You answered the wrong question K. He asked how many rounds do you take with you, not how many shots do you take on each deer.
We all know the old advice of never taking a shot when you have less than three rounds left unless it is to end suffering. So you would never go out with less than three rounds and if you are down to your last three rounds you should call it a day.
With me it depends on the rifle I'm using. If it is my Sako, 5 in the magazine plus five in a belt slide or in pocket loops. If it's one of the doubles it two in the chambers plus five in a belt slide or pocket loops.
The most I have ever shot on one stalk was five rounds to kill four deer on a cull. I only took two shots on the one deer because the stalker that I was with said "That's the worst bloody shooting that I've ever seen, you missed shoot again". I was confident that I hadn't missed but shot again as instructed. It turned out that he was looking at a totally different deer each time I shot.
Of course if you are away from home for the week or a week-end you will probably take 20 or so rounds in your luggage just to cover all situations.