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Subject: the flag (beginning of game) auction rss

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Alex Sorbello
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I find that player one has to much of a advantage with getting the flag and only 3 less.
I was wondering what you guys think of a bidding on the flag at the start of the game,
Each player receives 10 dubloens and makes a secret bid (use the action tokens for amount) reveal simultaneous.
winner pays to the bank the amount and gets the flag.
Game start as usual. on a tie bid again (money adds up)
I do not own the game yet but i found some flaws with it while playing. I'm hoping to get some info on this and see if others like it!
Thanks
lexen
 
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Alex Rockwell
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Re:the flag (beginning of game) auction
I absolutely agree, 3 less is not enough handicap.

How are you thinking of doing this auction?

Would the winner get the flag and then auction it? That would make sense to me. We'd have to experiment with how to do the auction...


I agree that something like this would improve the balance of the game.
 
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Anthony Simons
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Re:the flag (beginning of game) auction
I don't know so much; I think a handicap of 3 is too great; I don't see how having the flag at the start of the game infers any realistic advantage. Indeed, the value of the flag beyond an extra action in subsequent turns is debatable.

Perhaps I am missing something, but the first player only gets the flag to start, not a free action, so the 3 penalty is only penalising the freedom they have to place the flag and the privilege of last bid on it. Correct me if I am wrong.
 
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Jim Campbell
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Re:the flag (beginning of game) auction
fellonmyhead wrote:
Perhaps I am missing something, but the first player only gets the flag to start, not a free action, so the 3 penalty is only penalising the freedom they have to place the flag and the privilege of last bid on it. Correct me if I am wrong.


Sure...in addition to the placement of the flag and the last bid on it, they also get to auction the flag and make the money from that in addition to their ordinary tile auction. If the flag has an expected value of 10, this means that the flag auctioneer's minimum profit from that auction will be 5 ducats.

Jim
 
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Alex Rockwell
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Re:the flag (beginning of game) auction
Correct me if I am wrong.


Your worng.

The 3 penalty is supposed to cover their income from the flag. It doesnt cause the flag is worth more than that, probably more like 6, so this player will effectively have extra money.


One way to fix it that probably works best: No one starts with the flag. You choose a random player. That player begins bidding on the flag. High bidder takes the flag and pays the bank (taking the free action). Then that player places the flag, and you dont auction it that first turn.


Alternately: players begin by auctioning off the right to auction the flag.
 
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Jim Campbell
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Re:the flag (beginning of game) auction
Alexfrog wrote:
One way to fix it that probably works best: No one starts with the flag. You choose a random player. That player begins bidding on the flag. High bidder takes the flag and pays the bank (taking the free action). Then that player places the flag, and you dont auction it that first turn.


Alternately: players begin by auctioning off the right to auction the flag.


I prefer giving everyone 10 ducats and doing a single-bid simultaneous auction to be the first holder of the flag. I agree that the 3 ducat penalty is probably not enough, given that the flag has an expected value of at least 8. The first auctioneer's profit on the extra flag auction would thus seem to be a minimum of 4.

Jim
 
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Alex Sorbello
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Re:the flag (beginning of game) auction
Alexfrog (#42571),
in regard to your remark on the auctioning the flag in the first round by randomly selecting a player has one flaw!
That player bids zero and then tops the bid of the other players resulting in him having again an advantage.
I do believe an simultaneous revealed bidding is better to that aspect.
Lexen
 
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Alex Rockwell
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Re:the flag (beginning of game) auction
lexen wrote:
Alexfrog (#42571),
in regard to your remark on the auctioning the flag in the first round by randomly selecting a player has one flaw!
That player bids zero and then tops the bid of the other players resulting in him having again an advantage.
I do believe an simultaneous revealed bidding is better to that aspect.
Lexen


No, the player chosen to start doesnt get to bid at the end. This way whoever is last has the advantage unless the people earlier are pricing it correctly, in which case they had the advantage.

Alternately, this auction is not once around.


My preference in games is for game balance, even if it makes the game more fiddly or complicated. Being fiddly or complicated is a drawback one time, when you are learning it. Being unbalanced is a drawback every time you play it. Since if a game is good I intend to play it many many times, it is better to be balanced even if more fiddly. (Clearly, more balanced and not more fiddly is best). I dont mind adding a fiddly auction mechanism to the beginning of the game if it enhances balance more than a non fiddly mechanic (randomly handing out the flag at start).
 
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Anthony Simons
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Re:the flag (beginning of game) auction
Alexfrog (#42571),

The 3 penalty is supposed to cover their income from the flag. It doesnt cause the flag is worth more than that, probably more like 6, so this player will effectively have extra money.

