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Subject: Opening Share bidding in 2 player rss

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Alex Rockwell
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So 2 player is quite different than with more people. It might not be as interesting once you are very experienced with it, but I found it quite interesting at first.

Its a real challenge trying to determine what to bid on the opening shares, and round 1 as well.

WARNING: This is rambly! I'm part figuring this out as I go along.


Here is what I have found after a few games. This is all for 2 PLAYER ONLY! This doesnt apply to games with more players:

Each player starts with $60. The standard 'its worth about half your money' that works with 3-4 player now completely fails. If I win two shares for $30 each, you then win a couple for free, and then can get another in the first turn for almost free as well, and you crush me. So $30 is clearly too high.

$15 is clearly a good value. I can continue to win $15 shares for the entire starting auction, after which you get one for almost free during turn 1, but I remain way ahead. So $15 is too cheap.


$20 seems like a reasonable number to consider, as you expect around 6 auctions in the opening plus turn 1, and this would spend all the money of both players.


Lets say Player A wins Red for $20, and then bids $20 on Blue. Player B passes. Now player A has only $20 left. If they bid significantly less than 20 and let the opponent have it for 1 more, the opponent gets their 2 shares much cheaper and then has a lot more money left over to win shares in turn 1, or just to hold, and is way ahead. But if they big close to $20, player B passes again. A has 3 shares and is broke/almost broke. B wins a share for 'free'.

Turn 1 starts, A owns Red and thus Null capitalizes. B wins an almost free share again. A null capitalizes. The shares are 3-2 in A's favor however B still has a massive money advantage (~40+). A gets a bit more income but only 5-10. In round 3, B can crush A in bidding and equalize share count with a money lead, thus winning.


From this I find a couple things:
* Bidding $20 on everything in the opening loses.
* The Red share is good. With the Red share, is you get a big money lead on your opponent, you can capitalize two shares while they null cap once. If you have a lot less money you can null cap twice. By turn 2, people have both gotten a significant amount of income from a dividend round, so by then you are ok. If a player goes into turn 2 with equal shares and more money they probably win, and same with more shares and equal money. Ownership of the Red share allows you to be at a money disadvantage without it hurting as much, or allows you to capitalize more on a money lead.


At this point we have determined that the correct bidding range is in the $15-20 area. The Red share is a bit more valuable than others.

I also believe that the yellow share is worst and green is probably 2nd best due to high initial income (though perhaps blue beats it on income potential in the middle of the board?). Each player should end up on turn 1 after capitalizations are exhausted, with a company that they are the sole investor in. They will spend time improving their income in this company. More starting income tends to lead to more ending income. An advantage of green is that it can expand cheaply on the top of the board, while others must pay more to go through the mountains. Companies will quickly run out of money in 2 player, except for the ones your opponent has capitalized to dilute them.

There is also an advantage in shares with less max shares available. A lot of the game will be spent purposefully diluting opposing shares, and thus Red is least vulnerable to this while yellow is most. For this reason Blue might be better than Green. (I am undecided between them).


So how should the initial bidding go?

Lets say A wins Red for $20 and bids $16 on blue. If B passes, he bids $16 on yellow, leaving him with $8. B buys green for $9
Shares: A up 3-1, Money: A down $8 to $51.

A now null caps, B buys a (Red?) for $8, A null caps.

Turn 1 ends with A up 3-2 on shares, but down by $35. A gains 5-10 more income, but is still down $25-30 in round 2, where B equalizes the share lead and has more money left for a big advantage.

So that scenario was bad for A, but only slightly. If he can save more than $8, he drives up the price of the initial green share and the turn 1 share that B gets, and then eventually when B equalizes share counts in turn 2, the money is even.


Scenario 2:
A gets Red for $20. We know that if he now keeps bidding, $16, B lets him have it and wins. Lets A bids $15 and B bids $16. Is this good for B? A has $40 left to B's $44. Lets say B bids $15 on yellow and A bids $16 to win it. A has $24 to B's $44. A auctions green for $15.
If B wins it for $16, we have 2 shares each and and extra $4 for B. $24 to $28. Both people can reasonably bid up an auction so this is pretty fair, if A's shares are worth $4 more. Depending on the combo that might be true, however, is Red really $4 better, if you end up not being way up or down in money? I doubt it.

My current best guess as to share valuations are:
Red: $18?
Blue: $16-17
Yellow: $14-15
Green: $16-17

When you are ahead on shares and behind on money, you cannot pay the higher values anymore. You must bid the lower value and get it 'cheap' or let the opponent have it for $1 more.

