is set by the use of the taxation track (plus some contribution from how much the spice-sale and 5-ducat expedition cards cost to use, and how advantageous the upgrade-for-money cards are versus the spices/ships).

So my final conclusion is that the taxation track and taxation actions cannot be intrinsically underpowered. That scale is exactly what sets the prices for tiles in the auctions. However, taxation will be good or bad depending entirely on the groupthink. If you are in a group where the groupthink is for too low auction values, your best course of action is to maximize your taxation track and buy as many tiles as possible from the underbidders. If your groupthink is for too high auction values, you should underbid slightly, win tiles cheaply when your seat is favorable, make bids that encourage others to win their own tiles, and collect auction income from the other players, ignoring the taxation track. The other players will be forced to spend actions to tax, or you will win tiles cheaply starting in round 3 or 4 or so. If, on the other hand, the group is getting it right, you should be using the taxation action occasionally, when you are low on ducats, so that inflation harms others more than you; and preferably before others do, so that your income from taxation is worth more. Thus improving the taxation track should be of a power commensurate with the other tracks, and increases in power more the less others use theirs.

I suspect that in any group where taxation is not used at all, the groupthink is for overbidding. The converse should also be true, but winning versus overbidders is trickier to implement correctly than winning versus underbidders, so it may be less obvious and thus encourage groupthink in the overbidding direction.

In any case, I hope this stirs the pot and generates some more discussion on how prices really should get set in a game of Goa.
 
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Togu Oppusunggu
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Re:Groupthink, auction values, and the taxation track
Excellent analysis, George. This should help refine our thinking about the taxation track, which has been a bit of a mystery. I think there's a BGG article on group think in Modern Art also, which has some similar auction mechanisms.
 
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James Stuart
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Re:Groupthink, auction values, and the taxation track
I think the critical flaw in this article is that the tiles aren't valuable. It's true that only so many plantations are necessary, but that misses the point. There are plenty of tiles which are pure actions (the flag, which is 1 action + the benefit of setting the pace for the next auction; the 2 action token, the expedition cards, and so on), and the other tiles let you fill holes in your strategy. If I'm playing a standard expedition/harvest strategy, I'm going to need some supply of colonists and ships. If I pick up three ships via a tile, that has most likely saved me at least an action and change, if not more, depending on how undeveloped it is.

With only likely one move on the colonist track, I'm going to need more colonists to even have a shot of founding the 10 and 12's: I either find those colonists in my development cards, or I buy them on the auction track. A large part of the game is figuring out when tiles are valuable to a person, and using the flag, controlling whether or not they receive them.

In a non two-player game, this is the great weakness of the taxation track: you use an action, and it gives you a temporary advantage in the next auction, but in a four-player game, it is extraordinarily difficult to exert any meaningful control over the money supply: money gets distributed very quickly, and you almost never find yourself in a position where every other player cannot contest (which is the opposite of the two-player game, where gaining meaningful control over the money supply is very easy and profitable).

The difference between Modern Art is easy to articulate: in Modern Art, any inefficiency you take advantage of gains you victory points, and after some minor pressure in the first season, it's unlikely that players will be hindred by their money supply. In Goa, money advantages only turn directly into victory points on the last turn, and the market is constantly rebalancing to erase advantages.



 
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Arthur Field
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Re:Groupthink, auction values, and the taxation track
anonystu (#46239),

An interesting solution to the inflation problem is for the rich guy to always buy his own tiles and take money out of the game. This actually works pretty well, especially if he has the $4 red tile and can refill before the next auction.

A
 
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George Heintzelman
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Re:Groupthink, auction values, and the taxation track
anonystu wrote:
I think the critical flaw in this article is that the tiles aren't valuable. It's true that only so many plantations are necessary, but that misses the point. [...]


I should clarify, because this is a crucial point for understanding where my article is coming from. The tiles are , unquestionably, valuable -- the value that I quoted above is about what anonystu says, somewhere between 1 and 2 actions for most of the tiles. Winning more tiles than the other players is very important towards winning the game. What I don't think is very valuable is winning the tiles now rather than later (so long as you have useful things you can do with the actions you get in the meantime). There is some value to knowing what holes are being filled, of course, and having a minimum spice capacity early is important, but most of your actions will not be greatly enhanced by having a tile before you do them as opposed to after you do them.