So why aren't the subsequent flag players being penalised on their turn?

It doesn't make sense that you would want to penalise the first player to a greater extent when there is likely another player holding that flag for the first turn and auctioning it off in the second turn.

If you say they are penalised through what they paid for the flag, that cannot be right because most here seem to agree the expected value of the flag rises as the game goes on.

I would say that 3 is a balanced number to choose as penalty for being first, based solely on the fact that three of the subsequent four auctions (assuming four players of course) are chosen, started and finished by the other players. Their usefulness is arguable, but notwithstanding as immeasurable as the actual value of the flag to its auctioneer at the start of the game.

Further to this, if the flag really is worth 6, then the flag-bearer would have to bid everything to guarantee he takes it at 7. This leaves him with an extra action, but not a lot to do with it. Arguably the balance is against him at 3 less than the others for the first round, regardless of whether he sells the flag or buys it himself.
 
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Alex Rockwell
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Re:the flag (beginning of game) auction
fellonmyhead (#42745),

We arent trying to change how the flag works, just ensure that no one starts the game with a completely random advantage.

You say that 3 is fair for the first player to lose to be able to auction the flag. I would say its something more than 3 (5?). Regardless, if players bid for this first player priveledge, it is more balanced than an arbitrary number, unless that number is exactly correct. Even if it is correct, bidding for it will be equivalent among skilled players.
 
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Jim Campbell
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Re:the flag (beginning of game) auction
fellonmyhead wrote:
Further to this, if the flag really is worth 6, then the flag-bearer would have to bid everything to guarantee he takes it at 7.


Huh? If the flag is worth 6, then the flag auctioneer would never bid 7 on it because that would be incredibly stupid. I think you may be confused by what is meant when we say "worth"; we mean the estimated value of the benefits of that tile. The players are trying to buy items for less than they are worth, thus turning a profit. That worth is different from the incoming high bid, which was the effort of the non-auctioneers to bid higher than other players but lower than the worth of the tile.

If the flag is worth 6 then an incoming bid might be 3, 4 or 5, any of which the auctioneer will accept to maximize his profit on the transaction.

This leaves him with an extra action, but not a lot to do with it.

Saving it is allowed, and really good because saved actions are useful later. He can also use it to get 4 ducats.

Arguably the balance is against him at 3 less than the others for the first round, regardless of whether he sells the flag or buys it himself.

That's only true if the value of the flag is approximately 6, and there's just no way that it's so low. The extra action is obviously worth an absolute minimum of 4 ducats, so the question becomes: Comparing (a) auctioning the 2nd, 3rd or 4th item in the next auction to (b) auctioning the 1st (flag) item and the 5th item, is (b) worth at least 3 ducats more than (a)? The answer is obviously "yes", and I don't see how it isn't worth at least 4 more ducats.

So if the flag is worth at least 8 on turn 1, that's a guaranteed auctioneer profit of at least half that, or 4 ducats. I'll believe that flag + 7 ducats is a disadvantage when someone actually demonstrates one.

Jim

 
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Anthony Simons
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Re:the flag (beginning of game) auction
Alexfrog (#42763),

Everything else aside, the auction option you propose is still imbalanced in favour of one or more players. If the bid is not simultaneous, one bidder will have the optimal bid, but may not get the flag; in which case the flag bearer is at a disadvantage. Alternatively all players could bid below optimal and the flag bearer is at an advantage. The fact this was arrived at through auction does not make it "fair".

If a single, closed-fist bid is used then tiebreaking will, in all probability, be required. There is usually no reasonable way of doing this as if the closed-fist auction coninues for another round it could go on indefinitely. Such ties are usually broken in an arbitrary way, such as the player closest to the first player wins, or the roll of a die decides and so on.

IMNSHO you might as well settle for the 3 penalty, save all this messing about and get on with the game. In a nutshell, equivalence=ties, breaking ties=imbalance in favour of one player over the other (or if both players are forced down an expensive route, in favour of the other players over the tied players).

 
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Re:the flag (beginning of game) auction
jimc (#42770),

Huh? If the flag is worth 6, then the flag auctioneer would never bid 7 on it because that would be incredibly stupid. I think you may be confused by what is meant when we say "worth"; we mean the estimated value of the benefits of that tile. The players are trying to buy items for less than they are worth, thus turning a profit. That worth is different from the incoming high bid, which was the effort of the non-auctioneers to bid higher than other players but lower than the worth of the tile.


hey, I didn't value the flag at that, that was the siuggested value to which I responded. The flag will have a different value at different times to different players; the auctioneer must weigh up how much he is prepared to pay for it and this includes working at a loss if it would prevent other players from working at a much higher profit. This one auction isn't the entire game, which is many-faceted.

