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