A game is played involving a box of red and green sweets. There are more red sweets than green sweets.

The player repeatedly takes one sweet at a time from the box at random, without putting the chosen sweet back in the box. If at any point the number of red sweets removed is equal to the number of green sweets removed, the game stops and the player wins (and can eat the sweets).

It is found that the player has an equal chance of winning or losing this game.

If the box contains twelve sweets in total, find the number of red sweets.