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Subject: The Gotham Gambit: An Opening Analysis rss

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Benjamin Keightley
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In the three-player game, if you haven't won any of the first three auctions, let the NYC go to your opponent who still has cash, even if this means letting him have it for a little cheaper than it's worth. This will split the initial holdings 2/2/0, leaving you with $40. Each of your opponents will have at most $9. Depending on how your opponents behave, you will now have the opportunity to buy as many as three stocks for $9 each.

Stock in Wabash Cannonball is all really good, especially at the beginning of the game. There isn't a single stock that's worth less than $9, and none that have spending needs so high that overbidding is really required. If your opponents capitalize, you can blindly buy whatever they put up. What you choose to capitalize is mostly a matter of taste and whimsy--there are good arguments to be made for any decision.

The risk of this gambit is the possibility that your opponents will both choose to capitalize nothing. This is probably in each player's favor, as there is a 50% chance that neither of his stocks will get diluted. If they do this, you lose your advantage: your opponents now have the initiative, and you will have to scramble in the second round to build a portfolio.

The likelihood of cooperation depends on who has the PA. Here, to 'cooperate' is to capitalize nothing, and to 'defect' is to capitalize an opponent's stock. No matter where player A sits, he is highly motivated to cooperate. This is because defection by player A will result in a bloodbath (and three shares for you!), since B must also defect.

If A is your left-hand opponent, B is motivated to cooperate. This guarantees initiative for both him and A and does not carry any particular risk--you are still 50% likely to capitalize his stock versus A's. If he defects, you will almost certainly capitalize his stock next. This is not a nightmare scenario for B by any means, but I think cooperation is more likely here.

Defection by B is most likely if A is your right-hand opponent. A will almost certainly cooperate, and then you can encourage B's defection by capitalizing one of B's shares. Unlike the scenario above, now B's cooperation carries the 100% chance of one of his stocks being diluted while A receives full dividends for a round. B will frequently defect in this position.

I think this gambit offers good risk to reward value regardless of who bought the PA, but I will almost always attempt it if the PA went to my right-hand opponent.
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Mikko Saari
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Thanks, this sounds interesting. Worth a try, too bad I haven't had much of a chance to play three-player games so far.
 
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Mark Tyler
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Coca Lite wrote:
Each of your opponents will have at most $9. Depending on how your opponents behave, you will now have the opportunity to buy as many as three stocks for $9 each.

In our games we recognized that only one player will have 3 of the 7 shares available (4 shares via the initial offering and 3 more capitialized shares issued) before the first general dividend. With that in mind, one third of 40 is 13.3. This means getting two shares for $13 and one for $14 is ideal. If all players are following this strategy, the other players who have each purchased 2 shares have $13 or $14 left, not $9. I suppose if the other players don't care about getting a third share, then your numbers may be right.

Coca Lite wrote:
The risk of this gambit is the possibility that your opponents will both choose to capitalize nothing. This is probably in each player's favor, as there is a 50% chance that neither of his stocks will get diluted.

I'm not following this. Even if neither of your opponents capitalize a share, you will still have the chance to capitalize three shares before the first general dividend. What am I missing?

Coca Lite wrote:
The likelihood of cooperation depends on who has the PA.

I understand that with only three shares the PA is unstable but I'm not clear why this determines who will dilute what shares. I always figured diluting other's shares was good and diluting my own shares was bad unless I wanted someone else to have the same number of shares as me (to cooperate) and/or to help fund the railroad's operation. Maybe you can explain this PA cooperation thing in more detail.
 
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J C Lawrence
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m_r_tyler wrote:
I'm not following this. Even if neither of your opponents capitalize a share, you will still have the chance to capitalize three shares before the first general dividend. What am I missing?


You can choose the Capitalise action and not auction a share. This is a fairly common practice with all three actions in advanced play.
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Benjamin Keightley
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m_r_tyler wrote:
This means getting two shares for $13 and one for $14 is ideal.