This being largely true is the only thing that can allow an underbidder to prosper, and of course it isn't completely true; but I think it is true enough to allow judicious underbidding to survive in the right groupthink environment.

Interestingly, though, to the extent that it is not true, it increases a player's desire to spend all his cash buying tiles, and be broke starting the turn -- meaning he's more interested in carrying out taxation to inflate away the money supply of his competition! I think that in practice there's a balance, and that the balance should result in some (though not overwhelming) use of the taxation track by some players.
 
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Jim Campbell
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Re:Groupthink, auction values, and the taxation track
threlicus wrote:
The conclusion here is that, based on the auctions alone, groupthink is extremely important in Goa. Someone who overbids the group will run out of money, with his expenses exceeding his income, and will be unable to buy everything. If the game is long enough, someone who underbids the group slightly can end up winning more auctions cheaper eventually, and/or win the 3 VPs at the end of the game, without paying a large price in missed tiles. So, from the auction dynamics there is pressure to underbid.


Your model isn't much like Goa at all, which leads to a conclusion that doesn't apply well to Goa. In Goa, failing to buy a tile on turn 1 tends to be a big setback rather than merely an incremental deficit of 1 VP. This is because the game has a time limit that places a ceiling on one's maximum score. The less progress is made toward that maximum on turn 1, the lower that ceiling drops. It's hard to use all three actions effectively on turn 1 without buying a tile, and wasting an action then effectively reduces the number of turn 8 actions by 1. Marginal actions on turn 8 tend to be worth 2-4 points each.

In addition, players can and do raise money during and between the auctions. Players who choose to bid 10% more than the group can, in fact, sustain that effort for the whole game. The extra tiles are more than enough to make up for the actions they will sometimes spend on taxation.

So my final conclusion is that the taxation track and taxation actions cannot be intrinsically underpowered.

Indeed, the power of the taxation track is dynamic and will increase if the other players are consistently underbidding the tiles.

Thus improving the taxation track should be of a power commensurate with the other tracks, and increases in power more the less others use theirs.

I disagree, and think the the design goal for the taxation track was to make it (a) strong enough to allow a solo defector to raise enough cash to defeat underbidders and (b) weak enough that no matter how much it had been upgraded it would not provide a consistently good alternative to buying tiles (i.e. wait-and-tax should be a losing strategy, which it is). I think the track as designed provides just that sort of medium, and thus in a game full of willing defectors will strongly tend to be the least useful track. A group of skilled players will upgrade and use that track less than any other, and that was the intention of the designer.

Thanks for your observations,

Jim
 
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Jim Campbell
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Re:Groupthink, auction values, and the taxation track
ArthurF wrote:
An interesting solution to the inflation problem is for the rich guy to always buy his own tiles and take money out of the game.


I'd rather take the incoming bid and be the rich guy for an extended period of time than end my reign prematurely by buying my own tiles.

Jim
 
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Jim Campbell
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Re:Groupthink, auction values, and the taxation track
Winning more tiles than the other players is very important towards winning the game. What I don't think is very valuable is winning the tiles now rather than later (so long as you have useful things you can do with the actions you get in the meantime).

Early in the game, it's enormously valuable to win them sooner rather than later. Actions are woefully ineffective without buying tiles early in the game, and each wasted action in the early game is effectively one less action in turn 8. Actions in turn 8 tend to score 2-4 points each.

Later in the game, tiles offer a way to buy time (actions). The reason buying one immediately is better late in the game is simply because that tile isn't being sold later. Each player has a somewhat narrower range of methods they can use to buy time, and they must buy it immediately or not at all.

Waiting and refusing to buy doesn't work well in Goa, for a variety of reasons including the limited number of turns and currency inflation. A solo underbidder is unwittingly choosing to wait forever without starting to score points in large numbers.