Lets look at how this works.


A wins Red for $18 and bids $16 on blue. If he wins it, he has $26 remaining. He bids $15 on yellow. If he wins it, he has 11 left and bids 11 on green. B gets a green for 12 followed by a share next round for 11.

Shares: A up 3 to 2.
Money: B up $37 to $11. After dividend, B is ahead by about $18-20 on money. This is slightly in B's favor. B will equalize shares counts with a bit more money. But this is near even.


The problem here is that A won the first three bids and count drive up the final green. But lets say that he had lost yellow or blue instead, but then won green for $16-17. Now he is up 3-1 on shares with about $10 left, but his opponent has $44 instead of $49. The opponent wins a T1 share for $11 and has $33 left, a lead of $23. A gains an extra 5-10 in income and now the money lead is down to $15. This is now equal or in A's favor.


What we learned from that is:
* Ending up after the initial auctions with a 3-1 share lead and $10 left is good IF the opponent paid $15+ for their share (but not if they paid ~10). If they paid $12 its really close. (This also depends on which shares you have, and this requires you having the Red share to be true).
* You really need to have at least $10 left on the green share auction, to enforce a reasonable minimum on it and the turn 1 share auction. Each extra $1 you have allows you to milk TWO bucks from the opponent. If youre up 3-0 in shares here you can bid all your money on green and its great if you win it, the game is then over. So the opponent has to outbid you. They'll win green for your money + 1, then a share in T1 for however much money you have. Having more than $12 left when the green auction occurs and being up 3-0 in shares is probably a win.

I think this $12 rule sets the value of the first 3 auctions well. If you win them all for 17/16/15 you have $12 left and are in a good position. If they let you win Red for $17 and overbid your 16 on blue you are in good shape, you both paid $17 but you have Red. If they let you win Red for 17 and blue for 16 and overbid your 15 on yellow youre in good shape. You have Blue instead of yellow for the same price, and god Red at a decent price. Now you can bid ~17 on green. If they outbid you you have more money left. If they don't youre up 3-1 with $10 left, they get a $10 share in T1 but you out-income them, and after they equalize share counts in T2 you have more money.

If you win Red for $18 I would bid $16 on blue. If you lose it, you have Red for only $1 extra which seems good. If you win it I would bid 14 on yellow (saves the important $12). Losing that means you paid $1 more to have blue instead of yellow, which I'd take.

So is bidding $18 on red good?
If they bid $19, our goal is now to end up in a 2-2 position where the red advantage isnt as important, and with enough excess money to be ahead, since they paid several extra bucks for red. They bid $16 on blue. If you win this at $17 things are pretty balanced. If they get it and auction yellow for $14 you can let them have it and be in a pretty balanced 3 vs 1 share state where they have only $11 left. Or you can win it for $15 and bid ~$17 on green. If you win it the money is even and the shares are quite even. If they go $18 then they have $7 left, you get a $7 share in T1, they out-income you, and you equalize in shares on T2 without about the same cash left, pretty balanced.



After a fair amount of analysis, I think we come to ~16-17 being the right value for initial shares, with Red worth 18-19 and yellow a bit less (14-15). I'm unsure as to which of green or blue is better.


Winning the first 3 shares with $12 left is good. With under $10 left its bad, and with $10-11 left its about balanced, I believe.



Now, lets look at how much money each company 'wants' to have to reach key early income boosts. If your company is short, the opponent will choose to dilute your other (better capitalized) shares instead, and leave that railroad stuck in the early game.

Red needs $16 to hit Pittsburg. It should have this. Pittsburg is clearly its best target (unless youre blocking)

Blue needs $16 to hit Wheeling, which will be its standard target. If it moves before Red, it can hit Pittsburg for $16. Getting to Pittsburg first will shut Red out from it. If this occurs Red can go through Blue on a lower route to Wheeling for $18, which it probably will have. Blue might block this too if Red tries, screwing up both rails (but Red more). Clearly if you have Red and they have Blue, getting Red's move out first is key.

Yellow can hit Charleston for $14 or an extra mountain for $17 (it probably doesnt have $17 without another Cap). I'd think that $14 to go for Charleston would be the target.

Green with $14 can hit Albany and Buffalo. (Albany provides an important early $2 develop space, developing happens in 2 player!). With $15 it can get to Cleveland if it skips Albany. With $12 it can hit Buffalo. Green shouldnt have money issues.