If the flag is worth 6 then an incoming bid might be 3, 4 or 5, any of which the auctioneer will accept to maximize his profit on the transaction.


An incoming bid might be 7 if the flag is allegedly worth 6; this is the argument I have against this whole premise that knocking 3 off the first player's money is not enough - you don't know. Besides, a bid well above the worth of the flag might not be acceptable to the auctioneer if the action is more valuable to him than not having it at all.

That's only true if the value of the flag is approximately 6, and there's just no way that it's so low. The extra action is obviously worth an absolute minimum of 4 ducats, so the question becomes: Comparing (a) auctioning the 2nd, 3rd or 4th item in the next auction to (b) auctioning the 1st (flag) item and the 5th item, is (b) worth at least 3 ducats more than (a)? The answer is obviously "yes", and I don't see how it isn't worth at least 4 more ducats.

Because we don't exactly know what 4 ducats is worth, for a kick-off. Added to this that the 2nd tile up for grabs might just mean 3 VP difference, but the flag and the last tile might just mean an extra action and a couple of ships (= nothing, perhaps something in the long run). The answer is NOT obviously "yes".
 
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Jim Campbell
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Re:the flag (beginning of game) auction
fellonmyhead wrote:
IMNSHO you might as well settle for the 3 penalty, save all this messing about and get on with the game. In a nutshell, equivalence=ties, breaking ties=imbalance in favour of one player over the other (or if both players are forced down an expensive route, in favour of the other players over the tied players).


The flag auctioneer seems to have items worth between 11 and 12 ducats at the start of the game, instead of 10. That advantage of 1-2 ducats is awarded at random, which I think is not very good. If there is a sealed-bid auction and everyone bids 4, followed by an arbitrary method of awarding the flag, then the randomly awarded advantage is reduced to either 0 or 1. That's an improvement. Note that the more certain we are that the flag generates income of 5 rather than 4 the more likely it is that the bids will increase to 5 and negate that advantage.

Jim
 
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Re:the flag (beginning of game) auction
fellonmyhead (#42773),

Besides, a bid well above the worth of the flag might not be acceptable to the auctioneer if the action is more valuable to him than not having it at all.

This statement doesn't make sense to me - if the auctioneer wants the flag more than the incoming bid, doesn't that mean that the flag is worth more than the incoming bid? It seems like "worth" should mean "the greatest value assigned to the item by any player", since this is what the highest bid will be.

Because we don't exactly know what 4 ducats is worth, for a kick-off. Added to this that the 2nd tile up for grabs might just mean 3 VP difference, but the flag and the last tile might just mean an extra action and a couple of ships (= nothing, perhaps something in the long run). The answer is NOT obviously "yes".

I don't quite understand what jimc is saying, but it seems obvious to me. Using ducats as the common denominator, it doesn't really matter what a ducat is worth. I don't know if it's important whether you get to auction the 2nd, 3rd, 4th or 5th item. Absent that consideration, the player holding the flag gets to auction it on top of any other items. The flag can generate at least 4 ducats. Therefore, the flag provides at a minimum:

an extra action, worth at least 4 ducats;
an extra auction (the flag), worth at least the value of the flag, which is at least the 4 ducats the extra action gives;

So the flag should be worth at least 8 ducats, it seems to me.
 
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Jim Campbell
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Re:the flag (beginning of game) auction
fellonmyhead wrote:
hey, I didn't value the flag at that, that was the siuggested value to which I responded. The flag will have a different value at different times to different players; the auctioneer must weigh up how much he is prepared to pay for it and this includes working at a loss if it would prevent other players from working at a much higher profit. This one auction isn't the entire game, which is many-faceted.


First of all, we aren't talking about flag auctions in general but the first flag auction. Appealing to "well, we don't know which of a broad range of circumstances..." doesn't fly, because we do know what's happening on turn 1 within a fairly narrow range.

Second, the idea that the auctioneer may want to buy at a loss to prevent someone from making a large profit is generally going to be ill-advised. That could be a good idea in specific and unusual circumstances later in the game, in which the tile's EV for a non-auctioneer is very high and there are no other bidders and the EV for the auctioneer is very low. That's certianly not true of the flag on turn 1, however.

An incoming bid might be 7 if the flag is allegedly worth 6; this is the argument I have against this whole premise that knocking 3 off the first player's money is not enough - you don't know.