Jim
 
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George Heintzelman
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Re:Groupthink, auction values, and the taxation track
jimc (#46272),

I agree that in rounds 1 and 2 you really need to get a couple tiles, to get yourself up and running. Now, maybe it is my inexperience showing, but my strong impression is that once you're over that first hurdle and have space for a few kinds of spice, the synergy between tiles and actions is rather small.

Later in the game, tiles offer a way to buy time (actions). The reason buying one immediately is better late in the game is simply because that tile isn't being sold later. Each player has a somewhat narrower range of methods they can use to buy time, and they must buy it immediately or not at all.

Huh? That particular tile may not be sold later, but a different one certainly will be. It's true that if a particular tile will do stuff for you that nothing else will do, you have to pay for it, and pay for it now. But I think that is rare. My impression is that, in mid-game (up to say the last 2 rounds), most players can make good use of just about any tile, though of course some are worth more to certain players than others.

Waiting and refusing to buy doesn't work well in Goa, for a variety of reasons including the limited number of turns and currency inflation. A solo underbidder is unwittingly choosing to wait forever without starting to score points in large numbers.

If this is true, is it possible in your opinion to solo combat a groupthink of overbidders? If not, then they must not be overbidders, right? Then any price is okay as long as that's what the group thinks. That reductio ad absurdum is what led me down this path towards thinking about how to correctly defect on the low side; and the conclusion that ultimately it is the taxation track that determines at what pricing level it might be favorable to do so. (Note, this is not because the underbidder uses the track! He emphatically does not, because he has cash and others will not. It is because the other players will have to use the track to try to prove that the underbidder is an underbidder.) As I say, I think carrying this out is rather more challenging than combatting underbidder groupthink, for many of the reasons you point out; but I hope it does not prove to be impossible in the long run, or my opinion of Goa will drop.
 
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Jim Campbell
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Re:Groupthink, auction values, and the taxation track
threlicus wrote:
I agree that in rounds 1 and 2 you really need to get a couple tiles, to get yourself up and running. Now, maybe it is my inexperience showing, but my strong impression is that once you're over that first hurdle and have space for a few kinds of spice, the synergy between tiles and actions is rather small.


It's not really synergy that motivates my tile purchases, but incremental advantage. If I buy a double nutmeg plantation on turn 1, one approach is to upgrade the expedition card track twice and then assume that I will reload the plantation using harvests whenever I need nutmeg. But the game offers another approach in which I simply buy the nutmeg I need in the auction market. By doing that I convert money into one or more actions just as if I had purchased the flag, but with the advantage that not all players will actively desire a triple nutmeg plantation in the way they would want the flag. Each time I replace an ordinary action (such as a harvest) with a tile, that's one additional marginal scoring action I will take on turn 8. If the bottleneck in my process of upgrading the card track to level 5 is the 3 nutmeg, then buying those in the auction rather than using a harvest action can effectively increase my score by 2-4 points by freeing that action for some other scoring move.

To put it another way, I not only plan to avoid taxation, but also to avoid the ship and harvest actions as much as possible. Preferably, I never tax, make ships 2 or 3 times and harvest spice once or perhaps twice. The game isn't long enough to score efficiently while actually running the whole ship action/spice action/upgrade action(s) cycle; that only results in maybe 50% of actions scoring points in the second half of the game. The tiles and expediiton cards can be used to circumvent the need to operate that system.

If this is true, is it possible in your opinion to solo combat a groupthink of overbidders? If not, then they must not be overbidders, right?

I haven't been using the term "overbidders" because I don't think that they actually exist. First, a brief explanation of what I think is happening in the Goa auction. There is a seller who makes a profit no matter what the other players do, and buyers who bid for the right to take part in the profit along with the seller. Players who are willing to pay a higher percentage of the estimated value of the items will end up buying more of them those who aren't, because they don't really run out of money (everyone is almost guaranteed to make income when they sell, and there are some other ways to gain cash). With this in mind, I'll define some terms:

1. Underbidder: Player that consistently bids lower than what rational opponents should be willing to pay (for example, opens bidding on the turn 1 flag at 4 ducats or opens bidding on a double-nutmeg plantation on turn 1 at 7). This strategy is sustainable inefinitely due to its low cost, but is easily defeated by players who are willing to pay more.