In our games, it's rare for any player to end the first round with three shares. This means players are focused on having the cash for two shares plus enough extra to be able to remain competitive in auctions for the following round (after one dividend payment). So, winning bids for shares in the three-player game are usually between $15 and $20.

Quote:
I'm not following this. Even if neither of your opponents capitalize a share, you will still have the chance to capitalize three shares before the first general dividend. What am I missing?

As was pointed out earlier in the thread, a player turn consists of first making a decision and then optionally performing an action associated with that decision. The first round of Wabash Cannonball rarely sees three stocks actually go up for auction.

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Maybe you can explain this PA cooperation thing in more detail.

Who has the PA is relevant here only for turn order: will Player B in my scenario take his first turn before or after you?

Quote:
I always figured diluting other's shares was good and diluting my own shares was bad unless I wanted someone else to have the same number of shares as me (to cooperate) and/or to help fund the railroad's operation.

This probably deserves its own topic, but that's an awful lot of 'unless.' Most importantly, arranging for an equal partner in a company is probably the easiest way to get that company to Chicago. Putting your 'own' stock up for auction can make sense as early as the second turn. In the very first turn, though, diluting other players' stock (and/or protecting your own) very nearly always takes precedence.
 
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J C Lawrence
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Coca Lite wrote:
So, winning bids for shares in the three-player game are usually between $15 and $20.


Similar here except that the range is about $17-$23, but this is based on a pattern of 2-3 shares (usually 3) getting sold in the first round and then only 1-2 in the second as players start taking empty capitalisations. The reason for the delay is that by the second round players have determined what their initial cash/income trajectory will be, and will start gearing the game length to suit. The first round is too early for that.
 
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J C Lawrence
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clearclaw wrote:
Coca Lite wrote:
So, winning bids for shares in the three-player game are usually between $15 and $20.


Similar here except that the range is about $17-$23, but this is based on a pattern of 2-3 shares (usually 3) getting sold in the first round and then only 1-2 in the second as players start taking empty capitalisations. The reason for the delay is that by the second round players have determined what their initial cash/income trajectory will be, and will start gearing the game length to suit. The first round is too early for that.


My language choice is poor. Here in 3 player games shares during the initial auction go for $17-$23. The first round will thus start with two players with around $20 in-pocket and one player near flat broke. Shares in the first round of the game go for slightly less and 2-3 shares additional shares tend to sell then. After the first dividend is when taking empty Capitalisations tends to start in earnest if the game is going to go that way.
 
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Mark Tyler
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clearclaw wrote:
You can choose the Capitalise action and not auction a share. This is a fairly common practice with all three actions in advanced play.

I guess we haven't evolved to the advanced level as yet. We know it is an option to choose an action and not execute it, but lacked a real good reason for doing so. This thread has helped give some of those reasons.
 
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m_r_tyler wrote:
clearclaw wrote:
You can choose the Capitalise action and not auction a share. This is a fairly common practice with all three actions in advanced play.

I guess we haven't evolved to the advanced level as yet.


I was well into my 20s of plays before I started seriously thinking about it, well into the 30s before I had a real clue about hos to use it, and only now that I'm in the 40s of plays of Wabash Cannonball feel like I've a good handle on how to properly use the tactic. I'm clearly not the brightest bulb -- you should beat me by dozens of games.

Quote:
We know it is an option to choose an action and not execute it, but lacked a real good reason for doing so. This thread has helped give some of those reasons.


That should make the learning curve shorter and sweeter.

Also have a look at: http://www.boardgamegeek.com/thread/295309 It isn't the most perceptive strategy article ever, I was only about 20-something games in at the time, but it catches some basics.

There are also some good comments in Mikko's thread: http://www.boardgamegeek.com/thread/298689
 
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Ben Draper
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Sorry to revive a dead post, but this exact scenario occurred in our game last night, and I was interested in how I should have defended against it.