Yes, you do know...because it's the beginning of turn 1 and the positions are nearly identical. The flag's value to the players is knowable within a narrow range because as yet there has been no noise added to the system. Indeed an incoming bid might be 7 if the flag is worth 6, but if someone's determined to be an idiot there's no use trying to talk them out of it. Terrible moves can't be accounted for in the game design, but making the game fair in the context of reasonably good moves can and must be.

Besides, a bid well above the worth of the flag might not be acceptable to the auctioneer if the action is more valuable to him than not having it at all.

Again, I can imagine endgame situations in which no amount of ducats will increase one's score more than a specific tile. That's not the topic, however; this is a discussion about turn 1, when turning down a bid higher than the value of the tile is a terrible move.

Because we don't exactly know what 4 ducats is worth, for a kick-off.

Now you're claiming that we can't attempt to compare the value of any two items in the game if they are differently denominated. It might be more difficult in some cases than in others, but the idea that we can't is silly.

Added to this that the 2nd tile up for grabs might just mean 3 VP difference, but the flag and the last tile might just mean an extra action and a couple of ships (= nothing, perhaps something in the long run). The answer is NOT obviously "yes".

On turn 1, the difference between 2 and 5 might be significant, or it might not be. What we do know is that auctioning the flag will generate a profit of at least 3, probably between 4 and 6. That's enough ducats to make up for the difference between 2 and 5 with a surplus in most cases.

As an aside, the "extra action and a couple of ships" purchased on turn 1 are clearly worth at least 1 or 1.5 points without even considering the possibility of compounded earnings from reinvestment. Assuming the buyer is awake, they are not worth "nothing, perhaps something in the long run" when purchased so early.

Jim
 
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Re:the flag (beginning of game) auction
jimc (#42779),

First of all, we aren't talking about flag auctions in general but the first flag auction. Appealing to "well, we don't know which of a broad range of circumstances..." doesn't fly, because we do know what's happening on turn 1 within a fairly narrow range.

Obviously not; you want to penalise a player who has but two choices when the flag is auctioned; take the flag or take the money. Yes, he has last bid. However he also has 3 ducats less than the other players. The flag is guaranteed to sell to another player at 7 ducats as a result and anybody bidding lower is allowing the flag-bearer a choice. This means he has two choices at best, likely no choice at all. I'd rather have an action than 4 ducats more than the next player; clearly a disadvantage.

Second, the idea that the auctioneer may want to buy at a loss to prevent someone from making a large profit is generally going to be ill-advised. That could be a good idea in specific and unusual circumstances later in the game, in which the tile's EV for a non-auctioneer is very high and there are no other bidders and the EV for the auctioneer is very low. That's certianly not true of the flag on turn 1, however.

This is not likely to happen on the first turn on account of the restriction the flag-bearer has suffered through his penalty of 3 less ducats. He wouldn't be buying it at a "loss" because his maximum bid is 7 despite any "estimated value". That action attached to the flag gives it its worth, not potentially what the auctioneer might get for it. On the first turn he only has a choice while the bidding stays at or below 6. I agree the "specific circumstances" you describe are not the first flag auction, but I'm glad you see what I mean there.

Yes, you do know...because it's the beginning of turn 1 and the positions are nearly identical. The flag's value to the players is knowable within a narrow range because as yet there has been no noise added to the system.

The noise is already there, in the form of four tiles up for auction in the upcoming round. You still can't say for certain what the flag is worth; I can still say the auctioneer is sufficiently disadvantaged by being cut to 7 ducats. This is only going to rise if he sells the flag.

On turn 1, the difference between 2 and 5 might be significant, or it might not be. What we do know is that auctioning the flag will generate a profit of at least 3, probably between 4 and 6. That's enough ducats to make up for the difference between 2 and 5 with a surplus in most cases.

But profit does not equate to anything compared to the worth of that extra action. You can only buy actions through the flag or a tile. You seem to assume the player will always sell and not buy. I do not think it is stupid for him to buy the flag at 7 ducats, beyond that he has no choice. 3 ducats down is disadvantage enough.

Oh and calling people "stupid" and "idiot" for not playing it your way is very ignorant; consider that a different player mix will cause auctions to behave differently and as a result your extra auction is devalued as a fair means of distributing the flag at the start of the game.

Now you're claiming that we can't attempt to compare the value of any two items in the game if they are differently denominated. It might be more difficult in some cases than in others, but the idea that we can't is silly.