2. Overbidder: Player that consistently bids more than what rational opponents should be willing to pay. This isn't actually a sustainable strategy, since it doesn't take long to run out of money to an extent that fundraising can't fix. Since it isn't sustainable, this type of player doesn't really exist.

3. Rational bidder: Player that consistently tries to bid just high enough to get the items they want. Against an all-underbidder group, this means figuring out their irrational bid level and bidding about 20% higher until their bidding style changes. Against other rational bidders, this means estimating what they will be willing to pay and then trying to "steal" that bid before they can say it. As an example, a rational bidder on the flag auctioneer's left would bid 6 or 7 on the flag on turn 1. If the 2nd item in the turn 1 auction was a double nutmeg, a rational bidder would probably open the bidding at 10.

Overbidders lose because their strategy can't make good cashflow for any real length of time. In a group of underbidders a rational bidder will run away with the game, all else being equal. In a mixed group the underbidders are at a disadvantage to the rational bidders. In a group of rational bidders choosing to defect and start underbidding is a losing strategy.

...how to correctly defect on the low side; and the conclusion that ultimately it is the taxation track that determines at what pricing level it might be favorable to do so. (Note, this is not because the underbidder uses the track! He emphatically does not, because he has cash and others will not. It is because the other players will have to use the track to try to prove that the underbidder is an underbidder.)

Your conclusion that defecting and underbidding will result in one's having cash while others don't is mistaken. The underbidder doesn't get to sell five times in each auction, so for the most part everyone else just hands their money to each other. The underbidder will tend to have a cash advantage, but it won't be large enough to offset the disadvantage of failing to buy tiles. The other players can sustain their bidding strategy on the cash they make by selling tiles, ducats from expedition cards and (perhaps) a taxation action every 3 turns or so.

As I say, I think carrying this out is rather more challenging than combatting underbidder groupthink, for many of the reasons you point out; but I hope it does not prove to be impossible in the long run, or my opinion of Goa will drop.

Goa is not a game that offers 7 different ways to gain resources, each of which exists in perfect balance with every other. There is no viable "no-tile" strategy or "taxation" strategy, because the tiles are very strong and the taxation track is very weak (if the other players have any idea how to evaluate the tiles). Certain aspects of the game are much stronger than others, and that's the intention of the design. I like the game, have enjoyed playing and studying it, and don't consider it a flaw that not all parts of it are balanced in strength.

Jim
 
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Eric Brosius
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Re:Groupthink, auction values, and the taxation track
jimc (#46543),

You say

2. Overbidder: Player that consistently bids more than what rational opponents should be willing to pay. This isn't actually a sustainable strategy, since it doesn't take long to run out of money to an extent that fundraising can't fix. Since it isn't sustainable, this type of player doesn't really exist.

If all your opponents are bidding more than what rational opponents should be willing to pay, then for the most part they are paying each other. This means they are supporting each others' overbidding and it will take longer for any of them to run out of cash.

In this case, do you need to bid more yourself, or is there some alternative approach to use in order to exploit your opponents' "overbidding"?
 
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Jim Campbell
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Re:Groupthink, auction values, and the taxation track
Eric Brosius (#46585),

That's a good point. In a group of overbidders, they won't run out of cash as quickly; what does tend to happen is that they will typically buy 1 tile per round instead of 2. So the pressure to abandon overbidding might come from competitive pressure rather than cashflow problems when several players are overbidding. By not spending all or nearly all their cash on a single purchase, rational bidders can defeat overbidders by bidding somewhat less and having enough cash to bid at that level twice. Note that the rational bidder gets a large payment whenever they sell, while the others may get a winning payment from an overbidder or a lesser amount from the rational bidder. There is thus a progressive draining of cash from the overbidders to the rational bidder in that situation.