Player #1 (Me): PRR $20, C&O $20, Cash $0
Player #2: Cash $40
Player #3: B&O $20, NYC $20, Cash $0

Player #1: Null Cap
Player #2: Wins B&O for $0
Player #3: Null Cap
Player #1: Expand PRR
Player #2: Expand B&O
Player #3: Expand NYC
Player #1: Expand PRR
Player #2: Expand B&O

End of the round standings:

Player #1: PRR, C&O, Cash $16
Player #2: B&O, Cash $45
Player #3: B&O, NYC, Cash $14

Player #3: Null Cap
Player #1: Null Cap
Player #2: Wins NYC for $16
Player #3: Expand NYC
Player #1: ???

At this point, I (Player #1) felt like I had a huge advantage, with two undiluted shares compared to the others' two half-shares. But, with Player #2's cash advantage, he was able to take the overall share lead in subsequent turns, while maintaining his alliance with Player #3. The game went long (six rounds), and I made a gamble on Wabash when it came out, expecting it would last another round. When Player #2 ended the game that round (before I could expand Wabash at all), I was toast.

Other than not ensuring that the game would go long enough to cash in on my Wabash share, where did I go wrong?

 
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J C Lawrence
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BennyD wrote:
Player #2: Wins B&O for $0


Shares cannot be won for bids of $0.

Quote:
Player #3: Null Cap


Mistake. Not an unrecoverable mistake, but a significant one.

Quote:
Player #1: Expand PRR
...
Player #1: Expand PRR


I would have expanded the C&O instead. The dividend potential is slightly lower, but you're also less concerned by its eventual dilution.

Quote:
Player #1: ???


C&O, for the same reasons. The intent is to dead-dog the PRR so that it remains inactive and undiluted well into the game. However, given that you've already committed to the PRR, you might as well continue there, tho I do not like that course.

Quote:
At this point, I (Player #1) felt like I had a huge advantage, with two undiluted shares compared to the others' two half-shares.


Only if you can force a short game while luring P2 into a long posture. The problem is that P2's position is flexible and you've explicitly committed to a ~4 turn game. You have to get P2 to commit to a significantly different posture than your own.
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Ben Draper
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clearclaw wrote:
BennyD wrote:
Player #2: Wins B&O for $0


Shares cannot be won for bids of $0.


Ah, we've been mistakenly using the opening auction rules, wherein if all players pass, the start bidder wins the share.

Quote:
Quote:
Player #3: Null Cap


Mistake. Not an unrecoverable mistake, but a significant one.


Will you elaborate? A Null Cap ensures that Player #2 does work only for Player #3 this round, while also shutting Player #2 out of more shares. I assumed this was Player #3's best move.

Quote:
Quote:
Player #1: Expand PRR
...
Player #1: Expand PRR


I would have expanded the C&O instead. The dividend potential is slightly lower, but you're also less concerned by its eventual dilution.

Quote:
Player #1: ???


C&O, for the same reasons. The intent is to dead-dog the PRR so that it remains inactive and undiluted well into the game. However, given that you've already committed to the PRR, you might as well continue there, tho I do not like that course.


Concerning these two points, why is dilution of PRR worse than that of C&O? Is it because PRR is difficult to set up an alliance for, due to its low share count?

Quote:
Quote:
At this point, I (Player #1) felt like I had a huge advantage, with two undiluted shares compared to the others' two half-shares.


Only if you can force a short game while luring P2 into a long posture. The problem is that P2's position is flexible and you've explicitly committed to a ~4 turn game. You have to get P2 to commit to a significantly different posture than your own.


I understand how to force a short game (at least theoretically), but how do I force Player #2 into a long posture? Get him to commit to more shares, so he has less cash on hand, but a higher income potential? If so, how do I achieve this? Can't he just refuse to purchase shares I put up for auction?
 
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J C Lawrence
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BennyD wrote:
Ah, we've been mistakenly using the opening auction rules, wherein if all players pass, the start bidder wins the share.


Ooops. That's fairly significant.

Quote:
Will you elaborate? A Null Cap ensures that Player #2 does work only for Player #3 this round, while also shutting Player #2 out of more shares. I assumed this was Player #3's best move.


It wasn't terrible, but it gives you a significant positional advantage. The fact that he repeated the position a turn later merely further weakened his positional flexibility without getting a responding commitment either from you or P2.