Actually, all I was saying was that if the auctioneer buys his own flag he takes X ducats out of circulation, increasing the value of 4 ducats. This increase in value is effective immediately for subsequent auctions until the auction phase is over and somebody takes tax.

I still see no point in an initial auction; might as well roll a die and give the flag to the highest roller. If there is anything solid in your reasoning Im not seeing it.

Are you arguing that any other player will always bid at least 7 for the flag so the flag-bearer will always sell? Are you arguing the action has no value to the auctioneer? Are you arguing the action is always worth 4 ducats? Are you arguing that if the auctioneer is faced with a bid of X in the first round he should never bid X+1? Are you arguing (as you seem to be) that the answers to these questions are true regardless of the tiles subsequently up for auction? If your answer is yes to any of these I think you're wrong; if it isn't then I AM missing the point.
 
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Jim Campbell
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Re:the flag (beginning of game) auction
fellonmyhead wrote:

The flag is guaranteed to sell to another player at 7 ducats as a result and anybody bidding lower is allowing the flag-bearer a choice. This means he has two choices at best, likely no choice at all. I'd rather have an action than 4 ducats more than the next player; clearly a disadvantage.


Now it's clear to me why we are going back and forth in this discussion without seeming to make progress. I frequently mention an effect that is both critical to analysis of the game and of great value to the auctioneer; I think that you are ignoring that value and thus misunderstanding most of what I and others are saying about the bidding strategy. The effect can be summarized as:

When the auctioneer buys a tile, the effective price is equal to (2x - 1), where x is the actual purchase price in ducats.

In other words, if the incoming bid is 6 and I overbid and buy for 7, not only do I lose the 7 I pay but also the 6 I would otherwise have received, for a net loss of 13 or (2x - 1) where x = 7. When the incoming bid is 6 I am guaranteed to profit by 6, and any other choice I make must exceed 6 profit (or equivalent in spice, actions, etc.) to be better than that. From this we know that in order to buy the tile for 7 it must offer a minimum benefit of 13 ducats (or equivalent). On turn 1, the flag cannot be reasonably expected to offer 13, which is merely the break-even point and not the level at which the profit is larger than 6.

There is only one reasonable conclusion to reach from this: If the incoming bid in the first flag auction is 6, then it would be quite foolish for the auctioneer to buy the flag for 7. If that doesn't make sense to you, I give up and wish you well in your boardgaming.

Oh and calling people "stupid" and "idiot" for not playing it your way is very ignorant; consider that a different player mix will cause auctions to behave differently and as a result your extra auction is devalued as a fair means of distributing the flag at the start of the game.

I don't call anyone stupid. In the case of an extremely bad move I may characterize a move that way. Despite your objection that some demonstrably bad bidding choices might actually be justifable, I stand by my conclusion that we can rule out many possibilities as simply poor play.

Are you arguing that any other player will always bid at least 7 for the flag so the flag-bearer will always sell?

No, but an informed decision will yield a bid of 6, 7 or 8 which the auctioneer will accept if making an informed decision.

Are you arguing the action has no value to the auctioneer?

Certainly not; the value is more tightly defined (at 4-5 ducats) than at any other time in the game.

Are you arguing that if the auctioneer is faced with a bid of X in the first round he should never bid X+1?

No. If the incoming bid is 4 or less then the flag auctioneer should overbid. However, an incoming bid of 4 or less (or even 5) indicates that all but one of the auctioneer's opponents didn't make an informed decision.

Are you arguing (as you seem to be) that the answers to these questions are true regardless of the tiles subsequently up for auction?

Because the start positions are identical except for the flag and because the tiles in group one do not vary dramatically in strength, the collective and individual value of the tiles on turn 1 will be similar from game to game. That's part of the reason why we can draw these conclusions, because the opening situation is very "knowable".

Jim
 
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Re:the flag (beginning of game) auction
jimc (#42878),

I didn't miss this:

When the auctioneer buys a tile, the effective price is equal to (2x - 1), where x is the actual purchase price in ducats.


I think you are missing this:

When any player buys the flag, the effective worth (before any sale is to take place in the subsqeuent round - see below) is equivalent to a(N - 1) where N is the number of players and a the actual value of the action gained.

This works for the same reason your formula does but in reverse; the player has effectively gained an extra action and denied it to the other players. If you put (as you seem to - always) the worth of an action in terms of ducats, 4-5 I believe you said, that makes the action worth 12 - 15 ducats overall; so by your own statement the auctioneer does break even by bidding 7.

Added to this of course must be the subsequent (2x - 1) for round 2; this cannot be discounted when considering the flag's worth in round 1 (though you seem to say it can).