So far I'm not dissuaded from my conclusion that rational bidders tend, due to the structure of the game, drag underbidders and overbidders closer to the rational bid level. Underbidders get dragged there because of currency inflation combined with not getting any tiles, while overbidders get dragged there because of cash flow problems combined with not getting as many tiles as the rational bidding strategy can provide.

Jim
 
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George Heintzelman
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Re:Groupthink, auction values, and the taxation track
jimc wrote:
Note that the rational bidder gets a large payment whenever they sell, while the others may get a winning payment from an overbidder or a lesser amount from the rational bidder. There is thus a progressive draining of cash from the overbidders to the rational bidder in that situation.


This is precisely what I've been trying to say, although I've been rather long-winded and roundabout getting to it.

My final point is that whether the lower bidder in a group of overbidders is in fact being a rational bidder, or an underbidder, at a given price point, is determined by the per-action income available in the game, i.e. the taxation track (plus a contribution from expedition cards/spice sales), balanced against the value (in actions, roughly) of the tiles being bought. That means that if the high-bidding competition isn't developing the taxation track to at least have the possibility of taxing, the price level at which an underbidder becomes a rational bidder is lower.

Incidentally, I agree that there is a rational bidding level, although I can't say that I know what it is. But I think that the taxation track is crucial in determining what that bidding level is; and if the taxation track is not being used (or at a minimum threatened to be used) at all, that that rational level is not being found.
 
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Jim Campbell
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Re:Groupthink, auction values, and the taxation track
threlicus wrote:
My final point is that whether the lower bidder in a group of overbidders is in fact being a rational bidder, or an underbidder, at a given price point, is determined by the per-action income available in the game...


I agree with this, the money supply does indeed determine the overall price levels people pay for items.

That means that if the high-bidding competition isn't developing the taxation track to at least have the possibility of taxing, the price level at which an underbidder becomes a rational bidder is lower.

I disagree with this. If most or all players are bidding rationally, then income from tile sales is quite large; it's enough to sustain a consistent bidding strategy while completely ignoring the taxation track. Generally, it will be helpful to get the occasional 5-ducat card or whatnot, but taxation can be completely avoided. A single player who is consistently bidding lower than a group of rational bidders will tend to have more cash than they will, but not by a wide margin. Any shortfall the others face can be remedied with expedition cards or a very occasional 4-ducat taxation action. That taxation is infrequent enough that upgrading the track is still much less productive than the other options for those players.

Another thing that happens in such a game is that the lower-bidding player's strategic position erodes from buying few (or no) tiles, while they simultaneously accumulate a cash hoard. Inevitably, they must then make a high bid for a critical tile just to have a chance of winning; that purchase helps to replenish the cash supply of the higher-bidding opponents.

But I think that the taxation track is crucial in determining what that bidding level is; and if the taxation track is not being used (or at a minimum threatened to be used) at all, that that rational level is not being found.


The comparative aspect of the taxation track, i.e. that an action is always worth at least 4 ducats, has some role in determining the value of the tiles. Even at the beginning of the game there are far stronger actions one can take besides taxation. Upgrading the taxation track doesn't really change that because those resources could have just as easily gone toward upgrading a more effective track, such as the colonization or expedition card tracks.

The situation in which the taxation track can be used repeatedly to strong effect is when all players but one are undervaluing the tiles. In that case, the most efficiently profitable aspect of the game is certainly the tiles, so ducat income is far more important than it usually is. If the players are mostly or all rational bidders, the taxation track is not an important basis for determining tile value, because taxation is so ineffective that it can't be taken seriously as an alternative. It would be nice if, in games against strong opponents, we could compare the "action-value" of a prospective tile to the action-value of the ducats in the prospective bid. Unfortunately, the game doesn't allow cash to be raised efficiently enough for that comparison to be so simple. In a rational bidding environment, the basis for comparison will instead tend to be a more tactical "If I bid X for tile Y, what other opportunities will/might I be unable to exploit?" The comparison is about which of several tiles will be one's single purchase for the turn, or whether buying a particular item now precludes bidding on anything else until one's next sale, etc.

If the problems the game presents seem complex, it's because they are.

Jim
 
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