small world – Smallworld: what happens when you run out of coins

Your understanding is incorrect, as can be seen in the official rules. During setup, you put the coins to the side of the board:

Place all remaining coins, including all “3”s, “5”s and “10”s, in a Victory stash next to the board, within easy reach of all players.

Then, at the end of your turn, you receive 1 coin (i.e. one point) from the supply for each region your tokens occupy. It does not matter whether the region was occupied in previous turns or not, you always get that coin. The different denominations do not randomise how many points you get, they are just there to aggregate the points you collect (so if you occupy 10 regions, you can take a 10 coin).

When taking a new race, you pay 1 coin on each race above the one you take. Again, you do not put higher denomination coins down here, you always put down 1 coin per race.

This means that you can, in theory, know exactly how many points each player has at any point during the game. However, each player keeps their points hidden to make this information difficult to track, and no-one is required to confirm their current point total at any point during the game.