This doesn't effect the first move, only to subsequent

very first move of the whole game, not once per player.

If you are the starter, your opponent will do the second move as his first move.

According the rule number 3: "This doesn't effect the first move, only to subsequent."
If I am the starter and eat 3 cake at first the opponent can eat 3 cakes too.
I could not find a nice solution therefore I checked a solution and run some test
for example: there are 12 cakes:
Using [3,3,0,1][cakes % 4] rules for moving the starter is a winner but if i keep the rule the opponet should be a winner

1. I eat 3 cakes left 9
2. Opponent eats 3 cake left 6 (it is the first move of the opponent so according the rule it is OK)
3. From that point i cannot be a winner.
   If I eat 1 cake left 5 the opponent can eat 3 cakes left 2
   I can eat 1 or 2. So I eat just 1 left 1. The opponent cannot eat 1 cake (using the rule number 3) therefore i have to eat again so I lost a game.

Maybe I misunderstand the rules or there is a mistake in my workflow.
Could you explain what is wrong ?
Thanks