The main purpose of FairGame is to rise up through the ladders, with the main goal being to press the “Be Asshole” button, and thus earn a place in Chad's ritual. However, the process whereby which this is done is somewhat more nuanced than it may seem at first glance. In order to promote from a ladder into the next one, there are a few criteria which must be met.
Firstly, and perhaps most obviously, a ranker wishing to promote from their current ladder must be in first place on their ladder. If all the below criteria are met, and you are stuck behind someone who will not promote, consider throwing vinegar at them, and open the way for your own promotion.
Further, in order to promote, players must have a number of points exceeding the Ladder Base Point Requirement (LBPR, also known as the Promotion Threshold). The LBPR is calculated on a per ladder basis - it will be different on every ladder. More detailed information about how this is calculated is available here. Do note that these thresholds can vary wildly, from the Zero of a tiny ladder, all the way up to the tens of billions which Gigantic ladders may require.
In addition, for promotion to be available on a ladder, there must be a certain number of rankers present on said ladder - this is informally known as the Critical Mass. The function which determines this is as follows:
If Current Ladder (L) ≤ 10, then Critical Mass = 10
Otherwise (L > 10), Critical Mass = L
For example, for promotion to become available on ladder seven; ten rankers are required. However, in order to promote from ladder seventeen, seventeen rankers are needed. This increase in critical mass as the game progresses can have the impact of slowing down runaway lead groups. Thus, if you have fallen behind somewhat, don't panic. There is a very good chance that the pace of the round will slow down, allowing you a good opportunity to catch up to the leaders.
If a player has purchased (or otherwise has been granted) AutoPromote, these three criteria are the only ones which must be met in order to promote. However, in the event that AutoPromote is not owned (or perhaps obtainable), a fourth criteria must be met.
In order to manually promote, a player must meet what is known as the “Thirty Second Rule”. They are required to sit atop the ladder for thirty seconds, and also be in a position where, after their thirty seconds have passed, the player immediately behind them has already promoted, or if not, be unable to reach them within thirty more seconds. In practice, this can be difficult to gauge, and somewhat inconsistent. Best practice when promoting manually is to watch the Promote (or Be Asshole) button closely - sometimes it may light up a little earlier than expected.
Criterion 4 does not apply in the case where a player is promoting first from the ladder. In this case, they can manually promote as soon as they pass the LBPR / critical mass is reached. However, if the overtake happens against the ranker who is already at top-1 spot, the “Thirty Second Rule” applies and the overtaker has to gain point distance first before the button lights up.