I don't care if you are playing for ping pong balls, it concerns how many ping pong balls are coming out of the game. Look at the maximum rake, $3 versus 3£, taken from CarSun Poker's
rake table , more money is taken from the table in a £ game regardless of the stakes. The pots will be higher before any rake is taken, 5£(~$9.10) versus $5, but more money is taken from the game at each increment, .25 £ (~$0.46) versus $0.25.
Albeit there is more money on the table, but that has nothing to do with it.
The point is, you may as well play $2/$4 rather than 1£/2£ because you will pay less rake.
If you still want to dispute this, consider my wager. We will flip a coin, every time it lands on heads, I will give you $1. If it lands on tails, you give me a 1£. The amount of money we have is irrelevant. You may want to consider finding a better game, if not, well then you a sucker.....