I played this once at a Con, and got thoroughly beaten by a robber baron type player, who took me under his wing and then left me holding the company with no trains in it!
The game opens with the random seating using place cards.
Then, the first Stock Round begins with the sale of the private companies, starting with the smallest, but you can also put in a bid for one of the larger companies to try and secure it for yourself.
Once these are dealt with, Stocks in the main companies begins. Players are free to buy stocks in any available company and set the starting price of the stock anywhere from $67 to $100 each. Once 60% of stock in a company is bought, that railroad is floated and can begin to operate.
In the Operating Round(OR) a company places a tile on the board. Only yellow tiles are initially available, with green and brown tiles becoming available with later phases in the game to upgrade existing tiles on the board. Then, trains run between stations. A '2' train for example can only run to two stations. Revenue is earned from the value of stations along the route.
This can be paid out to stock holders as a Dividend, which puts the price of shares up, or kept by the company to finance larger trains or track laying, in which case the share price goes down. (Uniquely in 1830, the stock price can also go up a level if all stock is bought and go down a level as each share is sold back to the bank).
Companies can then buy more trains if they wish.
The game continues in this fashion, with stock rounds and operating rounds until the bank runs out of money, when the richest player wins.

This is our groups favourite 18XX game, but sadly rarely sees the light of day due to it being a long game, but a time limit can be put on the game, if time constraints apply.

SUMMARY:
A game of pure skill, with very little luck involved, which makes the game so enjoyable. Review by Brian