Lets look at income states of each rail after 3 expansions:

Red hits pittsburg and is making $15, it has MANY develop opportunities for +$2.
Blue hits Wheeling and is making $14, it has some mountains to develop.
Yellow hits Charleston and is makign $12. Bleah. $13 if it hits the extra mountain. but that means you overpaid for the yellow share. Yellow is worse! It has some good develops.
Green hits Buffalo and is making $13 with a couple develop opportunities (if it skips albany). But green starts out a bit better than the others, so you can leave it alone and develop another rail at start and get good income.


CONCLUSION

To summarize everything, making the following bids in the opening should result in you not getting screwed.

Red: ~$18.
Blue: 16-17. (If you have won more shares, you cant bid the higher amount).
Yellow: 14-15. (If you have won more shares, you cant bid the higher amount).
Green: ~16.

Obviously if your opponent is broke then you bid the amount they have left. If your opponent outbids these values, let them have it and you might be able to make them go broke and get into a won position. Also, if they overbid these, it lowers the future values slightly (because they are forced to give you a good deal, or make themself go broke such that you win).


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Alexfrog wrote:
Each player starts with $60. The standard 'its worth about half your money' that works with 3-4 player now completely fails. If I win two shares for $30 each, you then win a couple for free, and then can get another in the first turn for almost free as well, and you crush me. So $30 is clearly too high.

$15 is clearly a good value. I can continue to win $15 shares for the entire starting auction, after which you get one for almost free during turn 1, but I remain way ahead. So $15 is too cheap.


Good article, as usual.

I'm not sure if you realise this or if it's just the way you've written it, but there is a minimum bid during the initial auctions. So you can pick up shares dirt cheap, but never free.
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Alex Rockwell
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paulclarke339 wrote:


I'm not sure if you realise this or if it's just the way you've written it, but there is a minimum bid during the initial auctions. So you can pick up shares dirt cheap, but never free.


I meant "free" as in, for the minimum.
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Lee S
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I believe that in the opening round (and ONLY in the opening round) you can bid zero and, if everyone else passes, you win the share. Its in the rules, but I have never actually seen it happen.
 
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Josh Edwards
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Really? That's interesting to know.

Josh
 
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AxonDomini
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Raithe wrote:
I believe that in the opening round (and ONLY in the opening round) you can bid zero and, if everyone else passes, you win the share. Its in the rules, but I have never actually seen it happen.


Actually, there is a predetermined opening bid for every share in the first round. You can never bid zero for a share.
 
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Garcian Smith
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Can you make a similar article for a four player game?
 
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Steve Monofas
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Hello all.

I played yesterday night my first Chicago Express. It was a 4p game. I liked it, though I couldn't control some things due to inexperience of course.

I searched the forum wanted to see if it plays well with 2p. I found that it is on app store and I was excited.

I also found this thread and due to the fact that I trust Alex on other strategy articles, I started reading this and got surprised the depth that it has on a 2p. Although that if 2 players know that well, it isn't as exciting.

So, having studied all this I started a 2p game vs Ipod's AI.

I will post the game in the next post.
 
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Steve Monofas
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I started the game and I was first player.

I bid 18 on red. B passed and I got it. Everything up to normal now.

I bid 14 for blue and B let me have it. Thought that my opponent made a mistake there since we have an approx 16-17 for blue, so I won that fight there.

I bid low on yellow just to see B reaction. He bid 13. That is low you B, I up it to 14. He let me have it again.

I got in the situation that I have 3-0 shares and 14 money back. I am superb and ahead for the win.

Finally he buys green for 15. My money +1.

A - Buys red for 18
A - Buys blue for 14
A - Buys yellow for 14
B - Buys green for 15

Here is the current status before round 1.

Cash / Income:

A - 14 / 18
B - 45 / 08

So, thinking of round 1, I have an easy going. I null bid, he buys red for 14, I null bid again.

Round 1:

A : Null auction
B : Auction red for 14. Wins automatically.
A : Null auction

So after this the status is:

A - B shares is 3-2

Cash / Income:

A - 14 / 15
B - 31 / 12

I played up to here with this on mind, having 14 after my 3-0 sharing.

Alexfrog wrote:
Winning the first 3 shares with $12 left is good. With under $10 left its bad, and with $10-11 left its about balanced, I believe.


And of course the initial values for the shares.

Alexfrog wrote:
Red: ~$18.
Blue: 16-17. (If you have won more shares, you cant bid the higher amount).
Yellow: 14-15. (If you have won more shares, you cant bid the higher amount).
Green: ~16.


But with this,

Cash / Income:

A - 14 / 15
B - 31 / 12

isn't B a big favor?
 
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