Where numbers of things vary by player count I'm just going to give
the number for 4 players. For "cert" read "certificate" because oh boy
do I have to type it a lot.

Companies don't have to start by buying the Director's cert, you can
buy 10% certs. A company where any 10% certs have been bought but not
the Director's cert is a "Managed Company". You can hold two (or more)
10% certs and they don't automatically convert to the Director's cert.

Being the Manager of a Managed Company transfers pretty well like
being a Director - it's first come first served amongst players tied
for the most shares - except that if everyone sells all their shares,
the existing Manager continues in that role.

A Managed Company becomes operational when 3 10% shares have been
bought from the IPO (and it has a Manager, implying one share was
bought by a player, which is not a given, even if they are in the Bank
Pool and not currently held by players.

If someone buys the Director's cert (and I don't think you can do so
with a 10% cert and the money for another) it becomes a Directed
(normal) Company... but the buyer might not become the Director
because they still might not have the largest shareholding (eg I hold
3x10%, ceb with nothing buys the 20% Director's cert).

Of players who do have the largest shareholding (specifically in this
"Managed Company becomes a Directed Company" situation) the tiebreaker
is the player who bought the Director's cert; failing that, the
Manager; failing that, in order of play from the Manager.

Capitalisation seems to be incremental but at IPO price.

There are nine (relatively) ordinary companies in a game.

Three of those companies get Guaranty Company Warrants during setup
(which expire at Phase IV). If the company does not pay a dividend,
the Bank will pay a dividend of 5% of the current market value of the
company and the stock market price will not change.

The tenth company is the Great India Peninsula Railway. It has 10 10%
certs (so is always Managed) and also there are 10 Royal Bonds
convertible to 10% certs in the GIPR from Phase IV. This means the
company may have 20 10% certs in play which all pay 10% dividends...

It cannot operate until Phase II. Its first token is placed on any
open station by the Manager... or it can upgrade a dit (town) to a
"special" green city tile. It starts with 3 "exchange tokens"; if a
railway closes, the GIPR replaces the closed railway's home token with
one of these (if it has one) and the Manager may opt to replace other
tokens of the closed railway. It can't have two tokens in one city.

Privates are not bought from players by companies, but companies may
buy them from the IPO or the Market. A player who owns one can use
its special power on behalf of a company they are operating. A Private
closes when its special power is used, repaying the owner the face
value. They can be sold to the Market for face value.

In setup, all the 10% share certs and Privates are shuffled
together. 11 of these are dealt to each player, representing shares
they have the exclusive right to buy. Your hand of certs should be
kept secret.

Most of the remaining certs are arranged in 3 rows of 13 certs to form
the IPO. The 2-5 leftovers are immediately put in the Market; they
are considered to have been bought (ie, the company gets money for
them and they count towards a Managed Company being able to operate).

Each player then examines the certs they were dealt, decides on six to
keep, and discards the rest facedown into the centre of the table. The
rulebook suggests a company that's sold 40% or more of its shares is
more viable because it can buy two 2-trains, so you want to keep certs
where 40% of the company is available to purchase, either from your
own hand or in the IPO; failing that, consider the odds of picking up
more during the coming draft.

The discarded certs are then shuffled and placed face up. The
Director's Certs are added to them. Players pick certs one at a time
from this "draft" into their hand - one round in reverse turn order,
then in normal turn order. When they have all been picked, the first
stock round begins, with the player next after the last player to pick
one having the priority. 18xx.games card counts the certs your
opponents pick in Info.

Stock rounds begin with a round of sales. This is the only time you
may sell during a stock round. Sales do not change the price. There is
no limit on the number of certs of a company in the Market. You can't
sell the Director's Cert if the company would have no Director.  You
are not prohibited from buying shares in a company you sold in the
same stock round.

Then there are purchasing rounds. On your turn you can do one of the
following:

Purchase any number of certs in one company from your hand at face
value.

Purchase any number of Privates from your hand at face value.

Purchase one or two certs from one row of the IPO, which must come
from a specific end of the row (which on 18xx.games seems to be the
left, but Entities lets you see them in columns, top first). Face value.

Purchase one cert from the Market. Market value.

Purchase a Royal Bond (R100). These pay income, like Privates.

After Phase IV has started, convert a Royal Bond into a cert in the
GIPR by paying the difference between the R100 face value of the Bond
and the current GIPR market price, if higher. If the GIPR has not yet
started, its nominal market value is R112. The GIPR always gets R100
when such a conversion is done.