However, as I have said, the value of the ducat fluctuates, so the value of the action cannot be accurately measured that way. That action could be a colony, a valuable expedition card (which affords at least 1 VP) or 1-2 extra VP's for progress. You just can't buy those.

 
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Re:the flag (beginning of game) auction
fellonmyhead (#42896),

When any player buys the flag, the effective worth (before any sale is to take place in the subsqeuent round - see below) is equivalent to a(N - 1) where N is the number of players and a the actual value of the action gained.

This works for the same reason your formula does but in reverse; the player has effectively gained an extra action and denied it to the other players. If you put (as you seem to - always) the worth of an action in terms of ducats, 4-5 I believe you said, that makes the action worth 12 - 15 ducats overall; so by your own statement the auctioneer does break even by bidding 7.


I don't see how you can include the value of denying resources to others as part of the EV of an item. I may not understand (or maybe there isn't a common understanding of) what EV entails exactly, but I take it to be a loose proxy for VP. Expressing things in terms of VP is undesirable because (on top of it being vague) you can't leverage early VP for more VP later on, while you can leverage early ducats for more ducats (and so more VP) later on.

What I perceive as the problem with your logic is that if it is worth it to the auctioneer to bid 12-15 on the flag on the basis of denying the extra action to all other players, it is also worth 12-15 to each other player to deny the action to all other players. So there would never be an incoming bid of 7.

By my usage of EV, the flag is worth the best use of the extra action - if a player is more advanced in ducats, then the minimum value of an extra action is that taxation level. The EV may be more because of opportunities for founding colonies and advancing tracks, which translate into both VP and increased production capacity. So a better calculation of effective worth is max(a(N)).

A player may want to bid over their own EV (and over the EV of the flag to another player) for the flag (or any item) if they would prefer to handicap that player than improve their own position. I suppose the small element of chance in expedition cards and colony foundation can reward a player that takes a risky strategy.

Since i'm not as pro on gaming theory as others here, I'd appreciate any feedback on my thinking.
 
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Re:the flag (beginning of game) auction
crispyfloss (#42903),

I don't see how you can include the value of denying resources to others as part of the EV of an item.

Because bidding on your own item is denying resources to others, and this has value. If this doesn't, how does accounting for money you were denied apply to the estimated value?

Put more clearly, if by taking an action that gains you 1VP you are also denying another player 3VP (for example) then by the same "logic" applied to these ducats your net gain is 4VP and not 1VP. I know, I know; it sounds a bit fishy - but then so does all this valuation by the ducat.

We're now drawing closer to the problem I have with how some perceive the ducat to have actual value; as opposed to relative value, which is obviously the case.

If player 1 has 10 ducats and player 2 only 6 then player 1 can always take the auction for 6 or 7 depending on who bids first. Granted, unless you've tracked money closely you will have no indication who has what, but even with one hundred times more ducats each, player 1 would have to bid at least 60% of his money to guarantee a winning bid. If player 2 is the auctioneer, then the roles will be reversed for the next auction in so far as player 2 will now have 3 times as many ducats as player 1, and need only bid 4 of them to shut out player 1.

However, if player 1 was the auctioneer and closed his bid with a 7 (to outbid player 2's bid of 6), then those 7 go out of circulation; he now has the item in question and player 2 is only double player 1 in terms of wealth, and would have to leave himself with only 2 to shut out player 1 if his auction is next. The actual cost is 1 more than in the previous example, but the relative cost is much less.

What I perceive as the problem with your logic is that if it is worth it to the auctioneer to bid 12-15 on the flag on the basis of denying the extra action to all other players, it is also worth 12-15 to each other player to deny the action to all other players. So there would never be an incoming bid of 7.

This could be a problem with my logic, or it could be a problem with the logic on which it is based; that is, that an action is worth 4-5 ducats. That is one premise I will never play by. I tend to agree with you about what EV entails, which is why I cannot understand people quoting the flag at a specific ducat value or range of ducat values even at the opening of the game.

By my usage of EV, the flag is worth the best use of the extra action - if a player is more advanced in ducats, then the minimum value of an extra action is that taxation level. The EV may be more because of opportunities for founding colonies and advancing tracks, which translate into both VP and increased production capacity. So a better calculation of effective worth is max(a(N)).

That is a better description of its worth than I could have come up with, and certainly better than talking about ducat cost or potential ducat gain. My interpretation of that is it is worth as much as it is worth to the player to which it is worth the most - am I right?