Quote:
Concerning these two points, why is dilution of PRR worse than that of C&O?


Its just a cash flow question. If you can keep the PRR undiluted for long enough, you come out ahead. Even better, the C&O is a viable alliance candidate, but in a 3 player game the PRR is never a stable alliance candidate. The real problem however is that you're hung on P2's lack of commitment. So...the priority is just cash flow while you figure out how to get P2 to commit.

Quote:
Is it because PRR is difficult to set up an alliance for, due to its low share count?


The low share count isn't the problem, it is that there is no stable distribution. 2:1 is a dead company in a 3 player game, and the only other distribution is 1:1:1, which is utterly pointless.

Quote:
I understand how to force a short game (at least theoretically), but how do I force Player #2 into a long posture? Get him to commit to more shares, so he has less cash on hand, but a higher income potential? If so, how do I achieve this? Can't he just refuse to purchase shares I put up for auction?


Can he now? The key is to bid forking values in which if he lets you get them then you come out ahead, but if he wins them you get to force the game shorter so that he loses.
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Ben Draper
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clearclaw wrote:
Quote:
Will you elaborate? A Null Cap ensures that Player #2 does work only for Player #3 this round, while also shutting Player #2 out of more shares. I assumed this was Player #3's best move.


It wasn't terrible, but it gives you a significant positional advantage. The fact that he repeated the position a turn later merely further weakened his positional flexibility without getting a responding commitment either from you or P2.


I'm still unclear here. When you refer to "position", I assume you're referring to stock holdings and their implications. So, you're saying that Player #3's Null Caps were keeping both his and my (Player #1) holdings as they were, thus allowing me to keep my income potential advantage (my two full shares to his two half shares)?

Quote:
Quote:
Concerning these two points, why is dilution of PRR worse than that of C&O?


Its just a cash flow question. If you can keep the PRR undiluted for long enough, you come out ahead. Even better, the C&O is a viable alliance candidate, but in a 3 player game the PRR is never a stable alliance candidate. The real problem however is that you're hung on P2's lack of commitment. So...the priority is just cash flow while you figure out how to get P2 to commit.

Quote:
Is it because PRR is difficult to set up an alliance for, due to its low share count?


The low share count isn't the problem, it is that there is no stable distribution. 2:1 is a dead company in a 3 player game, and the only other distribution is 1:1:1, which is utterly pointless.


So, in a 3-player game, should the PRR owner generally ignore it all game, using its income to get into other profitable companies? Is their likely to be a scenario where PRR splits 1:1 long enough to create a reasonable alliance for pushing it forward? Or is the threat of the third share coming out enough to keep forward progress in check?

Quote:
Quote:
I understand how to force a short game (at least theoretically), but how do I force Player #2 into a long posture? Get him to commit to more shares, so he has less cash on hand, but a higher income potential? If so, how do I achieve this? Can't he just refuse to purchase shares I put up for auction?


Can he now? The key is to bid forking values in which if he lets you get them then you come out ahead, but if he wins them you get to force the game shorter so that he loses.


Hmmm... okay, this makes sense in a theoretical game. But, given this situation, where Player #2 has more than twice as much cash as either of the other two players, what possible bids do such a thing?
 
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J C Lawrence
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BennyD wrote:
When you refer to "position", I assume you're referring to stock holdings and their implications.


A position is an amalgam of many things: portfolio, cash, place in turn order, relative place in turn order to other player's and the portfolios (eg up or downstream of a minor shareholder), order relative to the start player for the current rounds, etc.

Quote:
So, in a 3-player game, should the PRR owner generally ignore it all game, using its income to get into other profitable companies?


No. Your task is to milk it for as much money as possible. How to accomplish that is going to depend on the gestalt of player positions around the table, and that varies from game to game.

Quote:
Is their likely to be a scenario where PRR splits 1:1 long enough to create a reasonable alliance for pushing it forward? Or is the threat of the third share coming out enough to keep forward progress in check?