The cert limit changes if companies close. Bonds do not count against
the cert limit. Certs in your hand don't either, because you haven't
bought them yet (and are never obliged to). You can own any amount of
a company.

The play order for the next stock round is in order of who passed
first, not clockwise from the first player to pass.

There are two ORs per SR.

You can lay four yellow track tiles, upgrade one track tile, or from
Phase IV remove one Gauge Change marker. However, when laying yellow
tiles you can only extend track on one route - they have to connect to
each other or through preprinted track (or existing tiles?  Rules seem
contradictory...) Private 2's special power to lay an extra yellow
tile is not restricted by this.

There are special FERRY tiles for J37 which are laid as yellow tiles
but cannot be upgraded. When the OO tiles are placed on Delhi and
Calcutta, the company laying the tile immediately decides where the
home stations in those tiles are, even if it is not one of the two
companies based there.

Track upgrades are not restricted by phase, but still go in the normal
yellow-green-brown-grey sequence.

You can upgrade a tile if you can reach some of the new track or if
you upgrade a city. Dits can be upgraded to "special" green City tiles
- these are #205 and #206, but not the other green City tiles. Dits
are just good; they don't count as stops - but you can't make a route
without two cities.

Dashed yellow lines on the map represent changes of gauge, which are
predetermined. When you lay track that crosses one, a Gauge Change
marker is placed; this counts as a zero-revenue stop. A train cannot
begin or end its route at one. From Phase IV (NB this is a later phase
than the one that begins with the purchase of the first 4-train) they
can be removed.

Two companies have two possible starting locations. It is permitted
for another company to token one of these forcing the company with two
locations to start in the other one.

There are a lot of weird trains in the later game. "x2" and "x3"
trains double or triple the route income. "E" trains run a route of
any length scoring N cities, but can't score dits at all. You can
visit both the stations on an OO tile, but not the multiple stations
in D23 Bombay or M10 Nepal.

The red offboard cities (eg D3 Lahore) are "variable value", scoring
their listed modifier plus the highest non-variable city on the route
(nominal R20 if all the cities are variable value).

There are some predesignated pairs of cities that give a flat bonus to
a train that runs a route including them. A E train must actually
score those cities to get the bonus. The bonus is scored after
doubling/tripling.

There are commodities in the game, each of which has a home hex and
destination location(s). The first company to run a train which passes
through home hex and destination location takes the commodity's
"concession marker" and gains that commodity's bonus revenue to this
run and any subsequent runs meeting that criterion. Only the company
with the concession may ever get this revenue. It is not doubled or
tripled. An E train does not have to score the cities to get the
bonus.

You can't half-pay. You can quadruple-jump.

The train limit is two, but at most one of them can be a Phase IV
train. Trains do not rust, but you can sell trains to the Bank
(exception: the 4x3 and 4x3E cannot be sold to the Bank). Some trains
are double-sided; you pick a side when buying them the first time, but
if resold to the Bank are stuck on the side you originally picked. You
can't sell a train you bought in this OR. There's no obligation to own
a train (and no Director liability at all), but you move one space
left if you are trainless at the end of the OR. You can buy trains
from other companies at any price from R1.

Companies can own certs and Bonds, and convert Bonds. They sell before
buying. They have a cert limit of three. They can only buy one cert
from the IPO at a time, never two, and can't buy their own IPO
shares. They can never be Directors or Managers.

Company assets - cash, purchase value of trains, and value of certs
owned - _do_ count for winning the game, with 10% of the Company's
assets being added to the Company's stock value.

List of Privates:

Swedish East India Company: costs R25, income R5, no special

Portuguese EIC: costs R35, income R5, one extra yellow track lay

Dutch EIC: costs R60, income R10, one extra upgrade

French EIC: cost R75, income R15, R40 discount on terrain costs during
one OR. (Does not grant the jewellery concession as the rulebook
suggests, editing error).

Danish EIC: cost R115, income R20, free token placement (not in
addition to normal placement), this can teleport (no route) and be put
in a city with no token space (if the city is upgraded, it will move
into any new empty spot).

British EIC: cost R150, income R25, gain jewellery concession, place
jewellery commodity in any hex with no station, can deliver jewellery
to any commodity's destination location for R20 revenue bonus.