A player may want to bid over their own EV (and over the EV of the flag to another player) for the flag (or any item) if they would prefer to handicap that player than improve their own position. I suppose the small element of chance in expedition cards and colony foundation can reward a player that takes a risky strategy.

Well I wasn't necessarily talking about self-effacing actions just to cripple another's score; rather I was talking about the hidden gain by causing another's loss (or prevention of their gain ).

Ultimately, do you feel that 3 ducats penalty for first flag-bearer is too low, too high or just right?

Since i'm not as pro on gaming theory as others here, I'd appreciate any feedback on my thinking.

I think you're a little more pro on logic than I am, and correct me if I am wrong but doesn't this max(a(N)) statement kind of say the value is beyond any bid any of the players are capable of in that first auction? If that is (or even possibly is) the case then -3 is enough, possibly more than enough for first flag-bearer.
 
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Re:the flag (beginning of game) auction
First of all, when talking about how much money the first player should start with, what is important is the amount of money that AUCTIONING the first flag is worth. I think that this is about 6. If the first player starts with 7+6 = 13 after that flag auction, they are up $3, with the negative that they didnt have a chance to buy the flag on turn 1, and that they now auction the 5th tile, and thus their money income from it wont be available until next turn, after some inflation occurs.

I dont think these are much in the way of drawbacks. I would certainly take this tradeoff every time, which makes me think that starting the first player with $7 is too much. If they start at $6, it seems much more fair, and I suspect their net gain (2 extra bucks versus those drawback), is between $0 and $1, which is on the level of the smallest money increment, and thus the most balanced possible.

In 2 player, I suspect that the bids will all be lower than in 4 player, and it may be that $7 is a better amount for 2 player.

Regardless, auctioning the ability to sell the first flag would be a balanced way of resolving the issue, as would just figuring out how much its worth and setting it at that.

The game designer seems to think $7 is fair. I say $6 is fair. I think we need more testing to find out. Regardless, its a relatively minor issue in the whole scheme of the game, and being off by $1 isnt going to break anything.
 
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Re:the flag (beginning of game) auction
Alexfrog wrote:
The game designer seems to think $7 is fair. I say $6 is fair. I think we need more testing to find out. Regardless, its a relatively minor issue in the whole scheme of the game, and being off by $1 isnt going to break anything.


Well said. I tend to think the designer did factor in the inability of P1 to use his second auction cash when he set the value at $7. Regardless, once "noise" is introduced in the system--and that happens very early--I think it'll be very difficult to ever discern the impact of the "unfair" price. Note too that P1 will likely be the next-to-last auctioneer in turn two, if P2 wins the auction (as seems likely, I think).
 
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Re:the flag (beginning of game) auction
fellonmyhead wrote:
I think you are missing this:

When any player buys the flag, the effective worth (before any sale is to take place in the subsqeuent round - see below) is equivalent to a(N - 1) where N is the number of players and a the actual value of the action gained.


No, I didn't miss it, because it's utterly and demonstrably false. Your formulation assumes that if one doesn't buy the tile then every other player buys the tile, which is obviously impossible since there can be only one buyer. The idea you seem to be reaching for does apply in a 2-player game, because in that case buying the tile actually does prevent the only opponent from getting it; anything one buys is not purchased by one's opponent. In a 2-player I can see how the tile's value would be equal to 2a. In a larger game, 2a is valid in a strict comparison between the outcomes for the buyer and the second highest bidder; it's false when comparing the outcomes for the buyer and opponents other than the second highest bidder.

This concept that there is some additional value in denying tiles to one's opponents is valid, and can be described in this formula, which has a huge asterisk:

The value of a purchased tile when adjusted for opponent's loss of opportunity equals n(a)/(n - 1) where a is the ordinary value of the tile to the buyer and n is the number of players.[Giant asterisk right here!]

[Note for giant asterisk]This formula doesn't work for evaluating an individual transaction in a game with more than 2 players, because the opponent loss is not spread evenly over all opponents. It does describe an effect that will tend to spread more evenly over a longer series of purchases.

It's valuable to know about this effect and account for it, but since the additional denial value is actually equal to a/(n - 1) the effect is not nearly as large as you thought.

Returning to the flag auction example with 4 players, if the incoming bid is 6 then to overbid at 7 the auctioneer must derive a benefit of at least 13 from the flag to make the same profit of 6. We must adjust for the denial value of the flag, so we calculate that the unadjusted value of the flag must be at least 39/4, or 9.75. That seems like a big breakthrough, since after subtracting the 4 ducats for the free action there's seemingly no way that the flag won't sell for at least 6 and make a total greater than 9.75.

