What is a certificate limit
Most 18xx games have a certificate limit.
For the uninitiated, a “certificate” in an 18xx game is a share in a public or privately held company. Whether it’s the director’s share that represents 20% of a public company, a normal share that represents 10% of a public company, or a deed representing 100% ownership of a private company, each count as one certificate as each is just one “piece of paper”.
A “certificate limit” means you cannot hold more than N pieces of paper that represent shares of public or private companies.
Why does a certificate limit exist
I think Tom Lehman puts it pretty well here.
The certificate limit is an artificial limit to compensate for the artificial investment situation of 18xx games, where there is no opportunity to make alternative investments outside of RRs.
I think this is a great answer in the context of 1846, however I prefer describing it this way in the context of all 18xx games:
A certificate limit becomes necessary when the collective capital of players exceeds investment opportunities available -- be they railroad companies or not.
To explain this a bit, let’s look at the earlier stock rounds of an 18xx game. Players attempt to find the best value shares and put themselves in position to acquire them. At this point in the game, does a certificate limit matter? Well… not really. There are ample places to invest and hard decisions to be had about where a player’s money should go. The limiting factor is not the number of investment opportunities available, but a player’s capital to invest into those shares.
However, for most 18xx titles, there is an inflection point in the game where that limiting factor changes. As more companies get floated, get set up with routes, and start buying permanent trains, players start to have more money than shares that are available for purchase. At this point, players have the capital to sell out every company. The certificate limit reintroduces a different limiting factor, not of capital but of quantity. The limit ensures there is still a decision space to prioritize good shares over bad ones because if at the end of the game, a player could buy every share available, shares are purchased not because they are good but because they exist -- which ultimately contributes to runaway leaders and boring stock rounds.
A certificate limit keeps the latter stock rounds interesting and early leaders from running away with the game.
Though I will say the strategies to get around cert limit are (personally) one of the most fun aspects of 18xx.