In 4-player, yes. In 3-player, possibly but I'd be leery and not count on it. Making it work ideally requires the partnership to succeed long enough to threaten Chicago and for P3 to capitalise the last PRR such that you can make the forking bid (if you win it you drive to Chicago at a profit, if they win it you run the PRR into the woods so that it can never reach Chicago).

Quote:
Hmmm... okay, this makes sense in a theoretical game. But, given this situation, where Player #2 has more than twice as much cash as either of the other two players, what possible bids do such a thing?


Start with a B&O. If you or P3 win it, P2's position is compromised. If P2 wins it, he's no longer so high cash and has started to commit. Later, rinse, repeat. He comes immediately after you in turn order, so you control initiative. Use that to force his position.
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Ben Draper
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clearclaw wrote:
Start with a B&O. If you or P3 win it, P2's position is compromised. If P2 wins it, he's no longer so high cash and has started to commit. Later, rinse, repeat. He comes immediately after you in turn order, so you control initiative. Use that to force his position.


If P3 wins it, doesn't that just further cement the P2-P3 alliance? P3 can push B&O and gain ground on both of us, and P2 still gains ground on me. That said, I can start the bid at a point that P3 can't overbid. But theoretically, if he had more money, wouldn't it be disadvantageous for me if P3 won the share of B&O?
 
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BennyD wrote:
I can push B&O and gain ground on both of us, and P2 still gains ground on me. That said, I can start the bid at a point that P3 can't overbid. But theoretically, if he had more money, wouldn't it be disadvantageous for me if P3 won the share of B&O?


Everything depends on both P2's and P3's reaction to the sale with their actions. The key is that there is no possible good resolution for P2. If you win it, P2 must win something, anything, for all of P3's cash (likely a C&O -- which is good for you). If P2 wins it, he's in a commitment bind and will likely capitalise either C&O or more likely NYC in attempt to resolve his commitment. Either is Okay for you, but NYC is better for P2 as it will force P3 to not null capitalise. (Your fear BTW is a 2:2 B&O split) If P3 wins it, then P2 is in deep deep trouble as the game has now been forced long and P2's posture is entirely short and you have a much simpler game to win.
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clearclaw wrote:
Everything depends on both P2's and P3's reaction to the sale with their actions. The key is that there is no possible good resolution for P2. If you win it, P2 must win something, anything, for all of P3's cash (likely a C&O -- which is good for you). If P2 wins it, he's in a commitment bind and will likely capitalise either C&O or more likely NYC in attempt to resolve his commitment. Either is Okay for you, but NYC is better for P2 as it will force P3 to not null capitalise. (Your fear BTW is a 2:2 B&O split) If P3 wins it, then P2 is in deep deep trouble as the game has now been forced long and P2's posture is entirely short and you have a much simpler game to win.


Hmmm... I'm still having a hard time following the reasoning of why certain actions are better for certain players. I think an annotated game would help me immensely. Do you know of such a thing being available?
 
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Sorry, nope.

The central core of Wabash Cannonball is that what is being sold and manipulated on each turn is the set of incentives that will drive future actions by all the players in the game, not the direct manipulations of e(V). Or, more directly, the value of something is in what that purchase by that player for that amount of money, will make all the other players do across the rest of the game. The game is a hugely sympathetic system.
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clearclaw wrote:
Sorry, nope.


Ever think about writing one?

Quote:
The central core of Wabash Cannonball is that what is being sold and manipulated on each turn is the set of incentives that will drive future actions by all the players in the game, not the direct manipulations of e(V). Or, more directly, the value of something is in what that purchase by that player for that amount of money, will make all the other players do across the rest of the game. The game is a hugely sympathetic system.


Yeah, this makes sense. I'm just having a hard time identifying how certain actions manipulate the future game state. My gaming muscles are so used to calculating EV, that they have a hard time disassociating decisions in Chicago Express from their direct EV.
 
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BennyD wrote:
clearclaw wrote:
Sorry, nope.


Ever think about writing one? ;)


If I were to do that, I'd start with another set piece article first.

Part of the problem with such annotated game is that they rapidly become competitions between diverse mental models of the game.
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