There is one problem, of course. Buying tiles isn't the only activity with inherent denial value; collecting payments from one's opponents also does this. Although in specific transactions the collection will be from a single opponent, the effect will tend to spread out over multiple opponents in the same way. The value of a payment adjusted for the denial effect will thus tend to be n(d)/n - 1 where n is number of players and d is the payment amount in ducats.

Returning again to our example, we now adjust the value of the incoming bid (which is still 6 ducats) to 8. To pay 7 and make a profit of 8 requires the flag to be worth 15; adjusting that 15 for the denial value of the item, we get 45/4 or 11.25. After subtracting the 4 ducats for the free action, the turn 2 flag auction needs to yield about 7 ducats for the auctioneer to gain the same advantage as they would by simply accepting the 6 ducat bid.

There is also a huge tactical problem if the first flag auctioneer buys the flag for 7. Now out of cash, the auctioneer is a non-participant in the next 3 auctions before selling the 5th item. That isn't just a loss of opportunity, but also removes a source of bids that would otherwise raise prices for the other players. In addition 7 of the 37 ducats have just left the game. That currency deflation reduces the price expectation of a tile from (p / 37) to (p / 30) a decrease of about 18%. Combining these effects, we see that for the next 3 tiles (a) prices are falling, (b) prices are falling more and (c) the flag auctioneer will not bid on any of them. That's a disaster.

However, as I have said, the value of the ducat fluctuates...

Indeed it does, as I've just demonstrated above.

...so the value of the action cannot be accurately measured that way. That action could be a colony, a valuable expedition card (which affords at least 1 VP) or 1-2 extra VP's for progress. You just can't buy those.

You can buy any scoring opportunity in the game by purchasing the tiles necessary to score those points. I can buy ships, spice, colonists, missions, the duty tile, actions and bonus plantation VPs during the auction. There is no type of scoring that can be achieved solely through the use of ordinary actions and/or the proceeds from ordinary actions. So yes, the value of an action can be measured in terms of ducats, although given the relative scarcity of tiles and the limited amount of turns in which to act that ducat price estimate can be made more difficult. Early in the game, it's easy to make ducat estimates because one still has a lot of time and flexibility and there are usually a variety of ways to solve the same problem. Later in the game, it's better to evaluate in terms of points.

Jim
 
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Re:the flag (beginning of game) auction
jimc (#42979),

Whilst I have already agreed elsewhere my suggested formula was inaccurate, this:

The value of a purchased tile when adjusted for opponent's loss of opportunity equals n(a)/(n - 1) where a is the ordinary value of the tile to the buyer and n is the number of players.

is also inaccurate to as great an extent in the opposite direction. The opponent loss is not spread evenly over all opponents as you say, but assuming all players value the tile equally (a1 = a2 = a3 = a4) the opportunity loss each player has is equal (and yes, the effect is not cumulative as you say).

In reality of course it is not equal, however at the start of the game - if it approximates to equal, which it ought to - the flag-bearer has every reason to want the flag as much as the other players. However, his bidding power is severely reduced by having 3 ducats less than any single other bidder. This is a severe disadvantage which is basically forcing a sale to another player. The flag is something a player should not wish to give away at the start of the game as that extra action will usually open up an opportunity to take an early and difficult to surmount lead.

For this reason alone, let alone the to-and-fro about EV, the flag-bearer is disadvantaged enough.

I am not going to dwell on this much longer, you have your opinion I have mine; but I will reiterate the main points of my argument:

1. Within the microcosmic economy of Goa, ducats have only relative value, so cannot be used universally as an exact measure of the value of any tile or action.

2. There are sufficient unknowns at the first turn to discourage me from assigning a fixed value to the flag or any particular tile under auction; the tile selection for auction may add value to the flag but will hardly detract from it.

3. A player starting with 3 ducats less than the other players is at a disadvantage due to low relative wealth for at least the first (flag) auction. If everybody values the flag at around 5 ducats this turn (i.e. they limit themselves to bidding no more than 5), then anybody but the flag-bearer will have enough remaining to participate effectively in future auctions if they purchase it. If everybody values it at 1, then even if the flag-bearer purchases it the relative wealth is still against him.

4. The flag-bearer cannot have his cake and eat it; if the opportunity arises for him to buy the flag or take the cash this does not equate to a win-win situation. This is different from tiles because generally taking one tile over another is less important at the start of the game (so a player is happy to get a tile whatever is on it - blank canvas thus marked, the strategy takes hold from there).

5. If subsequent auctions in turn 1 must be taken account in assigning value to the flag, so must subsequent turns as the action may be carried over.
 
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